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Introducing a Disturbance into Logit and Probit Regression Models

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  • PAUL D. ALLISON

    (University of Pennsylvania)

Abstract

Logit and probit regression models for dichotomous data make no explicit allowance for heterogeneity induced by omitted explanatory variables or by random fluctuations. This article considers several alternative models for incorporating heterogeneity by the inclusion of a disturbance term. When all the observations are independent, the presence of the disturbance has few empirical consequences. In particular, the variance of the observed counts does not increase and conventional estimators are still appropriate. For some models, however, the disturbance variance may invalidate cross-population comparisons. Quite different implications arise with grouped data when there is a single realization of the disturbance for each group. The observed variance is increased and conventional estimators are inefficient. Several alternative estimators are considered.

Suggested Citation

  • Paul D. Allison, 1987. "Introducing a Disturbance into Logit and Probit Regression Models," Sociological Methods & Research, , vol. 15(4), pages 355-374, May.
  • Handle: RePEc:sae:somere:v:15:y:1987:i:4:p:355-374
    DOI: 10.1177/0049124187015004001
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    4. D. A. Williams, 1982. "Extra‐Binomial Variation in Logistic Linear Models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 31(2), pages 144-148, June.
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