Using Heterogeneous Choice Models to Compare Logit and Probit Coefficients Across Groups

Abstract

Allison (1999) notes that comparisons of logit and probit coefficients across groups can be invalid and misleading, proposes a procedure by which these problems can be corrected, and argues that ``routine use [of this method] seems advisable'' and that ``it is hard to see how [the method] can be improved.'' In this article, the author argues that as originally proposed, Allison's method can have serious problems and should not be applied on a routine basis. However, this study also shows that his model belongs to a larger class of models variously known as heterogeneous choice or location-scale models. Several advantages of this broader and more flexible class of models are illustrated. Dependent variables can be ordinal in addition to binary, sources of heterogeneity can be better modeled and controlled for, and insights can be gained into the effects of group characteristics on outcomes that would be missed by other methods.

Arbeitsmarktflexibilisierung und Ungleichheit: Der Wandel der Risikomuster befristeter Beschäftigung in Westdeutschland

“…Likewise, it is possible that estimated coefficients remain stable over time although the true values have changed and this has been countervailed by changing residual variation. In contrast to standard logit models, heterogeneous choice models assume that the error variance varies systematically (for an overview, see Keele and Park 2006;Williams 2007). The variance component in heterogeneous choice models is modelled parametrically as…”

Born in the USA: a comparison of modals and nominal quantifiers in child language

“…In fact, a large value of the χ -square and a small p-value tell us that homoscedasticity cannot be assumed; see Breusch and Pagan (1979). Comparisons of effects across groups can be much more treacherous with logit than with standard linear regressions, (see Williams 2009), especially in the presence of heteroscedasticity. For this reason, since we are primarily interested in determining the effects of the variable Operator on the Answers, it is preferable to estimate separate models for the separate groups in order to avoid wrong parameter estimates.…”

Coverage of financing deficit in firms in financial distress under the pecking order theory

“…In the fi rst analysis, the System GMM methodology of panel data is used, which enables controlling for the model's individual heterogeneity and the existence of potential problems of endogeneity. Subsequently, in the study of the probability of issuing equity, we use, for the fi rst time in this kind of studies, a new Heterogeneous Choice Models (HCM) methodology developed by Williams (2009) applied to a logistic function. This methodology allows us to avoid the bias caused by the differences in the degree of residual variation between healthy fi rms and fi rms in fi nancial distress.…”

“…However, the inclusion of two groups of fi rms (healthy and distressed) makes it very probable that the homoscedasticity of random errors will not be fulfi lled because of the existence of differences in the degree of residual variation between both groups of fi rms. Unlike linear models, in non-linear models this fact gives rise to signifi cant biases in the estimation of the model parameters (Yatchew & Griliches, 1985). To overcome this problem in the current study, we performed an analysis using the Heterogeneous Choice Models (HCM) applied to a logistic function.…”

“…To overcome this problem in the current study, we performed an analysis using the Heterogeneous Choice Models (HCM) applied to a logistic function. These models control for the differences in the random error variance between the groups, which allows avoiding the biases in the estimations (Williams, 2009). The proposed model is as follows: (8) where Λ (.)…”