Comparing Coefficients of Nested Nonlinear Probability Models

TLDR: The KHB method as mentioned in this paper is a general decomposition method that is unaffected by the rescaling or attenuation bias that arises in cross-model comparisons in nonlinear models and can be extended to other models in the generalized linear model family.

Abstract: In a series of recent articles, Karlson, Holm, and Breen (Breen, Karlson, and Holm, 2011, http://papers.ssrn.com/sol3/papers.cfm?abstractid=1730065; Karlson and Holm, 2011, Research in Stratification and Social Mobility 29: 221- 237; Karlson, Holm, and Breen, 2010, http://www.yale.edu/ciqle/Breen Scaling %20effects.pdf) have developed a method for comparing the estimated coefficients of two nested nonlinear probability models. In this article, we describe this method and the user-written program khb, which implements the method. The KHB method is a general decomposition method that is unaffected by the rescaling or attenuation bias that arises in cross-model comparisons in nonlinear models. It recovers the degree to which a control variable, Z, mediates or explains the relationship between X and a latent outcome variable, Y ∗ , underlying the nonlin- ear probability model. It also decomposes effects of both discrete and continuous variables, applies to average partial effects, and provides analytically derived sta- tistical tests. The method can be extended to other models in the generalized linear model family.