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The Stata Journal
Volume 11 Number 3: pp. 420-438

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Comparing coefficients of nested nonlinear probability models

Ulrich Kohler
Wissenschaftszentrum Berlin
Kristian Bernt Karlson
Department of Education
Aarhus University
Anders Holm
Department of Education
Aarhus University
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 nonlinear probability model. It also decomposes effects of both discrete and continuous variables, applies to average partial effects, and provides analytically derived statistical tests. The method can be extended to other models in the generalized linear model family.
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View all articles with these keywords: khb, decomposition, path analysis, total effects, indirect effects, direct effects, logit, probit, primary effects, secondary effects, generalized linear model, KHB method

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