Response Time Modeling Based on the Proportional Hazards Model

Abstract

Response time data are regularly analyzed in psychology. When several response times are assessed per participant, it is common practice to use latent trait models in order to account for the dependency of the response times from the same participant. One such model is the proportional hazards model with random effects. Despite its popularity in survival analysis, this model is rarely used in psychology because of the difficulty of model estimation when latent variables are present. In this article, a new estimation method is proposed. This method is based on the rank correlation matrix containing Kendall's Tau coefficients and unweighted least squares estimation (Kendall, 1938). Compared with marginal maximum likelihood estimation, the new estimation approach is simple, not computationally intensive, and almost as efficient. Additionally, the approach allows the implementation of a test for model fit. Feasibility of the estimation method and validity of the fit test is demonstrated with a simulation study. An application of the model to a real data set is provided.

Notes

Note. θ = true value of work pace; M = average estimate over replications; SE = standard error of estimation; P = coverage rate of 95% confidence intervals. Results are based on 500 replications.