Fallacies and Paradoxes Caused by Heterogeneity

Sociological model building has made great advances during the last decades. Developing their own models as well as borrowing models from statistics, econometrics, psychometrics and biometry, sociological methodologists have been able to solve several long standing problems. Examples are: the treatment of dichotomous, ordinal and unordered categorical dependent variables using threshold and random utility maximization models such as dichotomous, ordinal and multinomial logit and probit models (Daganzo, 1979; McFadden, 1981; Maddala, 1983). These may be extended to model event histories with transition probabilities in discrete time (Allison, 1982; Arminger, 1984; Hamerle, 1985).the analysis of count data using loglinear models, which is especially useful for the analysis of contingency tables (McCullagh and Nelder, 1983).more generally, the analysis of dependent variables belonging to the exponential family using generalized linear models (McCullagh and Nelder, 1983).the treatment of event histories in continuous time and discrete state space with transition rate models (Tuma and Hannan, 1984; Heckman and Singer, 1984a, 1984b).the simultaneous estimation of factor analytic and structural equation models for metric observed variables, often carried out with the LISREL program (Jøreskog and Sørbom 1984), which has been extended by Muthén (1984) using normal distribution theory to include dichotomous and ordinal observed variables.