ERIC Number: EJ1278785
Record Type: Journal
Publication Date: 2020
Pages: 27
Abstractor: As Provided
ISBN: N/A
ISSN: ISSN-1536-6367
EISSN: N/A
Estimation of Mixture Rasch Models from Skewed Latent Ability Distributions
Measurement: Interdisciplinary Research and Perspectives, v18 n4 p215-241 2020
Mixture Rasch (MixRasch) models conventionally assume normal distributions for latent ability. Previous research has shown that the assumption of normality is often unmet in educational and psychological measurement. When normality is assumed, asymmetry in the actual latent ability distribution has been shown to result in extraction of spurious latent classes in MixRasch models. In this study, the assumption of a skew-t distribution for the latent ability was examined for its effect on reducing extraction of spurious latent classes. A simulation study was conducted with eight different latent ability distributions with varying levels of skewness and kurtosis, two sample sizes (600 and 2,000), and two test lengths (10-item and 30-item). Results showed that the 30-item test but not the 10-item test were robust to extraction of spurious latent classes independent of the sample size or the shape of the ability distribution. Use of a skew-t prior, on the other hand, reduced spurious latent class extraction for the 10-item test, particularly for the sample size of 2,000 for high levels of skewness compared to use of a normal prior. Thus, a skew-t prior was useful for reducing spurious latent class extraction for short tests, although it did not improve item parameter estimation compared to a normal prior.
Descriptors: Item Response Theory, Ability, Statistical Distributions, Sample Size, Test Length, Statistical Analysis, Foreign Countries, Achievement Tests, Secondary School Students, International Assessment, Mathematics Tests
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Publication Type: Journal Articles; Reports - Research
Education Level: Secondary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Identifiers - Location: Peru; Indonesia; Qatar; Colombia; Jordan
Identifiers - Assessments and Surveys: Program for International Student Assessment
Grant or Contract Numbers: N/A