Models of accuracy in repeated-measures designs

Accuracy is often analyzed using analysis of variance techniques in which the data are assumed to be normally distributed. However, accuracy data are discrete rather than continuous, and proportion correct are constrained to the range 0–1. Monte Carlo simulations are presented illustrating how this can lead to distortions in the pattern of means. An alternative is to analyze accuracy using logistic regression. In this technique, the log odds (or logit) of proportion correct is modeled as a linear function of the factors in the design. In effect, accuracy is rescaled in terms of a logit “response-strength” measure. Because the logit scale is unbounded, it is not susceptible to the same scaling artifacts as proportion correct. However, repeated-measures designs are not readily handled in standard logistic regression. I consider two approaches to analyzing such designs: conditional logistic regression, in which a Rasch model is assumed for the data, and generalized linear mixed-effect analysis, in which quasi-maximum likelihood techniques are used to estimate model parameters. Monte Carlo simulations demonstrate that the latter is superior when effect size varies over subjects.