The Effect of Ability Estimation Method and Sample Size on the Percentages of Model Misfitting Response Patterns and Distributions Characteristics of Person-fit Indices on Mixed-Format Tests

Abstract

This study aimed to detect the effect of the ability estimation method and sample size on the distributions characteristics of person-fit indices l_z(MIX) and l^*_z(MIX) and the percentages of the misfitting response patterns detected by these two indices in mixed-form tests. To achieve the purpose of the study, the researchers choose random samples (1000, 2000, 5000) of eighth grade students who responded to the mathematics items in the first booklet of the international TIMSS test 2015. The researchers also used three methods for estimating student’s ability (MAP, WLE, MLE). The results of the study showed that the percentages of misfitting response patterns for the two indices increase and the distribution of the two indices is close to a normal distribution when using the WLE method for ability estimation in the different study samples. The results of the study also showed that the percentages of misfitting response patterns for the two indices increase and the distribution of the two indices is close to a normal distribution by increasing the sample size in different ability estimation methods. The percentages of misfitting patterns detected by the index l^*_z(MIX) was higher than those detected by the l_z(MIX) index, and that the distribution of the l_z(MIX) index was closer to the normal distribution than the l_z(MIX) index in different methods for estimating ability and in all samples.

In light of the findings of the study, the researchers recommended using the l^*_z(MIX) index and the WLE method for ability estimation to detect misfitting response patterns in mixed-format tests.

DOI: 10.33977/1182-011-030-004