Dummy variables vs. category-wise models

Abstract

Empirical research frequently involves regression analysis with binary categorical variables, which are traditionally handled through dummy explanatory variables. This paper argues that separate category-wise models may provide a more logical and comprehensive tool for analysing data with binary categories. Exploring different aspects of both methods, we contrast the two with a Monte Carlo simulation and an empirical example to provide a practical insight.

Neighbourhood related diversity, human capital and firm innovation

“…To test for differences between different region types as well as sectors, category‐wise models are applied, that is, separate regressions are run for the industrial and the service sector and/or metropolitan, city, and rural regions. According to Holgersson et al (), category‐wise models are preferred to the dummy variable approach since the latter assumes equal variances of the different categories and is in most cases not invariant to the categorical coding.…”

On regression modelling with dummy variables versus separate regressions per group: Comment on Holgerssonet al.

“…However, I wish to point out that the parameters themselves change as a function of this coding scheme. In my opinion, Holgersson et al [11] did not discuss this issue thoroughly enough, although they do mention that "... the model itself is invariant to the coding of zeros and ones ...". In particular, β 0 in model (1.1) is the mean of Y in group 0 for X fixed at 0, whereas β * 0 in (1.2) is the mean of Y in group 1 for X fixed at 0.…”

“…One of the objections raised by Holgersson et al [11] states that the dummy variable approach is not invariant with respect to the coding of zeros and ones and therefore inferences are not invariant with respect to the choice of baseline.…”

“…Furthermore, assume that Y i = E(Y i |X i , D i ) + ϵ i , where the error terms ϵ i are iid N (0, σ 2 ) variables. Model (1.1) allows for interaction (i.e., the slope of X may differ across the two groups) and exemplifies the so-called dummy variable approach [11]. Labeling of the groups is essentially arbitrary, and therefore the regression model…”

“…In [11], models (1.1) and (1.2) were both estimated for a data set by Gujarati [6,7] and it was found that the parameter estimates and their standard errors differ between the two models. The authors therefore concluded that inferences about the parameters are not invariant with respect to the coding scheme (i.e., the choice of baseline).…”