Analyzing Response Times in Tests With Rank Correlation Approaches

It is common practice to log-transform response times before analyzing them with standard factor analytical methods. However, sometimes the log-transformation is not capable of linearizing the relation between the response times and the latent traits. Therefore, a more general approach to response time analysis is proposed in the current manuscript. The approach is based on the assumption that the response times can be decomposed into a linear function of latent traits and a normally distributed residual term after the response times have been transformed by a monotone, but otherwise unknown transformation function. The proposed model can be fitted by a limited information approach, using the matrix of Kendall's τ coefficients and unweighted least squares estimation. The transformation function can be determined by resorting to discrete time. The proposed approach offers a framework for testing model fit by comparing expected and observed correlations and for investigating the hypothesis about the form of the transformation function. The adequacy of the proposed approaches to model calibration and model validation are investigated in a simulation study. Two real data sets are analyzed as a demonstration of the model's applicability.