Relating Violations of Measurement Invariance to Group Differences in Response Times

Measurement invariance is an assumption underlying the regression of a latent variable on a background variable. It requires the measurement model parameters of the latent variable to be equal across the levels of the background variable. Item-specific violations of this assumption are referred to as differential item functioning and are ideally substantively explainable to warrant theoretically valid and meaningful results. Past research has focused on developing statistical approaches to explain differential item functioning effects in terms of item- or person-specific covariates. In this study, we propose a modeling approach that can be used to test if differences in item response times can be used to statistically explain differential item functioning. To this end, we operationalize a latent response process factor and test if item-specific group differences on this factor can account for the observed differences in item scores. We investigate the properties of the model in a simulation study, and we apply the model to a real data set.