Modeling continuous, skewed and heteroscedastic outcomes in psychology: Is generalized modeling the best 'fit'?

Some researchers in psychology have ordinarily relied on traditional linear models when assessing the relationship between predictor(s) and a continuous outcome, even when the assumptions of the traditional model (e.g., normality, homoscedasticity) are not satisfied. Of those who abandon the traditional linear model, some opt for robust versions of the ANOVA and regression statistics that usually focus on relationships for the typical or average case instead of trying to model relationships for the full range of relevant cases. Generalized linear models, on the other hand, model the relationships among variables using all available and relevant data and can be appropriate under certain conditions of non-normality and heteroscedasticity. In this paper, we summarize the advantages and limitations of using generalized linear models with continuous outcomes and provide two simplified examples that highlight the methodology involved in selecting, comparing, and interpreting models for positively skewed outcomes and certain heteroscedastic relationships.