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It is widely believed that a joint factor analysis of item responses andresponse time (RT) may yield more precise ability scores that areconventionally predicted from responses only. For this purpose, asimple-structure factor model is often preferred as it only requires specifyingan additional measurement model for item-level RT while leaving the originalitem response theory (IRT) model for responses intact. The added speed factorindicated by item-level RT correlates with the ability factor in the IRT model,allowing RT data to carry additional information about respondents' ability.However, parametric simple-structure factor models are often restrictive andfit poorly to empirical data, which prompts under-confidence in the suitablityof a simple factor structure. In the present paper, we analyze the 2015Programme for International Student Assessment (PISA) mathematics data using asemiparametric simple-structure model. We conclude that a simple factorstructure attains a decent fit after further parametric assumptions in themeasurement model are sufficiently relaxed. Furthermore, our semiparametricmodel implies that the association between latent ability and speed/slowness isstrong in the population, but the form of association is nonlinear. It followsthat scoring based on the fitted model can substantially improve the precisionof ability scores.

What Can We Learn from a Semiparametric Factor Analysis of Item Responses and Response Time? An Illustration with the PISA 2015 Data