期刊
PSYCHOMETRIKA
卷 -, 期 -, 页码 -出版社
SPRINGER
DOI: 10.1007/s11336-023-09936-3
关键词
factor analysis; item response theory; response time; PISA; cubic splines; copula; penalized maximum likelihood; cross-validation; model fit; local independence; bootstrap
It is believed that a joint factor analysis of item responses and response time (RT) can improve the precision of ability scores. This study analyzed the 2015 Programme for International Student Assessment mathematics data using a semiparametric simple-structure model and found that a simple factor structure can fit the data well under certain assumptions. Furthermore, the study discovered a strong but nonlinear association between latent ability and speed/slowness.
It is widely believed that a joint factor analysis of item responses and response time (RT) may yield more precise ability scores that are conventionally predicted from responses only. For this purpose, a simple-structure factor model is often preferred as it only requires specifying an additional measurement model for item-level RT while leaving the original item response theory (IRT) model for responses intact. The added speed factor indicated 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 and fit poorly to empirical data, which prompts under-confidence in the suitablity of a simple factor structure. In the present paper, we analyze the 2015 Programme for International Student Assessment mathematics data using a semiparametric simple-structure model. We conclude that a simple factor structure attains a decent fit after further parametric assumptions in the measurement model are sufficiently relaxed. Furthermore, our semiparametric model implies that the association between latent ability and speed/slowness is strong in the population, but the form of association is nonlinear. It follows that scoring based on the fitted model can substantially improve the precision of ability scores.
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