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

When size matters: advantages of weighted effect coding in observational studies

Contains fulltext : 166462.pdf (publisher's version ) (Open Access)To include nominal and ordinal variables as predictors in regression models, their categories first have to be transformed into so-called 'dummy variables'. There are many transformations available, and popular is 'dummy coding' in which the estimates represent deviations from a preselected 'reference category'. A way to avoid choosing a reference category is effect coding, where the resulting estimates are deviations from a grand (unweighted) mean. An alternative for effect coding was given by Sweeney and Ulveling in 1972, which provides estimates representing deviations from the sample mean and is especially useful when the data are unbalanced (i.e., categories holding different numbers of observation). Despite its elegancy, this weighted effect coding has been cited only 35 times in the past 40 years, according to Google Scholar citations (more recent references include Hirschberg and Lye 2001 and Gober and Freeman 2005). Furthermore, it did not become a standard option in statistical packages such as SPSS and R. The aim of this paper is to revive weighted effect coding illustrated by recent research on the body mass index (BMI) and to provide easy-to-use syntax for SPSS, R, and Stata on http://www.ru.nl/sociology/mt/wec/downloads. For didactical reasons we apply OLS regression models, but it will be shown that weighted effect coding can be used in any generalized linear model.5 p