Comparing Regression Coefficients Between Models using Logit and Probit: A New Method

Karlson, K.B., Holm, A., & Breen, R. 2012. Comparing Regression Coefficients Between Same-sample Nested Models Using Logit and Probit: A New Method. Sociological Methodology 42.

Posted: 20 Jul 2009 Last revised: 23 Nov 2012

See all articles by Kristian Bernt Karlson

Kristian Bernt Karlson

SFI - The Danish National Centre for Social Research; Department of Education, Aarhus University

Anders Holm

Aarhus University

Richard Breen

Yale University

Date Written: August 12, 2010

Abstract

Logit and probit models are widely used in empirical sociological research. However, the widespread practice of comparing the coefficients of a given variable across differently specified models does not warrant the same interpretation in logits and probits as in linear regression. Unlike in linear models, the change in the coefficient of the variable of interest cannot be straightforwardly attributed to the inclusion of confounding variables. The reason for this is that the variance of the underlying latent variable is not identified and will differ between models. We refer to this as the problem of rescaling. We propose a solution that allows researchers to assess the influence of confounding relative to the influence of rescaling, and we develop a test statistic that allows researchers to assess the statistical significance of both confounding and rescaling. We also show why y-standardized coefficients and average partial effects are not suitable for comparing coefficients across models. We present examples of the application of our method using simulated data and data from the National Educational Longitudinal Survey.

Keywords: logit, probit, logistic regression, scaling, confounding, statistical control, mediation

JEL Classification: C25

Suggested Citation

Karlson, Kristian Bernt and Holm, Anders and Breen, Richard, Comparing Regression Coefficients Between Models using Logit and Probit: A New Method (August 12, 2010). Karlson, K.B., Holm, A., & Breen, R. 2012. Comparing Regression Coefficients Between Same-sample Nested Models Using Logit and Probit: A New Method. Sociological Methodology 42., Available at SSRN: https://ssrn.com/abstract=1436349

Kristian Bernt Karlson (Contact Author)

SFI - The Danish National Centre for Social Research ( email )

Herluf Trolles Gade 11
DK-1052
Copenhagen K, DK-1052
Denmark

HOME PAGE: http://www.sfi.dk

Department of Education, Aarhus University ( email )

Tuborgvej 164
Copenhagen NV, DK-2400
Denmark

HOME PAGE: http://www.au.dk

Anders Holm

Aarhus University ( email )

Turborgvej 164
Copenhagen, Copenhagen 2400
Denmark
88889960 (Phone)

HOME PAGE: http://www.dpu.dk

Richard Breen

Yale University ( email )

493 College St
New Haven, CT CT 06520
United States

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