What Can We Learn from a Semiparametric Factor Analysis of Item Responses and Response Time? An Illustration with the PISA 2015 Data
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866916546076475392 |
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| author | Liu, Yang Wang, Weimeng |
| author_facet | Liu, Yang Wang, Weimeng |
| contents | 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 (PISA) 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_10079 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | What Can We Learn from a Semiparametric Factor Analysis of Item Responses and Response Time? An Illustration with the PISA 2015 Data Liu, Yang Wang, Weimeng Applications 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 (PISA) 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. |
| title | What Can We Learn from a Semiparametric Factor Analysis of Item Responses and Response Time? An Illustration with the PISA 2015 Data |
| topic | Applications |
| url | https://arxiv.org/abs/2303.10079 |