On regression modelling with dummy variables versus separate regressions per group: comment on Holgersson et al

In a recent issue of this journal, Holgersson etal. [Dummy variables vs. category-wise models, J. Appl. Stat. 41(2) (2014), pp. 233-241, doi:10.1080/02664763.2013.838665] compared the use of dummy coding in regression analysis to the use of category-wise models (i.e. estimating separate regression models for each group) with respect to estimating and testing group differences in intercept and in slope. They presented three objections against the use of dummy variables in a single regression equation, which could be overcome by the category-wise approach. In this note, I first comment on each of these three objections and next draw attention to some other issues in comparing these two approaches. This commentary further clarifies the differences and similarities between dummy variable and category-wise approaches.