The effects on parameter estimation of sample size ratio, test length and trait correlation in a two-dimensional, two-parameter, compensatory item response model with dichotomous scoring
Popp, Eric Carter
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This study used a monte carlo simulation to determine the influence of sample size ratio, test length and trait correlation on obtaining quality parameter estimates for a two-dimensional, two- parameter, compensatory item response model with dichotomous scoring. The study found that the quality of parameter estimates dropped sharply at low levels of sample size ratio and test length. The drop was greater when the traits were correlated. Generally, sample size ratio was the biggest influence on the quality of parameter estimates with it uniquely accounting for up to 87% of the variance observed. Test length was the second largest influence with the percentage variance accounted for being in the mid teens. However, for bias of discrimination parameters trait correlation was the largest influence accounting for up to 60% of the variance. The influence of sample size ratio, test length and trait correlation varied across item difficulty and discrimination levels. To aid the test developer in determining where the drop in parameter estimate quality occurs, tables were compiled providing the ratio of variance, root mean square error, and bias to average parameter level for various combinations of sample size ratio, test length and trait correlation. Similar tables listing the correlation of parameter estimates with true parameters were also compiled.