What is the mixed models controversy ? : reply to J . A . Nelder Viviana

We begin by apologizing for the lamentable omission of Professor Nelder’s interesting and controversial papers both in Lencina, Singer and Stanek (2005) and in Lencina and Singer (2006). Although the focus of our papers is much narrower than that of his articles, we feel that any manuscript touching the topic of parametrization and definition of hypotheses in linear mixed models should necessarily refer to his numerous contributions to this field. Essentially, we compare two stochastic models [one with constrained parameters, denoted CP and the other with unconstrained parameters, denoted UP by Voss (1999)] that are extensively employed to analyze data from balanced experiments with a fixed and a random factor. The two models generate different test statistics presumably directed at the same hypothesis, namely that of the nonexistence of the random factor main effect in the presence of the interaction. Differing opinions over which statistic should be used is what we call the “mixed model controversy” following Voss (1999). Our objective is to provide an answer to this very specific question. To retain this focus, we do not discuss the general issue of model building or add to a debate over the reasonableness of the hypothesis under investigation. We explicitly state this in the abstract of Lencina, Singer and Stanek (2005).