Balancing Type I error and power in linear mixed models

Mixed-effect models are frequently used to control for the nonindependence of data points, for example, when repeated measures from the same individuals are available. The aim of these models is often to estimate fixed effects and to test their significance. This is usually done by including random intercepts, that is, intercepts that are allowed to vary between individuals. The widespread belief is that this controls for all types of pseudoreplication within individuals. Here we show that this is not the case, if the aim is to estimate effects that vary within individuals and individuals differ in their response to these effects. In these cases, random intercept models give overconfident estimates leading to conclusions that are not supported by the data. By allowing individuals to differ in the slopes of their responses, it is possible to account for the nonindependence of data points that pseudoreplicate slope information. Such random slope models give appropriate standard errors and are easily implemented in standard statistical software. Because random slope models are not always used where they are essential, we suspect that many published findings have too narrow confidence intervals and a substantially inflated type I error rate. Besides reducing type I errors, random slope models have the potential to reduce residual variance by accounting for between-individual variation in slopes, which makes it easier to detect treatment effects that are applied between individuals, hence reducing type II errors as well.

A general fact about language is that subject relative clauses are easier to process than object relative clauses. Recently, several self-paced reading studies have presented surprising evidence that object relatives in Chinese are easier to process than subject relatives. We carried out three self-paced reading experiments that attempted to replicate these results. Two of our three studies found a subject-relative preference, and the third study found an object-relative advantage. Using a random effects bayesian meta-analysis of fifteen studies (including our own), we show that the overall current evidence for the subject-relative advantage is quite strong (approximate posterior probability of a subject-relative advantage given the data: 78–80%). We argue that retrieval/integration based accounts would have difficulty explaining all three experimental results. These findings are important because they narrow the theoretical space by limiting the role of an important class of explanation—retrieval/integration cost—at least for relative clause processing in Chinese.

According to the principle of parsimony, model selection methods should value both descriptive accuracy and simplicity. Here we focus primarily on Bayes factors and minimum description length, explaining how these procedures strike a balance between goodness-of-fit and parsimony. Throughout, we demonstrate the methods with an application on false memory, evaluating three competing multimonial proces tree models of interference in memory.