Copyright Sociological Research Online, 1996

The Career of Status Crystallization: A Sociological Odyssey

Abstract

Since it was first introduced half a century ago, Status Crystallization [SC] which is also know as Status Incongruence, Consistency or Inconsistency has been used in over 200 research papers. Many have accepted it and treated it as a potentially useful substantive construct and even generalized it somewhat. A few have tried to forge theoretical links between it and such related concepts as socialization and mobility. A third group has taken a more combative approach and declared it either theoretically vacuous or empirically irrelevant. Much of the debate is apparently a failed attempt at communication between the innumerate and the a- theoretical. This paper evaluates both of these tendencies through the examination of a selection of contributions to the debate. The conclusions reached include, first, that SC has never been appropriately measured or tested so that any claims regarding its efficacy are premature and second that a coherent sociological paradigm must have a place for SC in it. Any sociological theory which cannot provide a meaningful place for SC is deemed too restricted to be of any lasting interest. From this second point the paper addresses the role that operationalization and empirical research play in the formulation and refinement of social theories and the need for social theorists to become more methodologically astute. Building on insights derived from recent developments in chaos theory, the paper concludes with a general discussion of SC as a dynamic concept best modelled with differential equations.

Keywords:

Status Crystallization; Status Inconsistency; Socialization; Operationalization; Structuralism; Social Mobility; Dynamic Models; Chaos Theory

The Career of Status Crystallization: A Sociological Odyssey

1.1

Status Crystallization (SC) is a concept over half a century old. It's core principle is that people in society have certain expectations about how various kinds (or dimensions) of social status should correlate with one another. 'Crystallized' statuses are those which have all the various kinds of status at approximately the same levels. The educational attainment of a person is 'consistent with' the occupation help and the monetary compensation received. When the various measured dimensions of status are so correlated then the status of that individual is said to be 'crystallized' or 'consistent'. People with doctoral degrees who work as taxi drivers, bookstore clerks or gardeners are among those with uncrystallized or inconsistent positions on their various status dimensions.

1.2

SC can therefore be seen to result not from the individual's position in the social structure alone but experience of position (or positions) compared to some expected value. Much of the research on SC has, either implicitly or explicitly, treated it like a 'psychological stressor' in studies looking at phenomena ranging from voting behaviour to coronary heart disease. SC is at the same time a term with social structural and cognitive components.

1.3

The one division that is constant in all research oriented disciplines is the split between the theorist and the methodologist. While few people in sociology actually place themselves at either extreme it is nonetheless true that this division also characterizes much of the conflict in sociology. The other split lies within the theoretical ranks: the gulf that separates the structuralism of Durkheim and his approach to 'social facts' from the verstehen sought by Weber. Examining SC represents more than just chronicling a concept now at least 50 years old, more than examining an idea which has figured significantly in well over 100 major publications in the last 20 years. Examining SC reveals the complexities of sociology itself.

1.4

This paper is an overview of dominant themes and developments. Demands of brevity will inevitably force the exclusion of some highly interesting work. All the same the next section attempts to go into the operational specifics in some detail. While the temptation to skip this investigation may arise it is still desirable to endure it and to try to follow what seems to be, to some, as the way a great deal of time and effort have been wasted by social researchers talking past each other.

Historical Overview of the SC Controversy

2.1

Almost three generations of sociologists have responded with a mixture of enthusiasm and confusion to Gerhard Lenski's popularization of Status Crystallization in the social science lexicon. The enthusiasm derives from recognizing (if only implicitly) a theoretical paradigm which, by tying social-structural and social-comparative concepts together, represents the first systematic attempt to fuse sociology and psychology at both the theoretical and the methodological levels.

2.2

In 1944, Emile Benoit-Smullyan first suggested that Weber's concepts of class, status and party did not require that a person would be equally ranked on all three dimensions of stratification. It was further suggested that if a person were inconsistently ranked then this could result in distinct and observable forms of behaviour. A decade later, Gerhard Lenski (1954) employed Status Crystallization (later to be given aliases such as Status Consistency, Status Inconsistency and Status Incongruence) to represent a "non- vertical dimension of social stratification" in a study of voting patterns. For the present, SC will represent all of these terms. At the end of the paper these terms will be reintroduced to represent some alternatives to the way in which the term has been used.

2.3

Lenski was the first to attempt to operationalize the way the Weberian Status dimensions of Class, Status and Party (or Power) represented ways of ranking people from 'lower' to 'higher' and then to refine this categorization of people by arguing that there were other status-related social- structural influences on human perception and behaviour. He termed such influences 'non-vertical dimensions'. This choice of language was to prove unwieldy in the following years¹.

2.4

Lenski's original definition of SC has the following attributes, the original equation being:

[1]

Details of Lenski's Original Model

Terms in the Equation	Conditions of the Model
X1 = Occupation X2 = Income X3 = Education X4 = Race/Ethnicity (dropped in the 1956 paper)	All factors are equally weighted All measures are standardised The model (index) is additive (linear) The model (index) is time-insensitive*
XMi = Sample Mean for the specific Xi * While not made explicit by Lenski, this assumption will be important later

2.5

Initially, Lenski defined SC using the variables Occupation, Income, Education and Race/Ethnicity. Race/Ethnicity was dropped in the 1956 paper.

2.6

The concept was used by several researchers until it encountered the first of what was to be a sustained methodological assault on its adequacy.

2.7

In 1964, Blalock used a mathematical evaluation of Lenski's formulation to show that SC was a vacuous concept - at least as originally operationalized by Lenski.

2.8

According to Blalock (1964)² Lenski's original model could be expressed as:

[2-a]

Y = aX₁ + bX₂ + cX₃ + dX₄

(Here: X₁, X₂ and X₃ are measured status variables and X₄ represents Status Inconsistency. Y is any sociologically relevant dependent variable.)

2.9

Blalock further argued that X₄ (SC) could be formally expressed as a linear function of the original status variables as in:

[2-b]

X₄ = f (X₁,X₂,X₃)
{f a linear function)

2.10

It was finally pointed out that according to well known mathematical theorems, SC thus represents a simple linear combination of the original three dimensions. Consequently it does not in any way contribute any new information to that provided to the researcher by the initial measurements. Because the SC term contained no new information it could be equated to zero so that equation [2-a] could be rewritten without loss of information as

[2-c]

Y = a'X₁ + b'X₂ + c'X₃

2.11

Blalock's criticisms can be summarized as:

1. Lenski wanted a non-vertical dimension of social status
2. Non-vertical can be taken to mean linearly 'orthogonal to' the other dimensions.
3. Lenski's equation does not define an index which is linearly independent from its components and therefore...
4. The SC index as defined adds no new information and should either be dropped or re-defined in terms of a non-linear function of the components in order to be meaningful.

2.12

Blalock's solution was to treat SC as a multiplicative interaction of status dimensions. The foundation for this approach was apparently based exclusively on mathematical criteria since Blalock did not provide any detailed sociological or psychological interpretation of how a multiplicative interaction term would theoretically mirror what SC conceptually was³.

2.13

Clearly one would expect that, ceteris paribus, the greater the dissimilarities among various status dimensions the more pronounced should be the perception that such dissimilarities exist. Presumably, too, the perceived magnitude of the differences could be quantitatively related to other attitude and behaviour indices. Finally one could expect that such influences may vary with time (much as is seen with other adaptations to status changes as in the studies of bereavement and loss). None of these developments or alternatives were discussed by Blalock. The multiplicative interaction term is, also, only one of a myriad of non-linear (and time-insensitive) options open to modellers.

2.14

There the matter seemed to rest but in 1972, Jackson and Curtis⁴ published a study which sought out to map out SC's influence empirically. They took 43 dependent variables which they suspected to be susceptible to influences from social mobility and income. Following Blalock and operationalizing SC as the three-way multiplicative interaction of the three measured status variables, they then constructed a full range of multiplicative interaction terms and carried out 2,064 tests to predict the dependent variables.

[3]

Y = aX₁ + bX₂ + cX₃ + dX₁.X₂.X₃ [X₁.X₂.X₃ is the SC term]

2.15

Their study was the first which explicitly linked mobility and SC and to employ the criterion of predictive power as the sine qua non of an indicator's adequacy.

2.16

They found 'little or no evidence for mobility or inconsistency effects'. The logical question: 'What are the implications for social theory?' was never asked⁵.

2.17

In 1974 the lack of agreement regarding a standard definition of SC resurfaced. Hartmann reviewed the assumptions of the crystallization paradigm and noted that Status itself had dimensions (such as sex, age, race) which were not initially incorporated in Lenski's original operationalization. (Hartmann did not discuss or address the possibility of mixing ascribed and achieved status dimensions in such an index). To be fully consistent he suggested that SC be defined in terms of all n stratification dimensions (dimensions which were not enumerated).

2.18

One of the more sensible requirements for theoretically useful empirical studies is the systematic use of consistent and ideally the same operational definitions. This suggestion goes very hard in the other direction. The complications for testing and verifying the SC concept are obviously expanded greatly.

2.19

In an attempt to avoid a total relativization of the SC idea, Hartmann advocated the empirical identification of the 'core' status dimensions by using smallest space analysis. The core dimensions were to be computational, not theoretically, determined. This approach, itself, has another difficulty. It is simply the inability of factor analytic or similar techniques to differentiate between infrastructural and epiphenomenal associations⁶. Statistical packages do not have good theoretical judgement.

2.20

An ambitious attempt to comprehend and resolve these disputations came in the form of Hope's (1975) Diamond model. Hope rejected Jackson and Curtis on theoretical grounds. He began by arguing that Blalock's insistence on multiplicative interaction had subverted Lenski's original theory on narrowly confined methodological grounds. Perhaps for purposes of simplicity, Hope defined a SC model by reference to only two primary status dimensions (which are not specified a priori) and called them 'A' and 'B'.

2.21

He maintained that SC could be defined as a consequence of social mobility. Hope articulated his model which, while differing markedly from Lenski's operational definition was in a theoretical sense at least as credible an interpretation of Lenski's initial objectives as many other operational attempts.

2.22

Hope designed his model to do three things. First, to preserve the direction of social mobility (up or down), second to keep distinct all dimensions of change and third to retain information regarding the magnitude of social mobility. Theoretically Hope had explicitly tied social mobility and SC together in a social-structural and cognitive psychological fashion. His operational definition was a marginally time-sensitive measure but made no operational provisions for rate of change or time in status matters

2.23

Hope wrote his first equation as [4- a].

[4-a]

Y = aX₁ + bX₂ + c(X₁ - X₂)

2.24

Blalock objected on mathematical grounds almost identical to those he raised to Lenski's original formulation. The [X₁-X₂] term was obviously linearly dependent on X₁ and X₂. Therefore, he argued, the formula proposed by Hope did not add information but merely re-partitioned the variance of the X₁ and X₂ variables and generated a non-singular covariance matrix.

2.25

Hope responded by re-writing his equation as in [4-b]. This equation is clearly only a regrouping of terms. This, though, is not always a trivial transformation (since there is no particular need to reify primary measurements). Those familiar with the application of information theory to television and radio transmission will recognize the similarity to the multiplexing equations used to broadcast colour and stereophonic FM radio signals⁷.

[4-b]

Y = a(X₁ + X₂) + b(X₁ - X₂)

2.26

This approach made Hope's model mathematically valid but did not end criticism. In addition to Blalock's methodological critique, House (1978) claimed that there were theoretical flaws in the Hope Diamond. Using an algebraic discussion, House criticized Hope's initial equations [4-a and 4-b] by revealing them to be vulnerable to Blalock's original complaint of linear dependence.

2.27

House went beyond this, though, with two more theoretical points. He maintained that Hope's equations represented a re- definition of SC ... a re-definition which was Lenski's prerogative alone⁸. Hope had completed the equating of SC with mobility and in essence suggested a refinement in the way mobility is studied.

2.28

By this time, SC had entered the lexicon of sociological discourse even while esoteric arguments over its utility and validity raged. Whether methodologists knew what it meant - if anything - many researchers decided it did - or ought to.

2.29

Two articles by Harmon and Gray (1974 and 1976) attempted to apply Lenski's original definition of SC to a health related issue. Arguing that SC would be a stressor, the authors postulated that increasing SC would result in increasing rates of coronary heart disease. Their positive results were withdrawn in their second paper in which they discovered several sampling flaws which they felt compromized their findings. They did not, however, regard the SC measure as a priori invalid.

2.30

Hornung (1977) applied Hope's Additive Square (Diamond) model and obtained positive results for his operational measure. He found that as SC increased, psychological stress levels correspondingly rose. He also reported a non-linearity in the SC effect. Not only was the relative degree of inconsistency predictively important, but its effect also varied depending on the respondent's overall position in the status hierarchy. This result, while not counter-intuitive or even surprising, represents an added degree of operational complexity not anticipated in the previous theoretical discussions.

2.31

If SC is indeed to have its effects by being a psychological stressor then this requires some way of taking individual sensitivities to stress into account, an empirical or theoretical decision regarding the ways in which stressors may all be treated as equal and a way of determining their variable impact as a function of their interaction with other social attributes.

2.32

For others, though, SC had again fallen into disrepute. Blocker and Riedsel (1978) declared the entire concept 'moribund' and based this pronouncement on three supports. First, following Blalock's 1964 critique, the whole idea was exposed as mathematically inadequate. Second, little or no correlation was found between 'objectively' and 'subjectively' measured SC indices (people who ought to have been reporting high stress owing to SC did not, and so on). Third, the predictive utility of SC was 'non-existent' (although how much predictive power SC was supposed to have, or for what variables, or within which constraints, had never been theoretically debated).

2.33

The next year, Wilson (1979) and Zurcher and Wilson (1979) 'resurrected' the moribund concept by rejecting Blalock's arguments and siding with Hope regarding the possibility of defining SC in terms of mobility-discontinuities. They concurred with Hope further by allowing that Lenski probably had not intended a multiplicative interaction term to be the definition of SC and assumed that Blalock had both misunderstood and then mislead Lenski⁹.

2.34

Hope, however, was not fully accepted either. His equation was criticized because it loses information through the combination of terms¹⁰.

2.35

To preserve as much information as possible regarding psychological stress factors, they defined a psychological stress- model as in equation [5-a]. The measured variables were rated on a scale from [1,3] and the R² on stress was reported as 13% on a sample of white males.

[5-a]

Y = a(STATUS) + b(I - E) + c(I - O) + d(E - O) + e(I - R) + f(O - R) + g(E - R)

Where:

I = Income
E = Education
O = Occupation
R = Race
Y represents a generic psychological stress
STATUS = Composite Status Dimension. (Operational aspects not given in the paper, but this term is presumably some composite of I, E, O and R)¹¹

2.36

Zurcher and Wilson also returned explicitly to the explanatory appeal of SC by trying to suggest 'why' it was expected to work. They argued that SC was a psychological stressor, that psychological stress uniformly leads to the desire to engage in stress-reduction (an assumed relationship which is disputed in some psychological theories) and finally that stress reduction frequently involves changes in a person's religious and political attitudes and behaviours.

2.37

In this argument they identify rather well what is probably the reason for researchers not to abandon SC. Social status ranks, particularly those which are achieved, are themselves defined as having some regions of correlation. SC may related (and later writers would do so) to concepts of 'social justice'.

2.38

SC, then, is not simply a structural aspect but can only have a real effect if people recognize it. It depends on human cognition to exist and sociologists identify it or hypothesize it on the basis of verstehende. It consequently belongs equally to both the micro and the macro tendencies of sociology. The fact Zurcher and Wilson most likely realized this is further supported by their assertion that socialization was of central importance if SC effects were to manifest themselves.

2.39

They argued that SC and socialization are logically and theoretically related. Socialization forces could make certain kinds of inconsistency tolerable (the systematic underemployment of minorities for example)¹² and it could make certain responses to SC induced stress more probable (political versus religious activity). Socialization, they maintained, should predict both the direction and the degree of response. For example, those with high education and low income (such as unemployed PhD's in sociology) should be more strongly anti- government.

2.40

Despite the obvious appeals of this argument, Zurcher and Wilson hit trouble when it was time to operationalize this relationship.

2.41

Wilson (1979) also defined Socialization as:

[5-b]

Socialization¹³ Y = aX₁ + bX₂

and recalled Hope's definition of SC as

[4-c]

Y = a(X₁ + X₂) + b(X₁ - X₂)

2.42

In other words they asserted that SC and Socialization are formally equivalent. Leaving aside the claim that all these equations are mathematically identical (as obviously they are not) we still must ask if equation [5-a] can be logically posited as modelling Socialization. Does it have construct validity?

2.43

Socialization is a psychological process which theoretically mediates past environmental influences and future attitudes and behaviours. It is difficult to understand how the simple linear combination of two zero- order demographic attributes can be seriously described as a model for this process¹⁴. At best, this model stands as a crude first approximation.

2.44

Magnifying this defect, the model does not adequately reflect the way Socialization influences are described as operating. Since the authors argued that different combinations of specific status attributes would have different behavioural outcomes, we require a model that meaningfully discriminates the range of influence and combination of factors required to predict the desired behaviours.

2.45

Without digressing or complicating matters too much, it is sufficient to recall that when these papers were published, research into Socialization had identified such forms as child and adult, anticipatory and forced and so on. One of the most popular areas of Socialization research was in the area of Socialization of attitudes and Socialization of behaviours. (Liska (1975) also noted that the weak fit between attitudes and behaviours made psychological inferences based on behaviours or behavioural predictions based on attitudes a difficult task.)

2.46

To ask the question 'is SC cognitive or structural?' is clearly to miss the point. It is both. The real issue for theorists and researchers is: how do the structural and the cognitive components interact? This requires researchers to ask explicitly: 'What reference group's norms are involved?'.

2.47

The problems of deciding a priori on an SC rank which permanently dictated the weighting of the variables led Zimmerman (1978) to suggest that individuals may behave in accordance with their highest partial status rank (thus presumably 'claiming' the highest defensible status in a given social context). Even though his findings did not uphold this hypothesis, several operational problems to SC were discussed and SC's status as a psychological stressor was examined. Perhaps his most useful theoretical observation was tied to his assertion of the need to consider multiple reference groups when evaluating SC.

2.48

Lenski's original measure had used statistical aggregates to define the 'expected' relationships among the various status variables. This, though, effectively suggested a monocultural sample, a group which intrinsically shared the idea that the relationship between (say) education, occupation and income was and should be expected to be uniform for all members of society. Lenski recognized this and conducted his research on what he considered a roughly homogeneous group. Others who have attempted to use this idea have not always been so careful.

2.49

By 1983, Whitt proposed two alternate definitions of SC. Equation [6-a] simply factors in the zero-order status dimensions and augments them with dummy variables which measure status discrepancies. In [6-b] a composite status dimension would be augmented by the first-order dummy variables which are included to capture all of the status dimension discrepancies for all dimension pairs.

[6-a]

Y = aX₁ + bX₂ + cT₁ + dT₂

Where:

and clearly if X₁ = X₂ then T₁ = T₂ = 0.

[6-b]¹⁵

Y = a(X₁ + X₂) + bT₁ + cT₂

2.50

Lenski's original definition of SC sought to define an aggregate index which was constructed by comparing each individual status rank (Zero Order terms) to a composite social position index (a first order term such as a Social Position Index [SPI]) to yield a Second Order term. Whitt's definition has nothing higher than First Order Terms and very simple 'different' versus 'not different' ideas of inconsistency. The degree of difference or how long it might have persisted do not enter into the discussion. He also, by making 'status' a generic, moved the term into a very fluid definitional state.

2.51

Over the years the lack of precision (and agreement) on exactly what status dimensions were involved in SC had been apparent. Simpson (1985) mathematically defined SC by modifying Jackson and Curtis's approach and entering multiplicative interactions at only the two-way level. Simpson also elected to treat religion as a status variable.

[7]

Y = aX₁ + bX₂ + cX₃ + dX₁.X₂ + gX₁.X₃ + hX₂.X₃

where:

X₁ = Education, X₂ = Occupation, X₃ = Religion

2.52

This inclusion of religion is problematic for at least two reasons. Why did Episcopalians and Presbyterians fall on one side of a status line and all other Protestants on another? (Catholics, Jews and Moslems were totally excluded.) This compromise was apparently necessitated by the need to remain relatively close to a given algebraic model of SC, a model which ideally requires variables of interval/ratio levels of measurement but can be made with dummy variables.

2.53

If this demarcation is designed to stand in as a surrogate for SES (upper-class or mainstream versus marginalized creeds) then it seems superfluous. Religion is known (or at least assumed) to give its adherents an interpretative schema which presumably could allow them to cope in different ways with whatever stress flowed from SC effects. Weber's analysis of Protestantism clearly dealt with the matter of how religion aids in the interpretation of the world.

2.54

If the ideas of Zurcher and Wilson are to be taken seriously then the critical aspects of religion's relationship to experiencing SC would require knowing both how much worldly justice the creed told its followers to expect and the degree to which the nominal affiliate did in fact accept these teachings. Once again the dual nature macro/micro nature of SC becomes unavoidable.

2.55

Second, this expansion of SC to encompass religious affiliation echoes Hartmann's (1974) call for treating SC's dimensions as fully generic rather than restricted to the structural dimensions of status first suggested by Benoit-Smullyan as being consistent with Weber¹⁶. Simpson seems to have abandoned Weber twice.

2.56

A major theoretical problem with SC is one it shares with all other group-aggregate statistics: it operationally concretizes the group's membership, its boundaries and its response profile. This theoretical problem is little discussed and has the unfortunate capacity to reify hypothetical social-structural constructs¹⁷.

2.57

One study (Hawkes et al., 1984) provides a good example to illustrate the group sensitive nature of SC. Using the Wilson model [Equation 5], they investigated a split Mexican-American sample and reported: 'strong status inconsistency effects may exist in subpopulations but remain hidden in samples of the general population'.

2.58

This is precisely the type of obscuring effects that are generally attributable to the 'ecological-fallacy' but is perhaps more accurately termed generalisation-specification problems. The complicating factor here is that we are not faced with region effects but a generalisation of these effects to social-psychology¹⁸.

2.59

The Hawkes et al.'s results found 'little or no' SC effect in the general population. They also stated that for Mexican- Americans, job satisfaction is high when the occupational prestige is high and the educational attainment is low but satisfaction is low when the prestige of the occupation is low and the person's educational attainment is high. Anglo-Americans, in contrast, exhibit job satisfaction increases in response to increases in income levels alone (a zero- order effect). The two groups differed in terms of their zero- and first-order associations with the dependent variable of job satisfaction. It is also worth noting here that the independent variables are social-structural and the dependent variable is cognitive. Different ethnic groups are shown to have different cognitive responses to similar structural conditions.

2.60

Socialization or enculturation is not a single event but an ongoing process. If SC effects depend on the ways in which structural position is interpreted or experienced then it is also necessary to deal explicitly with matters regarding the temporal components: 'How long has this status situation been present?'.

2.61

Holmes and Butler (1987) made systematic attempts to investigate the implications time has for SC. In a study of military personnel they showed that those in low rank for a long service time exhibited more racial separation than other groups. Those with high rank and short service periods had higher job satisfaction. For them, SC was defined using the two variables of rank and time-in-military- service. This explicit recognition of the importance of 'time in status' was long overdue and clearly showed the need to relate SC to social mobility in a consistent theoretical fashion.

2.62

Social mobility along one or more status dimensions must necessarily result in SC effects. SC is, in this fashion, best seen (if time-sensitive measures are used) as a possible rough indicator of the rate of mobility as well a measure of mobility discrepancies. Separating these effects would argue against an aggregate measure.

2.63

The matter of mobility, also, reminds researchers of those who, through success, sometimes become 'too good' for the friends they left behind or those whose downward mobility becomes 'an embarrassment' for the still-wealthy country club crowd. The reason for selecting a certain reference group (and noting it may not be the group of either aspiration or affiliation) had not been given any careful consideration by SC researchers up to this time. Neither (but this topic must await more detailed work) are clashes between achieved and ascribed status variables. Does, for example, anticipatory Socialization contribute to SC?

2.64

In an attempt to deal explicitly with the reference group aspects of SC, Brown et al. (1988) returned to Lenski's original dimensions (Education, Occupation and Income) and based their discrepancy scores on National means for each variable. (Lenski's definition used the sample mean as the basis for comparison). They did not construct Lenski's index but instead coded the inconsistency score to reflect the respondent's probable expectation of 'distributive justice'¹⁹.

2.65

If both occupational status and income compensated the respondent adequately for his or her educational investment then the individual was scored as 'consistent'. People were also coded as 'over rewarded', 'under rewarded' and 'mixed rewards' relative to the national population means. Their overall conclusion was that SC seemed to be of little predictive utility for a large range of fundamentally interesting dependent variables. As long as the entire nation could be taken as effectively monocultural.

2.66

This use of the entire nation as a reference group stands diametrically opposite to Schrum's (1990) expression of Status Inconsistency as a dyadic phenomenon. Schrum followed Lenski and defined SC as that which 'occurs when an individual actor has unequal or conflicting ranks in two or more different social hierarchies. e.g. great wealth and low prestige'.

2.67

One of his taxonomic innovations was to replace the definition of Status Incongruence (previously used in the literature as being synonymous with SC) as a "property of dyadic relations denoting inequality between two actors along a single structural dimension.".

2.68

If two people are ranked on two dimensions each and if one is higher than the other on the first and lower than the other on the second dimension, the two people are said to have 'Inconsistent Incongruence'. Here, the individual experiences Incongruence (Consistent or Inconsistent) as a consequence of comparisons with each 'significant other' he or she encounters, rather than with the 'generalized other' of orthodox Symbolic Interactionist theory (see, for example, Blumer, 1969a).

2.69

Shrum's decision is the equivalent of scrapping SC as a structural phenomenon and treating it as a cognitive process. SC was moved from the world of macro sociology to the world of micro sociology.

2.70

Also in a 1990 paper, Kerschke-Risch introduced some additional definitional clarifications to SC and shifted the reference group to a mid-point between these two viewpoints. Groups smaller than national samples, but larger than dyads, could be based on sex (and presumably other discriminating variables) but aside from the common sense appeal of this decision little theoretical defence or constraint is provided. Is race appropriate? Native language? Religion (especially in places like Northern Ireland or Former Yugoslavia)?

2.71

Her definitional refinements used Income as the individual's 'reference dimension' (in some ways recalling Brown, Cretser and Lasswell's notion of 'distributive justice' but made the definition more rigorous). If one's Income rank exceeded one's Education rank, 'Positive SC' was assigned. If Income was too low, 'Negative SC' resulted²⁰. Additionally she also separated Objective and Subjective SC to produce a fourfold taxonomic structure. Results of this study also showed SC to be of little predictive value regardless of how defined. Its only area of success was in predicting voting behaviour (as in Lenski's 1954 study) where she observed that Positive SC is more likely to vote conservative. This much being said, however, the thrust here is to harken back to treating SC as some kind of 'Socialization' as opposed to 'structural' idea.

2.72

There is much more to the saga of SC than this but these items do represent some of the more critical attempts to come to grips with the theoretical and methodological concerns surrounding this concept.

2.73

The foregoing review, depending on one's viewpoint, can be seen in two ways. When viewed by engineers and other 'hard science' specialists it confirms their worst fears about sociology's status as a pseudo science. To those more accustomed to examining the history of science rather than the sanitised versions presented in textbooks see a typical example of a discipline engaged in empirical research learning to use its conceptual and mathematical tools.

Methodological and Theoretical Issues

3.1

Rather than simply walking away from this debate it is instructive to look at it more closely. First, let us agree that the concept itself is intuitively appealing. Some part of the sociological imagination says it ought to work. It is doubtless this appeal, and not its empirical triumphs, which is responsible for the repeated attempts to employ it.

3.2

These attempts, however, have on the whole been disappointing. It may be that SC is simply too subtle or complex a measurement for the current state of the art. On the other hand, the attempts to operationalize and employ this concept are quite instructive to social researchers generally. Understanding where and why things went awry can serve as cautionary tales at the very least.

3.3

SC research can be seen as manifesting specific examples of the pitfalls which await many social researchers. What follows uses SC as the substantive focus but the issues involved are obviously highly general.

Methodological Issues

3.4

SC theorists and researchers have identified the following issues as in need of clarification.

• Is SC to be restricted to the structural dimensions implied by Weber in Class, Status and Party (often measured as Income, Occupation and Education)?
• What is the appropriate mathematical formula to use for SC?
• Will the SC index formula take into account the dynamic aspects of social life by dealing directly with rates of mobility and direction of mobility? Is SC a static or a dynamic concept?
• Will the reference value used to calculate the 'inconsistency score' be based on structural or cognitive criteria and if based on structural criteria then what reference group or groups is/are appropriate?
• Some theoretical basis is needed to outline the kinds of observable effects SC should have and how strong they should be.

3.5

Let us consider these in order.

The Dimensions of SC

3.6

As Table One shows, the underlying dimensions and operational approaches to SC have been far from uniform or stable.

Aspect of SC Model
Selected uses of Status Crystalization	Variables or Dimensions	Status Dimension Type (achieved/ ascribed)	Levels of Measurement for variables	Reference Group for Comparison	Source of Reference Value for Inconsistency Calculation	Time Factor (Static or Dynamic)	Type of Formula for SC term.
Lenski (1954)	Occupation, Education, Income, Race/Ethnicity	both	ratio index (variables are interval)	sample	sample (mean for variable)	static	quasi linear (root of squares)
Blalock (1964)	Lenski's (O, E, I)	achieved	interval	sample	Sample	static	multiplicative interaction
Jackson and Curtis (1972)	Lenski's (O, E, I)	achieved	interval	sample	Sample	static	multiplicative interaction
Hartmann (1974)	determined by factor analysis	both	interval	sample	sample	static	linear
Hope (1975)	optional	achieved1	ordinal2	sample	sample	Dynamic	linear
Wilson and Zurcher (1978)	Race, Income, Education, Occupation	both	nominal and interval	sample	sample	static	multiplicative interaction
Whitt (1983)	optional	achieved1	ordinal2
	sample	sample	static	linear
Simpson (1985)	Education, Occupation, Religion	achieved	nominal and interval	extra-sample (e.g. national)	sample and national/ population	static	multiplicative interaction
Holmes and Butler (1987)	Military Rank, Time in Service	achieved	ordinal and interval	sample	population	Dynamic	linear
Brown, Cretser and Lasswell (1988)	Lenski's (Income as reference)	achieved	interval	extra-sample (e.g. national)	national/ population	static	linear
Schrum (1990)	arbitrary	achieved	ordinal	sample	dyadic	static	linear
Kerschke-Risch (1990)	Sex, Income and arbitrary	both	ordinal	geographic, structural and subjective	sample	static	linear

¹This status attribute is apparently not specified in the model directly. The attribute given here is taken from the study cited.
²This level of measurement will change depending on the actual variables selected as part of the measurement. The entries given here are the attributes of the variables in the study cited.

3.7

Many which seem clear at the level of abstract theory concepts become less clear at the operational level. One can have a reasonably good idea of what a bird is but when asked a companion question 'rate the following birds regarding how good they are as examples of birds' the matter becomes less clear. McNeill and Freiberger (1993, pp. 84 - 85) report that when respondents were asked to rate birds on a scale from 1 (excellent) to 4 (poor) it was found that robins scored 1.1, eagles 1.2, wrens 1.4, ostriches 3.3 and chickens 3.8. Bats scored 5.8.²¹

3.8

By analogy it is probable that the concept of 'status' can also be treated in this way. Some operational definitions of status (and hence SC) may employ component variables which are less ideal examples than others. In addition to the 'classical' status measures of occupational prestige, income level and years of education, researchers have employed residence location (Lenski, 1954; Hollingshead and Redlich, 1958), religion (Simpson, 1985), race (Wilson and Zurcher, 1978), military rank (Holmes and Butler, 1987) and sex (Kerschke-Risch, 1990). Other researchers have left the matter of how to measure status open (Hartmann, 1974; Whitt, 1983; Schrum, 1990). Suffice to say, the brief review of SC presented above demonstrates a rather fast-and-loose approach to the underlying dimensionality of SC.

3.9

While one cannot reconstruct the motives for those decisions it is probable that two distinct criteria, one theoretically rooted and the other statistical, were involved. A theoretically based definition of SC would work carefully from first principles to arrive at an operational definition and then engage in empirical research to see what this concept actually influenced in the observable world. The alternate approach seems to have been a quest for some kind of indicator which had fairly good predictive utility and which could be finessed into being called a measure of SC.

3.10

When people attempt to converse and cannot understand one-another they are in the Tower of Babel. When people arbitrarily and unilaterally change the meanings of words they have gone through the looking glass and have taken on the mantle of the Queen of Hearts. Confucius, in The Rectification of Names, explained the value of consistent use of terms. One can only hope contemporary sociologists will come to agree. Given this lack of agreement on what SC really means it is hardly a surprise to realize how diverse the mathematical formulations have been.

Mathematical Formulae

3.11

The adequate empirical exploration of any sociological concept requires at least two related stages. First it is necessary to pay attention to identify the appropriate underlying dimensions or variables. Second one must translate these measures into a mathematical formula which is theoretically adequate

3.12

The matter of mathematical formulae arises whenever there is more than one variable being measured and these variables must be combined in order to yield a measure which is more theoretically meaningful. The mathematical formula operationally defines the concept once the variables have been measured. It is generally hoped that all measured variables are on the same theoretical 'level' (that is: attitudes, behaviours, demographics, attributes of other aspect). For now, SC studies have exhibited a certain degree of inconsistency regarding not only the measured variables to be used but also to the type of mathematical formula which is employed to operationalize the concept.

---

Table 2: Table of Selected Equations Used to Operationalize SC

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Source of Equation or Model	Operational Model or Equation
Lenski (1954)[1]
Blalock (1964)	Y' = aX1 + bX2 + cX3 + dX4
Jackson and Curtis (1972)[2]	Y' = aX1 + bX2 + cX3 + dX1.X2.X3
Hartmann (1974)[3]	SC = fsc1z1 + fsc2z[2] + ... + fscnzn
Hope (1975)[4]	Y' = a(X1 + X2) + b(X1 - X2)
Zurcher and Wilson (1979)[5]	Y' = a(STATUS) + b(I - E) + c(I - O) + d(E - O) + e(I - R) + f(O - R) + g(E - R)
Whitt (1983)[6]	Y' = aX1 + bX2 + cT1 + dT2
Simpson (1985)[7]	Y' = aX1 + bX2 + cX3 + dX1.X2 + gX1.X3 + align=lefthX2.X3

¹ The original formula had the variables Occupation, Income, Education and Race/Ethnicity. Race/Ethnicity was dropped in the 1956 paper.
² Dimensions are arbitrary. Note that the SC term is a single three-way multiplicative interation term.
³ This is a general Factor Score equation and not necessarily the one Hartmann employed. If Hartmann did employ a model of this form then it is essential that each variable be ratio to allow the calculation of standardized (z) scores and factor score coefficients (fsc). Once Factor Analysis has been used to determine the dimensions of stratification this model becomes effectively the same as that of Blalock with factor dimensions being substituted for measured variables.
⁴ SC is an algebraic difference which takes into account direction of mobility. It does not treat SC as an independent dimension to the structural attributes.
⁵ STATUS is operationalized in a manner unspecified. I=income, E=education, R=residence, O=occupation. The concept of SC here is raw discrepancy between variables (apparently scaled according to the same metric) with the algebraic sum of the differences. Such a measure is insensitive to mobility direction and can lead to zero terms if mobility patterns are in flux.
⁶ The terms T_i are defined in the text. They represent attempts to take direction of mobility into account.
⁷ SC is determined as a multiplicative interaction term. Two-way interactions are used here, indicating a semi-composite concept of the variable SC. No three-way term is employed. Reasons for these decisions are not clearly given in the paper. Contrast this with the Jackson and Curtis decision cited above. Note that the variables here are education, occupation and religion. Treatment of Religion as a ratio variable (a mathematical requirement for multiplication) is somewhat unorthodox.

---

3.13

When Lenski proposed a 'non-vertical' aspect of status, it is reasonable to assume he did not want a mere re-statement of the original dimensions. He clearly wanted something that would be related to an individual's stratification position but not simply a restatement of it. It is also unlikely that he would have been theoretically justified in restricting this idea to 'multiplicative interaction' only. Southwood (1978), in an excellent but often neglected study of interaction effects, elaborated five ways in which statistical interaction can be operationalized. The key to his approach is to tailor the precise type of interaction employed to fit the substantive theory being investigated.

3.14

A few remarks on the nature of indices (composite measures) are now in order. The concept of volume is a composite measure which is symmetric in the present use of the term. A pan 5 cm square and 1 cm deep will have the same volume (composite index value) as a 25 cc. cup with a height of 6 cm. Depending on the context, however, these two containers might not be of equal effectiveness. The pan will allow water to evaporate or freeze more quickly, the cup will allow beverages to be more easily transported. For other purposes (such as the weight of the contained liquid) the shape is irrelevant. Composite measures augment the information provided by the measured variables rather than replacing them. The empirical observation of a composite variable's effectiveness requires that an appropriate variable be used to indicate this influence. The observation variable (appropriate dependent variable) must have a considerable part of its theoretical construction made of all the dimensions involved in the composite.

3.15

Dealing strictly with zero-order approaches mistakenly sacrifices higher order concepts by supposing they preclude the use of zero-order measures. Anomie (which may easily find in SC a sufficient if not necessary cause) is clearly intended to be a time-sensitive and most likely symmetric concept. A rapid change (in any direction) in any status dimension should lead to anomie. The fact that the dimension of response may be determined in part by the dimensions which changed does not make anomie a theoretically meaningless concept. This only occurs if all the responses can be determined in whole in such a fashion.

3.16

If a mathematical formula is going to be used to generate or define a term (such as SC) then the formula used requires just as much attention as the development of questionnaire items which provide the raw data to construct the indices. Those survey researchers who painstakingly try to control for wording, context effects, order effects and transfer effects (Converse and Presser, 1986) in order to assure a faithful operational definition of conceptual primitives are not well served unless just as much care and precision goes into the determination of the mathematical formula by which these data will be combined.

3.17

It will be recalled that Lenski's original formula used the sums of squared differences. In squaring, the sign of the distance is lost and with it information about direction. In practical terms, this loses the information which differentiates upward from downward mobility (in dynamic measures) or more generally which dimensions are higher than the others. Symmetric measures of inconsistency make the statistical (and therefore, hopefully, theoretical) assumption that there is no reason to suppose that people with PhD degrees working for a minimum wage need to be differentiated from high-school dropouts in the upper social and income tiers. Within a cognitive understanding, the question arises: are such subdimensions as effort and reward important? Should theory or conjecture dictate an asymmetry (that is: differences should be expected between the worldviews of poor scholars and the worldviews of rich illiterates) then the formula needed must be able to exhibit asymmetric characteristics.

Static and Dynamic Aspects of SC: The 'Time' Variable

3.18

The mathematical formula must not simply be capable of detecting asymmetries. Several researchers have identified theoretical ties linking SC to mobility. To explore the possibility of this connection what is needed is both time-sensitive data and a formula which includes time as a dimension.

3.19

Mobility is the change of position (however defined) through time. Status is crystallized when mobility on all dimensions has halted. The term 'halted' will also have to be defined in terms of the number of time periods which elapse with no status changes. Status 'crystallization' is conveniently and accurately seen as a process while status 'inconsistency' as a state - however fleeting - frozen in time. Most studies cited above are more accurately phrased as status 'inconsistency' studies since the static nature of the data do not really allow for other interpretations.

3.20

In any event, the Time dimension of SC's operationalization will be needed to determine if the inconsistency being measured is one which is crystallized or still in flux.

3.21

Whether one moves from one structural location to another or experiences a shift along one or more of the primary stratification dimensions; experiences, attitudes and behaviours are likely to shift in response. Old crystallized attitudes must be uncrystallized and re-crystallized. Stress (however defined) may well be a lagging indicator of social mobility.

3.22

Equally important is the rapidity of SC onset. Sudden loss or gain of status along a dimension will quite possibly have short-, middle-, and long-range effects similar to those seen in the substantive areas of life-cycle and life-passage analysis. Going from rags to riches over several years by dint of hard work needs to be analytically separable from making this transition thanks to a lottery ticket. SC and mobility overlap when changes along one stratification dimension are not paralleled on the other dimensions.

3.23

It is also necessary to decide if the kind of mobility being operationalized is continuous or discontinuous. Class position in Marx's or Weber's sense is a discrete structural location which is qualitatively different from other classes. In systems such as Warner's the differences between classes seem more quantitative in nature²².

3.24

Attempts to preserve the 'direction of mobility' by Hope or the use 'highest available status' by Zimmerman are intimations that an asymmetric measure is sought. If a composite measure - one which combines status dimensions into an index - is also required then this constraint places additional restrictions on the kinds of mathematical formula which can be used to calculate the index. Lenski's use of squared differences, for example, is not satisfactory if the direction of mobility is desired. To follow Hope's suggestions and to abandon the index for this reason, though, may be premature.

3.25

Gathering both structural location and cognitive data could, when combined with time-sensitive methodology, start to make systematic observations as to how the structural and the cognitive influence one another.

3.26

Summarizing to this point it is apparently necessary to draw a clear distinction between Status Inconsistency and Status Crystallization. The first of these is researchable using cross-sectional data collections such as social surveys. The study of Status Crystallization, on the other hand, must be able to examine a social process and therefore requires at least a cohort design and ideally a panel design.

Reference Groups, Ecological Fallacies and the Social Context

3.27

Ecological Fallacies are said to arise when researchers expect the individual members of some aggregation to share a trait or attitude such as when assertions like 'that area of the city votes for Party C' are made. Manifestly it is not the piece of ground which casts ballots but the people who live there. Presumably if the people who lived there now were to disperse and be replaced by others of a distinctly different cultural background and political views the voting patterns would change accordingly.

3.28

Ecological Fallacies are special cases of contextual errors in that they deal with errors which relate directly to geographic (ecological) boundaries. The same potential errors exist, though, when any attempt is made to move from one unit of analysis (e.g. individual) to another (e.g. voting region, social class). SC is uniquely susceptible to contextual fallacies or complications and as such present us with an ideal opportunity to examine these matters more closely. In particular, SC's sensitivity arises because of its social-psychological nature: because it involves the cognitive dimension along which the individual evaluates whether or not an 'inconsistency' in fact exists, and relative to what standard it may be said to do so.

3.29

SC research focuses attention directly on the need for great care in deciding questions relating to Units of Analysis and abstraction, standardization of operational definitions and in particular decisions about time as a central factor. The amount of time spent in the same 'inconsistent' status may be crucial in determining the intensity or scope of SC's effect. The rate of social mobility may be just as important as the distance and direction travelled.

3.30

It is not generally possible to compare an individual's score on a given variable with an 'expected', 'mean' or 'appropriate' value (the social aggregate on which this would be based would be simply arbitrary: a sample, a nation, an ethnic group).

3.31

Alker (1969) formulated an Ecological Correlation Model. This model explicates the kinds of statistical relationships which can be identified between pairs of levels of social analysis. This formulation is particularly pertinent insofar as it directly and systematically deals with the kinds of interpretation and comparison questions which also embrace SC studies.

[8]

3.32

Equation [8] shows how the covariance of aggregate statistics can be conceptually partitioned according to a priori taxonomic boundaries. Failure to take explicit note of these can lead to several types of fallacious interpretations. For any given set of observations the magnitude of the errors introduced is indeterminate. In general we only know that these kinds of errors could occur. We do not know if they will or if they do how large they will be or where they will manifest themselves.

3.33

The interpretative fallacies listed below do not apply to ecologically defined areas alone. They apply to any generalization from one level of analysis to another. The only safe way to evaluate the attributes at various levels is to employ random sampling at each level of potential interest.

Ecological and Related Fallacies

Ecological Fallacy: Assumes the Between- Regions covariance replicates the Between-Individuals covariance. Individualistic Fallacy: Generalizes from the Individual to the entire group. Selective Fallacy: Generalizes from a sub-group to an entire population. Universal Fallacy: Generalizes from the entire population to a particular sub-group. Contextual Fallacy: Generalizes from one sub-group to another. Cross-Level Fallacy: Assumes that the covariance within a region represents the covariance between regions.

3.34

The difficulty this raises for SC is central. SC is a measure which compares a person's status to a normative standard defined in terms of that person's reference group. Whether it is Lenski's use of a group mean statistic in the calculation of percentiles, or Hope's less troublesome but still precarious subtraction of ranked (according to what?) status scores, these problems remain: what is the reference group, why was it chosen and in what other reference groups could the various individuals be legitimately counted as members?

3.35

This relates directly to SC interpretations whenever the specific inconsistency under study is an inconsistency which compares an individual's particular status ranks to a group which may not be the 'appropriate' reference group for that person. The problems for SC are, actually, even more serious since individuals can have more than one reference group - even for the sake of status considerations - and their attachments to these groups are not necessarily equal.

3.36

A logical extension of this to population sub-groups is also possible. A person's status attributes may be inconsistent with one- another with reference to national patterns but not with respect to more salient expectations. People may be members of a specific minority group for which this 'inconsistency' is entirely 'normal'. If members of an identifiable group discover their status patterns are significantly different from the majority group this could in turn become the basis for heightened group identity and even the start of a social movement (Blumer, 1969b).

3.37

In other words, an individual's status can be consistent with respect to his or her minority group but inconsistent with the norms of other reference groups. In an extension which was clearly anticipated by the Hawkes et al. (1984) study, such conditions allow SC to be defined polymorphically²³ (one which has the same theoretical aspect but is operationally distinct for various levels of abstraction)²⁴ and therefore generalized as a group attribute: a structural feature. The problems are compounded if one attempts all this using a dynamic approach rather than the essentially static model outlined by Alker.

Predictive Power: Operationalizing Adequacy

3.38

Many of the writers who pronounced SC a 'moribund concept' did so because of the lack of predictive utility or predictive power their own operationalizations of it added to a regression model.

3.39

Not all theoretically useful insights can be seen to have high predictive power. The theory of evolution has not, as yet, predicted anything. Despite Sir Karl Popper's refusal to regard Evolution as a 'theory' very few would deny its fruitfulness as an explanatory system or as an incentive to conduct research in such areas as molecular genetics and environmental biology. Even if we allow predictive power a major role we are still faced with the following set of questions.

3.40

Predictive power in any sociological model is elusive in any event.

• Exactly how large an R² is sought?
• Why was this magnitude selected?
• Does predictive power play the same roles in both basic research and applied research?

3.41

These questions could clearly occupy many pages of discussion. What is more interesting is the apparent lack of interest surrounding them.

3.42

The use of predictive power is understandable given the orientation of many social scientists to move away from basic or exploratory research and towards research which has a direct application to one or more of the problems which exist in society. Social engineering is more easy to explain and justify as a goal than is research into theoretical relationships which are of such limited predictive power as to be useless to policy makers and social critics.

3.43

The presence of great predictive power is always satisfying to researchers. It's absence, however, cannot be taken as evidence of an inadequate theoretical insight. Operational, sampling and other research-related matters must first be ruled out. It should also be noted that detecting a group of dependent variables for which SC is a 'useless' predictor helps map the empirical scope or range of the SC index.

Theoretical Issues

4.1

Three main theoretical question are brought into relief in the examination of SC.

4.2

• SC has inspired a significant number of inconsistent operational definitions. Does SC belong to a group of related ideas rather than being a single unalloyed notion?
• How does SC relate to macro-sociological theory and what insights does it provide?
• How does SC relate to micro-sociological theory and the linking between the macro and the micro levels of theorization?

Conceptual Families

4.3

Throughout the career of SC, it has been operationalized in numerous ways. These alternative operationalizations have included different mathematical formulae, different measured dimensions, different ways of defining the reference groups (cognitively or structurally) and different ways to handle time and rates of change. One could allege (with some justification) that the use of so many alternatives is a tribute to the willingness of sociological researchers to ignore the goal of replication studies or the scientific traditions of consistent definitions. More generous critics will be able to argue these various approaches all 'sort of' deal with the same 'general concept' of Status Crystallization.

4.4

It is possible and indeed necessary to define SC in accord with the underlying notion of SES in the study. For each SES indicator, whether it is that of Hollingshead and Redlich (1958), Galtung (1976), Wright and Perrone (1977), Weber (1978), Holmes and Butler (1987), or any of the myriad others (Powers, 1982; Ortega and Rushing, 1983) a distinct operationalization of SC is demanded. At the very least this provides a comparison between SES and SC so that one can compare the predictive power of SC to its parent.

4.5

In order to retain, albeit with some restrictions, the flexibility of a such generalizations while staying reasonably close to the mathematical operational definition, the most likely resolution would involve treating SC not as a single concept but as a family of closely related concepts.

4.6

Families, in the mathematical sense, make use of the same general formula from one application to another, but allow for some variation in the values of parameters in the equation itself. Treating SC as a family would not only require the use of the same mathematical formula from one research event to another but would also mean using exactly the same variables (measured in the same way). This would allow researchers to investigate the scope and range of effectiveness of SC across research contexts.

4.7

Borrowing from computer science terminology, a 'polymorphic' operation (such as addition or multiplication) is one which uses the same symbol (+ or x) regardless of the conceptual categories of the objects being operated upon. Multiplying such diverse entities as scalars, vectors, matrices or complex numbers are all symbolised with the 'x' operator. The operator is thus polymorphous - it takes the form appropriate for the particular kind of number type involved.²⁵

4.8

In an extension of this, SC has been used by researchers as if it were polymorphic. Instead of using exactly the same measured variables each time, variables which were taken to be 'alternative operational forms' or substitute measures for the abstract theoretical status dimensions of interest were substituted.

4.9

The use of such polymorphism requires some care, particularly in interpretation. If one's empirical expectations are taken from published reports of multiplying two scalars together, research in which a complex number is multiplied by a matrix is likely to yield results which are difficult to interpret. By analogy the different kinds of objects (complex numbers, matrices, etc.) can be taken as measures based on different paradigms (cognitive, structuralist, psychoanalytic, feminist, sociobiological etc.) and combined by different operations (multiplication, subtraction etc.) or formulae used to calculate SC. The failures to get consistent results are not surprising. The failure to get expected results depends, additionally, on what is expected and why.

4.10

To date, SC has been ostensibly defined as a family of polymorphic variables with several formulaic alternatives being used as if they were interchangeable. While this may be easily rationalized at abstract conceptual levels it makes operationalization an unwieldy exercise and the interpretation of results somewhat untidy. The fact that this situation has persisted for three generations says equally interesting things about the theoretical sophistication of methodologists and the methodological sophistication of theorists.

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Table 3: Tabular Representations of Various SC Theoretical Relatives
The table shows families of similar theoretical concepts and thus the basis of polymorphic operationalizations

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Unit of Analysis Ultimate Holder of Inconsistent Status	Reference Group for Unit of Analysis
(Individual or Group)	individual (self or 'significant other')	sub-group to which individual belongs	sub- group different from individual's	national, population or total society
Individual	psychological	initial definition	anticipatory socialisation	melting pot model
Sub-group to which individual belongs	local village, community or ethnic group. Individual responses to stress	homogenious value consensus	ethnic rivalry, Balkanization	structured social inequality
Different sub-group	competing ethnic group, target social group.	useful for intra-group friction studies, Collective feelings of loss/gain.	evangelism/ moral imperialism	dominance or oppression, separatist movements
Nation, Population or Total Society	aggregate statistics for more abstract comparisons (few direct psychological implications)	useful for general indices of discrimination or collective mobility	useful for comparative studies of social mobility or stress responses in cultural contexts	nationalist or patriotic movements

This table shows how the concept of SC has been 'intuitively' treated as a family of related concepts and thus a prime candidate for 'polymorphic operationalization'. Such attempts have never been systematically undertaken in the social sciences. Polymorphic mathematical formulae are so called because they reveal the same theoretical relationships among salient variables at different levels of research abstraction. By so doing, they also require that if the kinds of status measures (structural or cognitive) be retained throughout. This will most likely mean substituting group means for individual scores at the appropriate places. Also retained throughout is the mathematical formula by which these measures are combined.

Main Diagonal Entries are sui generis notions of harmony or proper reward structure in a monoculture.

The upper triangle of cells contains some theoretical paradigms which are candidates for examination.

The lower triangle of cells contains some research areas which are candidates for examination.

Note:

1. All of these entries are time-dependent and thus require dynamic operationalization
2. Boundaries separating the levels in the table are fuzzy
3. Each research undertaking will have a paradigmatic requirement of cognitive as well as structuralist measures.

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The Macro Focus: Structuralism

4.11

Structuralist theories have always been at a disadvantage when attempting to explain how change occurs. It is one thing to generate a series of historical examples which describe how the functions of one structural entity (the family, for example) are hived off into newer structures (schools, businesses) and represent structural change. It is quite another thing to explain or describe the process in some fundamental level. The question 'why' is never fully captured by the answer to 'how'.

4.12

The most common structural metaphor used in sociology - that of a living body - has been extensively discussed and is often employed to illustrate such notions as functional dependence, the maintenance of equilibrium and the division of labour. As a source of analogy for these features it is quite useful. Other social phenomena - the breaking up or coming together of nation- states, multi-cultural societies and so on - are often extremely difficult to cast into the biological-structural analogy.

4.13

Structures, alternately, can be discussed architecturally. The divisions that are now rooms could have had their functions and even their spaces defined by existing network groupings. Socially necessary functions which are performed by the same group in one culture may only require one room while those other cultures which subdivide these tasks may require a structure of more differentiation. Rooms, like structures, can gain or lose functions through time. Living bodies, when cut in half, seldom survive. Families which find themselves placed in houses with half the number of rooms will normally make the necessary adjustments and continue. Walls, like laws, can be changed but with difficulty and consequences which are often unexpected²⁶.

4.14

The architectural analogy, like the biological analogy for structure, will clearly have serious limitations. Architecture, though, is a social product which by its very nature conforms itself to the available technology, ecology and biological needs of the social members which created it (Watkin, 1977). Forms (such as Doric columns) are retained from the past for conscious reasons of tradition or aesthetics and persist not simply because of parasitism or the slowness of evolution's editing.

4.15

The use of these two related but distinct uses of the term "structuralism" has a point. Structuralism is more a metaphor than a paradigm.

4.16

Structural descriptions or categories are usually semi-permanent patterns of fluctuations at other more closely 'real' regions (Bates and Peacock, 1989). In Taoist approaches, the structural components (including personalities) are combinations of the elements of wood, earth, fire, water and metal. The dynamism arises with the flow of energy according to the balancing of yin and yang. Medieval European alchemists saw four elements (earth, air, fire and water) and combined them with Aristotelian laws of motions which sent things towards their 'ideal nature'. Freud's id, ego and superego structures were crystallization's of various interactions all ultimately energised by the libidinous tensions arising from Eros and Thanatos. Contemporary physics treats the 'real' as the flux of fundamental matter/energy bits which interact and change in accordance with the four forces currently identified. What we call 'real' is a collection of transient patterns which remain stable long enough for humans to take them seriously and give them names. The flux and the real are cognitively, not ontologically, different.

4.17

For social sciences, a structuralism which systematically ignores the reality of flux will only fortuitously avoid being a projection of a theorist's personal experience. A psychology which treats putative social patterns (patriarchy, social classes, castes, ethnic groups, etc.) as if they were manifestations of 'ultimate reality' will only fortuitously avoid being a projection of the theorist's ideological aspirations.

4.18

Some researchers have tried to use ascribed attributes as status dimensions. Mobility along these dimensions is impossible. In mobility terms an 'ascribed status' is one which has a zero rate of change. One's attitude to being in that group, naturally, can vary significantly.

4.19

In short: It may not be possible ever to separate fully the objective from the subjective, the structural from the cognitive²⁷.

The Micro Focus: Socialization

4.20

Throughout the career of SC researchers have variously dealt with the question of how people 'ought to' respond to status assignments. Stress, feelings of injustice and other personal (i.e. psychological) factors have often been introduced as implicitly intervening stages which separate two macro- structural observables - the 'inconsistent' status and the behavioural sequels which are propagated by this social fact.

4.21

SC is a concept which requires a model or theory which a social-structural condition (ranking on social status dimensions) assumes or requires this structural location will produce various kinds of psychological responses (notably stress) and that these responses will result in behavioural patterns which are observable at the macro level. Socialization is also regarded as some kind of requirement for the stresses which SC is deemed to cause. SC's impact (as evidenced by the attempts to express its stress as a 'social justice' issue) requires the making of a value judgement on the part of those who experience it.

4.22

People who suffer malnutrition because of their poverty will experience the health complications associated with this condition whether they 'believe' they are disadvantaged or not. The same cannot be said for the perception of 'injustice'.

4.23

Attitudes which are deemed to be caused by structural factors (e.g. SC) which produce behaviours which are observable at the macro level offer fascinating macro/micro research opportunities.

Equation [9] represents an early Attitude-Behaviour model by Fishbein (1967).

[9]

Where:

NB_i = Normative Belief
B = Behaviour
M_c = Motivation to Comply
RHd = Reinforced Distribution
A = Attitude
A_act= Attitude to the Action
BI = Behavioural Intent

4.24

This model of Attitudes (surely to some extent the consequence of socializing forces?) and Behaviours is over a decade prior to Wilson's (1979) rather intriguing proposal (equation [5- c]). Aside from marvelling at the lack of sophistication in translating some penetrating English-language ideas into mathematical expressions it is difficult to comment at all²⁸.

4.25

The exploration of linkages between Socialization and change in structural location (mobility) does implicitly address the need for theoretical linkages between the cognitive and the structural. It also identifies SC as a topic for which those linkages are particularly important.

4.26

If SC is a psychological stressor then it may have a range of effects (including stress-reduction techniques) which do not correspond to their dependent variables under study) which interacts with all the other predisposing, enabling and triggering factors essential for the behaviour to take place.

4.27

One additional comment is in order. The notions not of how SC ought to work but also that it ought to exist in the first place, these claims could all serve as examples of Weber's verstehende soziologie in action. What makes the question even more interesting is the intuitive validity of its underlying psychological processes. Just as cognitive psychology has arisen to bypass behaviourism's refusal to discuss 'inner states', so, too, a purely structuralist sociology is proving inadequate to examine SC and related ideas.

Reconsidering SC

5.1

SC is a theoretically compelling idea which has so far kept returning to the attention of social researchers. The reason for this is apparent. The concept itself is more than intuitively appealing. If SC has no detectable effects then at least one of the following is true:

• Feelings of injustice do not influence attitudes to society
• Feelings of injustice do not influence behaviour
• Feelings of injustice do not cause psychological stress
• Neither feelings of injustice nor psychological stress are initiated by 'anomalies' In the reward system of a culture
• Socialization is not a factor in determining attitudes (including attitudes regarding justice)
• Socialization patterns may differ among cultures, subcultures and other groups but attitude profiles for these groups remain constant
• Research techniques in sociology are not yet sufficiently advanced to deal with the above questions definitively.

5.2

This list, while not complete, is sufficient to show that a sociology that cannot incorporate SC will be theoretically incapable of dealing with the role of human consciousness in society. Orthodox Marxism, in defining human consciousness as totally derivative from structural conditions, offers the option of defining away this limitation. The alternative is to recognize the opportunities for working towards a quantitative analysis of these relationships.

Towards a New Formulation

6.1

Throughout this paper attention has been given to the apparently free manner in which the actual operational definitions of SC were undertaken. If SC is to be given a useful operational definition then the following issues must be explicitly handled.

• Is an SC index needed at all?
• How shall the dimensions of SC be determined?
• Should SC be a static or dynamic index and if so how will the distinction between a static and a dynamic index be made?
• Should SC be a directional index?
• How does SC differ from or relate to social mobility?
• How will the measure deal with 'reference levels'? If status dimensions are inconsistent then what collective or normative levels will be used to decide if people are being over- or under-rewarded?

6.2

Taking these points in order:

Is An SC Index Needed At All?

6.3

The question was raised several times as to whether an index of SC was needed at all. To this two comments are possible. First one notes theoretically such an index represents the existence of a higher-order relationship than ones which can be directly identified from observed variables. As noted earlier, indices are such composites as 'volume' and to insist only measured variables be used is an extreme form of operationalism. Second, it is fair to point out that SC has not yet really been given a serious test. The numerous difficulties and complications presented in this paper make it highly likely that even if SC does exist as a detectable effect it would have been observed by the techniques employed thus far.

The Dimensionality of SC

6.4

While it is impossible to restrict arbitrarily the dimensions along which SC effects might be observed it is also crucial to the scientific enterprise that definitional consistency be observed. If researchers are to avoid more misunderstandings in future, then the same terms should have the same meanings across research studies.

6.5

Composite measures can be required theoretically or can be suggested experientially. 'Volume' can quite appropriately be seen as an obviously useful three-dimensional index combining the three one- dimensional attributes of length, width and height. Whether the usefulness would be so apparent to us if we ourselves were not compelled to travel with suitcases may reveal the need for an experiential encounter with the composite idea.

6.6

The dimensionality of SC is also confined to the dimensionality of social status itself. Given the wide range of ideas surrounding exactly what status is and how it ought to be measured we unavoidably encounter the complications surrounding the disputes in how to deal with the realities of social stratification.

Should SC be a Static or Dynamic Index?

6.7

If we define SC as a dynamic process the definition will give us the capacity to exhibit a static nature as well. If the phenomenon is really highly stable or constant through time (either always or sometimes) then a formula which is intrinsically dynamic will not vary but be a constant. If attributes of individual's worldviews or life experiences do not remain constant throughout life this hypothesis can be directly examined as well. Assuming the data exist it is advantageous to define SC in dynamic terms.

Should SC be a Directional Index?

6.8

If at all possible the index should be directional in order to deal with those hypotheses which have arisen suggesting the direction of change is important. We should not assume those relationships we can test.

Reference Groups and Levels

6.9

The reference level of the index is in many formulations and discussions mandatory for calculation. What is meant by 'appropriate' is either determined subjectively or objectivity. If the former then it is not a structural attribute and if the latter then the researcher is left with the tasks of deciding to which reference group the respondent belongs. Even this is not as easy as it looks.

6.10

Social policy decisions such as affirmative action not only attempt to introduce an additional concept of distributive justice (one based on group membership) but also change the perception of benefits of membership in specific groups may confer (and in some cases include various assemblies seeking to be formally designated as such a group).

6.11

While in theory it may be possible one day to employ the reference groups or ideal value for a string of status variables, it is unlikely we have the ability to do so any time soon. The selection of a reference level is in essence an assumption about how status "ought to" correspond to one-another. The designation of a reference group, similarly, requires the researcher to decide the respondent's demographic attributes determine his or her cultural sensibilities.

6.12

If possible, then, our operational attempts should seek to avoid this approach to standardization. Doing so, it is realized, will require abandoning Lenski's original formula. In highly homogeneous societies his desire for using an index calculated with such value-consensus-based expectations might be practicable but if we want something which will also be viable in pluralistic and multicultural societies then we must, for the time being, set this approach aside.

Relation to Social Mobility

6.13

Social mobility is change along the specific dimensions of social stratification or ranking²⁹. SC is easily distinguished as a higher-order term which deals with how the change in mobility components interact with one- another. SC and related terms may arise most obviously as indices or composite measures. SC research is contingent upon mobility concepts just as mobility research is itself contingent upon social stratification concepts.

A Speculative Suggestion

7.1

The above points are useful in providing some rough guidelines as to the kinds of data required and the properties of the mathematical formula to be used to operationalize SC.

7.2

Most if not all the objectives for an SC measure can be met with a model based on differential equations. A differential equation expresses a rate of change and the direction of that change. If the rate of change is irrelevant to one or more attitude or behaviour items then this will be indicated by this differential term being of no empirical utility. If SC's rate of change impact is to be studied then the use of differentials is worthy of closer investigation.

7.3

An SC index which attempts to meet the above objectives will require the underlying social status dimensions to have been already decided.

7.4

The actual status dimensions used here are Lenski's (Education, Occupation, Income). In order to make use of them we are first going to have to determine the degree to which we can measure the status components of a person's educational accomplishments, income levels and occupation³⁰.

7.5

One could easily believe that a DPhil degree in Classics from Oxford or Cambridge would have significantly higher generic status (not to mention taking longer to get) than a law degree from a mid-level North American university. The likely earning potential of these two degrees could well be the inverse of this approach to status determination.

7.6

We should note, too, that the relevance of education to status is linked to determining the economic sector one can enter as well as having a contribution of its own based on the number of years endured. (The simple linear relationship between status and years of education is probably only valid throughout the years of compulsory education or to the maximum number of years in the uniform curriculum of the society or state under consideration.)

7.7

The ways in which these measurable attributes relate to 'status' is not at all clear a priori. The advent of multidimensional scaling techniques may resolve much of these initial problems but it is highly advisable that in any SC-oriented research the actual data collection instrument include a highly refined technique for determining directly the status rankings of the respondents.

7.8

What follows is both highly speculative and quite general. It is put forward only as a tentative and heuristic proposal to illustrate at least one potential direction for future work in the study of SC and related phenomena.

7.9

The use of mathematical terminology is largely guided by the definitional precision it brings to the discussion and not primarily because it is believed the operational rigour required by these formulations is currently attainable. For this reason no attempt is made to suggest what the actual functions for the relationships might be.

[10]

Status = W {f(x), g(y), h(z)}

where:

W is a function of f, g and h (differentiable with respect to "time")
f(x) is the partial status of educational attainment
g(y) is the partial status of occupational attainment
h(z) is the partial status of income attainment
and the functions f, g and h are time-dependent and differentiable

7.10

The status function for income status is probably not linear either. The status improvement gained in going from the 10^th to the 25^th percentile is probably not the equivalent of going from the 60^th to the 75^th.

7.11

Some differential associations which can be defined using the above ideas are:

[11]

dW/dt = Status Mobility

where df/dt, dg/dt and dh/dt are rates of mobility for the specific status dimensions and the sign of the differential gives the direction of mobility³¹.

7.12

And if we define

CSS₀ as a Composite Status Score at time t = 0 then

[12]

Status Inconsistency= SI = U{(f_t-CSS₀),(g_t- CSS₀),(h_t-CSS₀)}

7.13

U is a function. If U is defined as multiplication then SC is analogous to 'volume' as it would be with the mobility measure above (but not the same 'volume' since this value could be calculated in a way very similar to Lenski's original approach).

7.14

A zero value would then indicate 'no inconsistency'.

7.15

The calculation of the CSS is, of course, a return to the dilemma of the reference level problem discussed above. If we treat the CSS as a constant term (and here we find the real value in using an aggregate CSS score) then we could differentiate this expression to eliminate the constant term.

7.16

The rate of change of this value can be given as:

[13]

dSI /dt = SC
(a possible redefinition of SC)

and would represent, depending on the sign of the term, the rate of status convergence or status divergence.

7.16

If SC = 0 then this would indicate there is no change along the status dimensions. Status would be 'crystallized' but not necessarily in a state which would be regarded as 'equitable' or 'just'. Such a condition could arise if the legitimacy of the patterns of social inequality was coming into question (Smith, 1995).

7.17

One other realization can be had here. Equations [11] and [13] represent the same family of differential equations. Here is the way in which status crystallization and mobility can be seen to be equivalent ideas.

7.18

Such a calculation procedure represents an attempt to finesse the definition of SC into something we can actually evaluate. This finesse allows us to slip away from either the complications of determining a reference level for the individual respondents or differences in rates of change along the various status dimensions. If, however, the actual 'distance travelled' is important then it cannot serve our purposes.

7.19

If the difference in the rate of change is of potential interest then an additional equation is needed.

7.20

The following equation might be a worthwhile starting point.

[14]

(another possible redefinition for SC)
(f, g and h are the equations taken from [10] above).

7.21

The ratios with respect to the f' term are selected somewhat arbitrarily but not totally. f was used earlier to represent 'education' which can be regarded as the single most easily controlled of the achieved status variables. It matters less which of the terms is the numerator and which the denominator. (Putting the smaller in the denominator would make unity the lower bound and avoid the need to work with purely fractional values.) Any deviation from unity would indicate a 'decrystallization trend' and the greater the value the more rapidly this would be taking place. The higher the value the more rapidly the status variables are 'getting out of sync' with one another.

7.22

Equation [14] obviously reduces to

[15]

7.23

This reduction reflects the decision to use f as a reference status, a decision which was prompted by the difficulties in defining some absolute reference level. These decisions are not carved in stone. They are as much for convenience as any other reason. Future commentators will doubtless be able to improve significantly on these preliminary ideas.

Some Implications of this Formulation

8.1

What follows are themselves highly speculative and are only included to illustrate some of the potential new pathways for research which may be available if the above suggested formulations prove to be possible.

Patterns of Social Inequality

8.2

How long does an inconsistent status have to persist before it is an actual status rank? How many people have to occupy this rank before it is regarded as a structural entity? These questions directly regard social structure not as a permanent feature of society but as a relatively stable period in the flux of social relations (Berkowitz, 1982; Smith, 1996).

8.3

By explicitly expressing time and directionality in an index, this formulations allows at least conceptually for the analytic distinction between transient and endemic patterns of the allocation of power and privilege. Transient patterns such as those currently visible in the post- industrial Western economies are not stable enough for a long-term political response to form and thus are more likely to inspire individual or self-improvement oriented attempts to cope with the changes.

8.4

If the patterns persist for what is seen as a long time (and the attributes of this time scale is itself in need of research) the feelings of dissatisfaction will have sufficient time to incorporate themselves into group-identity definitions (and the groups can be defined in terms of race, sex, class, caste, tribe, ethnicity and so on) and result in fluctuations in the patterns of social legitimacy.

Dynamical Social Structures

8.5

One of the commonest features of all social theories is the idea of a structure. Sociological structures are understood as patterns of action or conduct. More accurately, however, we should realize that a pattern must also last long enough (i.e. the underlying process must change slowly enough) and be of sufficient interest to warrant a name. Structuralism is now being recognized as an heuristic which has serious limitations (e.g. Bates and Peacock, 1989) and two of the most discussed are the inability to deal with 'change' (are we studying the flux or the way people attach and change the names they give to patterns in the flux?) and the inability to link the micro and the macro levels together (as manifested in the SC debate itself). In the last decade the explosive growth in the study of chaos has led to a renewed interest in exactly how order and chaos, stability and change, are related to one-another.

8.6

Chaos theory (e.g. Robertson and Combs, 1995) provides a paradigm which automatically incorporates both change and the ability of micro events to spawn macro consequences (the so-called 'butterfly effect'). Chaos, however, is a property of dynamic systems. Static entities by their very nature cannot exhibit it. Chaos, in treating change as normal demands that we reconceptualize 'structures' as patterns which humans can perceive long enough to deem them worth naming³². For chaos theorists, stability is just a very slow rate of change. Chaos theory forces us to make a distinction between structural change and the subsequent attachment of labels to commonly perceived patterns. In short, social change becomes at least in part as much a problem of cognitive psychology as one of changes to the system being observed.

8.7

If the benefits of chaos theory are to be accepted then part of the cost is the redefinition of key concepts in accord with the logic of the new paradigm. In the current case this means redefining social structures as patterns in the flux of the real and not as Platonic absolutes.

8.8

As this paper has tried to show, SC is a concept which is inherently dynamic and cross-level (micro-macro). It is thus a natural candidate for inclusion in a dynamic paradigm of society even as it is apparently incapable of adequate operationalization or testing in the more static models from which it sprang. SC may therefore represent one of the infamous loose ends of the structural-functional paradigm, a seemingly innocent anomaly which when tugged brings down the entire edifice.

8.9

As we know, too, dynamic models already exist and are well understood in other scientific fields. Perhaps the closest field to the social sciences in which these models are found is the emerging field of ecology.

Parallels with Ecological Models

8.10

Relating the SC debate to the problems encountered with ecological correlations does not circumscribe fully the ways in which these fields of study are similar. The application of differential equations suggested above was itself largely inspired by those used in ecological research.

8.11

Making the appropriate allowance for the role of human cognition it is still possible to argue that social status is a kind of environmental resource and some people are better adapted to exploiting the resources available than are others. Changes in the social environment can tip the delicate balance and change the selective advantages of those in the existing population³³.

8.12

At the metaphorical or anecdotal level this is well known. Whether the parallel can be extended to the kind of precision and logical rigour demanded by the use of mathematical models is something we now need to consider.

Time-Sensitive Research and Data Collection

8.13

All of the proposals involving differentials and differential equations are predicated on the existence of data collected at the proper level of abstraction using (most likely) a panel-design so that the necessary zero-order equations can be discovered in the first place. Almost none of the research done in contemporary sociology is of this type.

8.14

The absence of the necessary form of data cannot serve as the justification for a return to the manifestly oversimplified operationalizations already attempted. As long as theoretically reasonable data remain unavailable or uncollected the work done on SC will be within the tradition of qualitative research.

Some Limitations

9.1

Three further matters which now need to be recalled are:

• How big an R² component should SC contribute to a regression model?
• How does SC's influence on attitude and behaviour fluctuate from subgroup to subgroup or through time?
• To what extent is it necessary to normalize the status function for each occupational sector in order to calculate both Status and SC?

9.2

At the present state of the art of sociological theory it is advisable to explore these last topics empirically.

9.3

Empirical explorations do not need to be confined to the quantitative. Not discussed in this paper is the question of underlying cultural ideology. The common ideas in the modern (and post-modern) West which separate status ranks into the achieved and the ascribed may not be subtle enough to deal with non-western cultures such as China (e.g. Hsu, 1967), Japan (e.g. Nakane, 1970), or India (e.g. Dumont, 1980; Kolenda, 1981). These assumptions may not really reflect the actualities of Western societies either. The emphasis on quantitative approaches in this paper should not be interpreted as an attempt to assign ethnographic research to a secondary position. If nothing else they serve as checks against oversimplifications.

Concluding Remark

10.1

SC is an idea which, intuitively, has strong appeal. It may even be the case that this very appeal was responsible for the way so many investigators abandoned proper research protocols and produced a string of studies which are rarely comparable to each other. It may be that SC, as a concept, was never actually tested at all. Not only are all the major operationalizations inconsistent with each other, several appear to be inconsistent with the underlying concept itself. It may now be time for theorists to overcome their innumeracy and phobic regard of mathematics even as quantitative methodologists seek to understand more clearly what kinds of human beings their mathematical models seem to be describing.

Notes

¹In the more mathematically precise terminology of contemporary science, such influences would now more than likely be termed 'second-' or 'higher-order' terms, 'resonance factors' or 'interaction effects'. It is also reasonable (in the case of Social Mobility) to note that social location, change of location (mobility) and increasing rate of mobility (acceleration) all represent terms which are obviously related but not linearly dependent on one another. The structural and cognitive dimensions are also contenders.

²Blalock's formulations do not specify the actual measured variables. His discussion was based on purely mathematical criteria. He did not attempt to discuss the theoretical dimensions which his interaction effects would detect such as exactly what sociological or psychological meanings might be attached to a multiplicative interaction term when used as a 'dimension' of analysis.

³Multiplicative interaction terms are sufficient but not necessary. Equally valid - if the independence criterion alone is used - would be reciprocals [1/(x1 + x2)], trigonometrics [sin(x1 + x2)], logarithmics [log(x1+x2)] and so on. Clearly, these functions are more 'complex' than straight multiplicative interactions and could have been excluded through the invidious application of Occam's Razor. Closer to the traditions of empirical science would have been either (1) to use other theoretical results to place deductive boundaries on the form required of the index function or (2) to collect as much information as possible and compare the empirical predictive utilities of a wide range of candidates. These options were not made explicit either by Blalock or Lenski, but were partly employed by Jackson and Curtis (1972).

⁴As with the Blalock example, Jackson and Curtis did not directly discuss which variables were to be used to measure status.

⁵In other words, the long-believed-to-exist affects of social mobility (one of which Durkheim called anomie) could not be detected with this technique.

⁶This confusion spreads well beyond sociology. For a major example of this difficulty, see Noam Chomsky's (1965) Aspects of the Theory of Syntax.

⁷One critique of Hope which did not appear in these papers is one which could have been made. Lenski may well have intended SC to be a composite-dimension index: one which collected together the individual variances between positions on individual status dimensions and the overall social position index of the individual. This point will be more fully discussed later.

⁸House, of course, has a point. To be sure, social mobility may well have an influence on the effect SC has on another variable. The same could be true about the starting and stopping points of the mobility journey as well as the distance travelled and the time taken. This does not mean however that a single measure ought to try to measure all of them at once. It is a perfectly legitimate theoretical position to argue that there is an SC-rate of mobility-range of mobility complex in which all two- and three-way interactions are theoretically meaningful and require empirical documentation.

Lenski's original arguments excluded both the rate of mobility and particular information about the range of mobility (the starting and stopping points on given component dimensions). This should not be taken as the wholly different assertion that these other terms are theoretically or predictively inconsequential. This is clearly a wrong interpretation, but one which may explain the desire of some researchers (e.g. Hope) to capture this information in the SC Index itself. This apparent wish to overload the index may reflect the relative lack of sophisticated mathematical modelling in mainstream sociology and the pronounced exclusion of time dependent (rate of change) terms from the models we do have. These lacks are not empirically noticeable in survey research dominated environments but there is no reason why our theories must be constrained by the current limits of our data.

⁹Lenski noted his own weakness in operationalizing concepts and thanked Blalock for assistance in his 1964 paper.

¹⁰This, of course, is true of all composite indices and higher order terms. 'Area' loses information about length and width. An area of 10 square feet can arise from an infinite number of length-width pairs. The issue of theoretical relevance alone determines the justifiability of most higher order terms.

¹¹Note here that while Income, Education and Occupation are generally accepted as operational aspects of the achieved status dimension, Race is ascribed. This generates a status construct that combines these two aspects into a single index. While potentially of some theoretical and empirical use, such undertakings are generally most useful if they are based on solid research foundations.

In a certain sense, this approach represents an attempt to step back several paces and to search inductively through various kinds of inconsistencies to see if some patterns that 'looked like' an SC effect could be detected.

¹²This point brings in Reference Group theory. This shall be more thoroughly discussed below in the consideration of ecological and auto- referential or recursively-defined indices.

¹³Wilson (1979: p. 1235) described this equation as 'the model used to represent status inconsistency's competitor as an explanation of the effects of ranks on individual attitudes and behaviours - Socialization'. He not only operationalized Socialization in this rather oversimplified fashion, he made the theoretical assertion that SC and Socialization were mutually exclusive. Aside from seeing this as a continuation of Durkheim's railings against psychological reductionism it is difficult to fathom the justification for this.

¹⁴The model would also require some sensitivity to the non-static attributes of a feedback process which presumably continues throughout life.

¹⁵The term 'a(X₁ + X₂)' is a composite status term following Hope and the two T₁ and T₂ terms being grouped (in the text) as 'composite inconsistency' terms but are obviously being decomposed in the model when written as an equation. A composite inconsistency term would most likely have to be written as b(T₁ + T₂) so that the inconsistency effects were non- separable after the fact.

¹⁶A Chemical Engineer known to the author delights in remarking: 'Sociological methodology is the technique whereby rubber rulers are employed to measure temperature'.

¹⁷This point is potentially related to such notions as Mills' misplaced concreteness. The acceptance of many sociological 'truths' is more rooted in ideology than anything else.

¹⁸Ecological effects are only relevant as such when climatological influences are primary. If the 'region' effect is itself a stand-in for socio-cultural variations (such as are found in the regional response patterns to abortion-related issues as reported in Adamek (1985)) then the generalization to a social-structural/social-psychological paradigm has been implicitly carried out.

¹⁹The 'probable expectation' is clearly a cognitive rather than structural measure. The study did not provide any rationale for the implicit assumption that expectations of distributive justice even exist, or given that they exist that they would manifest themselves in this manner. This point is tightly tied to Ecological Fallacy dangers, at the methodological level.

²⁰Lenski's original formula squared the differences in order to combine positive and negative inconsistencies. Kerschke-Risch's decision to separate them amounts to converting one of Lenski's assumptions into a testable hypothesis.

²¹The fact bats scored 5.8 on a scale with a maximum value of 4 has some interesting implications for those who use Lickert scales.

²²Discontinuous class boundaries also raise the prospect of being in a transition status near the class boundaries where membership becomes fuzzy (Negoita, 1981). Deciding on which reference group to use for such persons (whether mobile or not) is not always clear.

²³As is doubtless apparent at this juncture, the same context-oriented criticisms can also be applied directly to such well-known SES measures as the Blishen scale, the Pineo-Porter scale and the Hollingshead-Redlich index. Intriguingly Blishen and Carroll (1978) discussed such contextual anomalies but did not interpret their findings in the light of the theoretical matters discussed above.

²⁴A polymorphic definition would allow SC to be defined for intra-group, individual to group, group to population and any other combination of reference groups. The definitions will obviously have slight operational and calculation differences but will still be recognizably the same overarching concept.

²⁵An example of complex and scalar addition using polymorphic operators is used to represent symbolically that adding two complex numbers and adding two scalar numbers would appear the same.

²⁶Some societies have far different attitudes to walls than others. Contrast the North American and Japanese notions to walls that keep strangers out and walls inside the home itself.

²⁷The author hopes the folly known as postmodernism is well enough understood that this comment is not taken as an endorsement of social relativism.

²⁸Sociology has several examples of unawareness of relevant work done in closely related fields. Shrauger and Schoenman (1979) published a devastating critique of symbolic interactionism. Israel Scheffler (1967) produced an equally savage attack on the work of the late Thomas S. Kuhn.

²⁹This makes the distinction of ascribed and achieved status important. Individuals can only experience mobility with reference to their ascribed status attributes as a result of changes of macrosocial proportions. For example, one cannot change one's sex or race but the status implications of possessing a particular ranking in either of these dimensions can clearly change its consequences.

³⁰Education is probably the central or pivotal variable here since it is the most rooted in achievement of the three. It might be desirable to attempt to define an 'expected status' as a fuzzy set of values for occupation-income pairs inside the range made socially legitimate by the given education level. We note, too, that education has two major kinds of degrees: occupationally specific (like engineering degrees) and occupationally diffuse (such as BA with a concertation in Victorian Poetry) which may complicate the actual perception of 'incongruence' by the person with these particular qualifications. Since education is a socializing factor it might also make people respond differently to the apparent choices life gives them.

³¹Using differentials would also allow for:

[11-a]

d''W/dt = acceleration of the rate of mobility

and similar expressions. Whether or not they would have any empirical utility can only be surmized at this time but the option to investigate this feature is now present.

³²Phrased in this way we also are invited to address directly the task of trying to tease out the subjective and objective aspects of perception.

³³This century the West has, for example, apparently prized those who have high IQs (Hernnstein and Murray, 1994) but some other contemporary authors (Goleman, 1995) hold that 'emotional intelligence' may be of equal value for attaining wealth and power at present.

Corrections

Following correspondence between the author and Gerhard Lenski, the following corrections were made:

¶2.4, ¶2.5, ¶3.6, ¶3.12 The fourth of the Lensk's original variables was reported as Residence. This has been replaced with the corrected variable Race/Ethnicity.

¶3.6 Lenski's 'Status Dimension Type' now reads both rather than achieved only.

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