A study of power and type I error rate to the likelihood ratio statistics in IRT.

In this report we studied the power land the type I error rate) of the like lihood ratio statistic used in BILOG (v. 3.04) to prove de fit of the model to the items. For this, we used a test size fixed (75 items) and four samp le sizes (100, 250, 500 and 1000). Further, we used three ability distribut ions: one centered N(0,l) and another two noncentered: N(-1,1) and N(1,1). We also manipulated the mean discrimination in 25 of 75 items in six condit ions (.3, .6, 1.0, 1.2, 1.5 and 1.8). The results showed that the power of the likelihood ratio statistic is low when the sample size was 100, althoug h the discrimination parameter was .3 or 1.8. The power increased with the sample size, although this statistic cannot detect items that not follow th e I-p model, independently if the discrimination parameter was 1.0, 1.2 or 1.5. Finally, the type I error rate adjusted to the nominal levels, except when the sample size was high.