Copyright Sociological Research Online, 1996
|Terms in the Equation||Conditions of the Model|
X1 = Occupation
X2 = Income
X3 = Education
X4 = Race/Ethnicity (dropped in the 1956 paper)
XMi = Sample Mean for the specific Xi|
* While not made explicit by Lenski, this assumption will be important later
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
and recalled Hope's definition of SC as
and clearly if X1 = X2 then T1 = T2 = 0.
X1 = Education, X2 = Occupation, X3 = Religion
|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|
|Wilson and Zurcher (1978)||Race, Income, Education, Occupation||both||nominal and interval||sample||sample||static||multiplicative interaction|
|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|
|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.
|Source of Equation or Model||Operational Model or Equation|
|Blalock (1964)||Y' = aX1 + bX2 + cX3 + dX4|
|Jackson and Curtis (1972)||Y' = aX1 + bX2 + cX3 + dX1.X2.X3|
|Hartmann (1974)||SC = fsc1z1 + fsc2z + ... + fscnzn|
|Hope (1975)||Y' = a(X1 + X2) + b(X1 - X2)|
|Zurcher and Wilson (1979)||Y' = a(STATUS) + b(I - E) + c(I - O) + d(E - O) + e(I - R) + f(O - R) + g(E - R)|
|Whitt (1983)||Y' = aX1 + bX2 + cT1 + dT2|
|Simpson (1985)||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 Ti 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.
|Ecological and Related Fallacies|
|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.
Equation  represents an early Attitude-Behaviour model by Fishbein (1967).
NBi = Normative Belief
B = Behaviour
Mc = Motivation to Comply
RHd = Reinforced Distribution
A = Attitude
Aact= Attitude to the Action
BI = Behavioural Intent
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
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.
CSS0 as a Composite Status Score at time t = 0 then
and would represent, depending on the sign of the term, the rate of status convergence or status divergence.
(another possible redefinition for SC)
(f, g and h are the equations taken from  above).
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:
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.
¶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.
BATES, Frederick L. and PEACOCK, Walter Gillis (1989) 'Conceptualising Social Structure: The Misuse of Classification in Structural Modelling', American Sociological Review, vol. 54, August, pp. 565 - 577.
BENOIT-SMULLYAN, Emile (1944) 'Status, Status Types and Status Interrelations', American Sociological Review, vol. 9, April, pp. 151 - 161.
BERKOWITZ, Stephen D. (editor) (1982) An Introduction to Structural Analysis: The Network Approach. Toronto: Butterworths.
BLALOCK, Hubert M. (1964) 'The Identification Problem and Theory Building: The Case of Status Inconsistency', American Sociological Review, vol. 31, February, pp. 52 - 61.
BLALOCK, Hubert M. (1967) 'Status Inconsistency and Interaction: Some Alternative Models', American Journal of Sociology, vol. 73, pp. 305 - 315.
BLISHEN, Bernard R. and CARROLL, William K. (1978) 'Sex Differences in a Socio-Economic Index for Occupations for Canada', Canadian Review of Sociology and Anthropology, vol. 131, pp. 71 - 79.
BLOCKER, T. Jean and RIEDESEL, Paul L. (1978) 'The Nonconsequences of Objective and Subjective Status Inconsistency: Requiem for a Moribund Concept', The Sociological Quarterly, vol. 19, Spring, pp. 332 - 339.
BLUMER, Herbert (1969a) Symbolic Interactionism: Perspective and Method. Berkeley: University of California Press.
BLUMER, Herbert (1969b) 'Social Movements' in Barry McLaughlin (editor) Studies in Social Movements. New York: Free Press.
BROWN, Wayne Curtis, CRETSER, Gary A. and LASSWELL, Thomas E. (1988) 'Measuring Status Inconsistency: More Trouble Than It's Worth?', Sociological Perspectives, vol. 31, no. 2, pp. 213 - 237.
CHOMSKY, Noam (1965) Aspects of the Theory of Syntax. Cambridge, Mass: The MIT Press.
CONVERSE, Jean M. and PRESSER, Stanley (1986) Survey Questions: Handcrafting the Standard Questionnaire: #63 in the Quantitative Applications in the Social Sciences Series. Beverly Hills: Sage.
DUMONT, Louis (translated by Mark Sainsbury, Louis Dumont and Basia Gulati) (1980)  Homo Hierarchicus: The Caste System and Its Implications. Chicago: University of Chicago Press.
GALTUNG, Johan (1976) 'Social Position and the Image of the Future' in H. Ornauer, H. Wiberg, A. Sicinski and J. Galtung (editors) Images of the World in the Year (2000): A Comparative Ten-Nation Study. Mouton-The Hague-Paris: Humanities Press.
GOLEMAN, Daniel (1995) Emotional Intelligence: Why It Can Matter More Than IQ. New York: Bantam.
HARTMANN, Moshe (1974) 'On the Definition of Status Inconsistency', American Journal of Sociology, vol. 80, no. 3, pp. 706 - 721.
HAWKES, Glenn, R., GUAGNANO, Gregory A., ACREDOLO, Curt and HEMLICK, Sandra A. (1984) 'Status Inconsistency and Job Satisfaction: General Population and Mexican-American Subpopulation Analyses', Sociology and Social Research, vol. 68, no. 3, pp. 379 - 389.
HERNNSTEIN, Richard T. and MURRAY, Charles (1994) The Bell Curve: Intelligence and Class Structure in American Life. New York: Free Press.
HOLLINGSHEAD, August de Belmont and REDLICH, Frederick C. (1958) Social Class and Mental Illness. New York: John Wiley and Sons.
HOLMES, Malcolm D. and BUTLER, John Sibley (1987) 'Status Inconsistency, Racial Separation, and Job Satisfaction: A Case Study of the Military', Sociological Perspectives, vol. 30, no. 2, pp. 201 - 224.
HOPE, Keith (1975) 'Models of Status Inconsistency and Social Mobility Effects', American Sociological Review, vol. 40, June, pp. 322 - 343.
HORNUNG, Carlton A. (1977) 'Social Status, Status Inconsistency and Psychological Stress', American Sociological Review, vol. 42, August, pp. 623 - 638.
HOUSE, James S. (1978) 'Facets and Flaws of Hope's Diamond Model', American Sociological Review, vol. 43, no. 1, pp. 439 - 442
HSU, Francis Ling Kwang (1967) Under the Ancestors' Shadows: Kinship, Personality and Social Mobility in Village China. Garden City NY: Anchor.
JACKSON, Elton F. and CURTIS, Richard F. (1972) 'Effects of Vertical Mobility and Status Inconsistency: A Body of Negative Evidence', American Sociological Review, vol. 37 December, pp. 701 - 713.
KERSCHKE-RISCH, Pamela (1990) 'Statuskonsistenz: Ein neuer Ansatz fur eine alte Theorie', Zeitschrift fur Soziologie, vol. 19, no. 3, pp. 195 - 202.
KOLENDA, Pauline (1981) Caste, Cult and Hierarchy: Essays on the Culture of India. New Dehli: Meerut Folklore Institute.
LENSKI, Gerhard E. (1954) 'Status Crystallization: A Non-Vertical Dimension of Social Status', American Sociological Review, vol. 19, August, pp. 405 - 413.
LENSKI, Gerhard E. (1956) 'Social Participation and Status Crystallization', American Sociological Review, vol. 21, August, pp. 458 - 464.
LENSKI, Gerhard E. (1964) 'Comment', Public Opinion Quarterly, vol. 28, Summer, pp. 326 - 330.
McNEILL, Daniel and FREIBERGER, Paul (1993) Fuzzy Logic: The Discovery of a Revolutionary Computer Technology and how it is Changing Our World. New York: Simon and Schuster.
NAKANE, Chie (1970) Japanese Society. Berkeley: University of California Press.
NEGOITA, Constantin Virgil (1981) Fuzzy Systems. Tunbridge Wells: Abacus Press.
ORTEGA, S. T. and RUSHING, W. A. (1983) 'Interpretation of the Relationship Between Socio-Economic Status and Mental Disorder: A Question of the Measure of Mental Disorder and a Question of the Measure of SES', Research in Community and Mental Health, vol. 3, pp. 141 - 161.
POWERS, Mary G. (editor) (1982) Measures of Socioecnomic Status: Current Issues. Boulder, CO: American Academy for the Advancement of Science.
ROBERTSON, Robin and COMBS, Allan (editors) (1995) Chaos Theory in Psychology and the Life Sciences. Mahwah, N.J.: Lawrence Erlbaum Associates.
SCHEFFLER, Israel (1967) Science and Subjectivity. Indianapolis: Bobbs-Merrill.
SCHRUM, Wesley (1990) 'Status Incongruence Among Boundary Spanners: Structure, Exchange and Conflict', American Sociological Review, vol. 55, August, pp. 496 - 511
SHRAUGER, J.S. and SCHOENMAN, T.J. (1979) 'Symbolic Interactionist View of the Self-Concept: Through the Looking-Glass Darkly', Psychological Bulletin, vol. 86, pp. 549 - 573.
SIMPSON, John H. (1985) 'Status Inconsistency and Moral Issues', Journal for the Scientific Study of Religion, vol. 24, no. 2, pp. 155 - 162.
Smith, R. David (1995) 'Social Engineering in the Post- Modern World: Chaos Theory, Social Legitimacy and Public Policy' in A. Albert (editor) Chaos and Society. Amsterdam: IOS Press.
SMITH, R. David (1996) 'Social Structures and Chaos Theory', paper given at Essex '96 Fourth International Social Science Methodology Conference, July 1 - 5, Institute for the Social Sciences, University of Essex, Colchester, UK.
SOUTHWOOD, Kenneth E. (1978) 'Substantive Theory and Statistical Interaction: Five Models', American Journal of Sociology, vol. 83, no. 5, pp. 1154 - 1203.
WATKIN, David (1977) Morality and Architecture. Chicago: University of Chicago Press.
WEBER, Max (edited and translated by Guenther Roth and Claus Wittich) (1978) Economy and Society: An Outline of Interpretative Sociology. Berkeley: University of California Press.
WHITT, Hugh P. (1983) 'Status Inconsistency: A Body of Negative Evidence or a Statistical Artefact?', Social Forces, vol. 62, no. 1, pp. 201 - 233.
WILSON, Kenneth L. (1979) 'Status Inconsistency and the Hope Technique, I: The Grounds for Resurrection', Social Forces, vol. 57, no. 4, pp. 1229 - 1247.
WILSON, Kenneth L. and ZURCHER, Louis A. (1978) 'Status Inconsistency Revisited: An Application of Hope's Analytic Model', Sociological Symposium, vol. 24, Fall, pp. 1 - 26.
WRIGHT, Eric Olin and PERRONE, Luca (1977) 'Marxist Class Categories and Income Inequality', American Sociological Review, vol. 42, no. 1, pp. 32 - 55.
ZIMMERMAN, Ekkart (1978) 'Bringing Common Sense Back In: Some Neglected Assumptions in Status Inconsistency Theory', Archives Europeennes de Sociologie, vol. 19, no. 1, pp. 53 - 73.
ZURCHER, Louis A. and WILSON, Kenneth L. (1979) 'Status Inconsistency and the Hope Technique, II: A Linear Hypothesis About Status Enhancement, Status Detraction, and Satisfaction with Membership', Social Forces, vol. 57, no. 4, pp. 1248 - 1267.