Semi‐parametric proportional hazards models with crossed random effects for psychometric response times

Abstract

The semi-parametric proportional hazards model with crossed random effects shares two important characteristics: it avoids explicit specification of the response time distribution by using semi-parametric models, and heterogeneity that is due to subjects and items is captured. The proposed model has a proportionality parameter for the speed of each test taker, for the time intensity of each item, and for subject or item characteristics of interest. It is shown how all these parameters can be estimated by Markov Chain Monte Carlo methods (Gibbs sampling). The performance of the estimation procedure is assessed with simulations and the model is further illustrated with the analysis of response times from a visual recognition task.

A semi‐parametric within‐subject mixture approach to the analyses of responses and response times

“…We adopted a categorized response time model as it is a relatively easy and effective method. However, we note that other semi‐parametric possibilities exist, including the proportional hazards model (Kang, ; Loeys et al ., ; Ranger & Ortner, , ; Wang, Fan, et al ., ) and the linear transformation model (Wang, Chang, et al ., ). An advantage of adopting these models over our model is that they do not rely on arbitrary decision about the number of thresholds Z and the position of the thresholds b zi .…”

“…A key characteristic of this framework is that the responses and response times are independent, conditional on the underlying latent speed and latent ability variables. Various instances and extensions of the general approach have been developed since then, including, for instance, multilevel models (Klein Entink, Fox, & van Der Linden, ), models for different distributions of the response times (Klein Entink, van Der Linden, & Fox, ; Loeys, Legrand, Schettino, & Pourtois, ; Ranger & Kuhn, ; Ranger & Ortner, , ; Wang, Chang, & Douglas, ; Wang, Fan, Chang, & Douglas, ), and models for personality data (Ferrando & Lorenzo‐Seva, ,b). Also, some of the earlier approaches (e.g., Roskam, ; Thissen, ) are special cases.…”

Hidden Markov Item Response Theory Models for Responses and Response Times

“…This measurement model is subsequently connected to the measurement model for the responses. For example, the person and item parameters from both measurement models can be considered as random variables that have a common multivariate normal distribution across the models (Glas and van der Linden, 2010;Klein Entink, Fox, & van der Linden, 2009;Loeys, Legrand, Schettino, & Pourtois, 2014;, 2009a. Other researchers have simplified this model by only assuming a common distribution for the speed and ability variables (Molenaar, Tuerlinckx, & Van der Maas, 2015a;Ranger & Ortner, 2012;Wang, Fan, Chang, and Douglas, 2013).…”

Response Mixture Modeling of Intraindividual Differences in Responses and Response Times to the Hungarian WISC-IV Block Design Test

“…Arguably the most popular approach to the analysis of responses and response times is the so-called hierarchical model of Van der Linden [32,33] (see also [34][35][36][37][38]). In this approach, first, a measurement model is specified for the responses.…”