A novel method for modelling interaction between categorical variables

Contains fulltext : 168867.pdf (publisher's version ) (Open Access)Sweeney and Ulveling (1972) introduced weighted effect coding, where the estimates for categories of nominal and ordinal variables are deviations from the arithmetic mean, typically from a sample. This somewhat neglected parameterization is preferred over the well-known effect coding (ANOVA) if the data are unbalanced (i.e., when categories hold different numbers of observations) and was recently revived in this journal (te Grotenhuis et al. 2016). In this paper, we show that weighted effect coding can also be applied to regression models with interaction effects. The weighted effect coded interactions represent the additional effects over and above the main effects obtained from the model without these interactions. This is a useful alternative to effect coding when the data are unbalanced as in most observational data. In this contribution, we describe this novel parameterization and provide syntax, data, and examples in SPSS, R, and Stata on http://www.ru.nl/sociology/mt/wec/downloads. For didactical reasons we apply OLS regression models, but weighted effect coded interactions can be used in any generalized linear model. Throughout this text we use the word 'interaction', while other researchers prefer 'moderation'.5 p