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Average Effects Based on Regressions with a Logarithmic Link Function: A New Approach with Stochastic Covariates

Published online by Cambridge University Press:  01 January 2025

Christoph Kiefer Open the ORCID record for Christoph Kiefer [Opens in a new window]  and
Axel Mayer Open the ORCID record for Axel Mayer [Opens in a new window]
Christoph Kiefer*
Affiliation:
RWTH Aachen University
Axel Mayer
Affiliation:
RWTH Aachen University
*
Correspondence should be made to Christoph Kiefer, Institute of Psychology, RWTHAachen University, Jägerstraße 17/19, 52066 Aachen, Germany. Email: [email protected]
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Abstract

Researchers often use regressions with a logarithmic link function to evaluate the effects of a treatment on a count variable. In order to judge the average effectiveness of the treatment on the original count scale, they compute average treatment effects, which are defined as the average difference between the expected outcomes under treatment and under control. Current practice is to evaluate the expected differences at every observation and use the sample mean of these differences as a point estimate of the average effect. The standard error for this average effect estimate is based on the implicit assumption that covariate values are fixed, i.e., do not vary across different samples. In this paper, we present a new way of analytically computing average effects based on regressions with log link using stochastic covariates and develop new formulas to obtain standard errors for the average effect. In a simulation study, we evaluate the statistical performance of our new estimator and compare it with the traditional approach. Our findings suggest that the new approach gives unbiased effect estimates and standard errors and outperforms the traditional approach when strong interaction and/or a skewed covariate is present.

Keywords

negative binomial regression modelaverage treatment effectsstochastic covariatescount data
Type
Original Paper
Information
Psychometrika , Volume 84 , Issue 2 , June 2019 , pp. 422 - 446
Copyright
Copyright © 2019 The Psychometric Society

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Footnotes

Electronic supplementary material The online version of this article (https://doi.org/10.1007/s11336-018-09654-1) contains supplementary material, which is available to authorized users.

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