Statistical Methods for Analyzing Collapsibility in Regression Models

Clifford C. Clogg, Eva Petkova and Edward S. Shihadeh

Journal of Educational and Behavioral Statistics, 1992, vol. 17, issue 1, 51-74

Abstract: We give a unified treatment of statistical methods for assessing collapsibility in regression problems, including some possible extensions to the class of generalized linear models. Terminology is borrowed from the contingency table area where various methods for assessing collapsibility have been proposed. Our procedures, however, can be motivated by considering extensions, and alternative derivations, of common procedures for omitted-variable bias in linear regression. Exact tests and interval estimates with optimal properties are available for linear regression with normal errors, and asymptotic procedures follow for models with estimated weights. The methods given here can be used to compare β 1 and β 2 in the common setting where the response function is first modeled as X β 1 (reduced model) and then as X β 2 + Zγ (full model), with Z a vector of covariates omitted from the reduced model. These procedures can be used in experimental settings ( X = randomly asigned treatments, Z = covariates) or in nonexperimental settings where two models viewed as alternative behavioral or structural explanations are compared (one model with X only, another model with X and Z ).

Keywords: omitted-variable bias; nested models; generalized linear model (search for similar items in EconPapers)
Date: 1992
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Persistent link: https://EconPapers.repec.org/RePEc:sae:jedbes:v:17:y:1992:i:1:p:51-74

DOI: 10.3102/10769986017001051

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