A Comparison of Limited-Information Test Statistics for a Response Style MIRT Model

An increased use of models for measuring response styles is apparent in recent years with the multidimensional nominal response model (MNRM) as one prominent example. Inclusion of latent constructs representing extreme (ERS) or midpoint response style (MRS) often improves model fit according to information criteria. However, a test of absolute model fit is often not reported even though it could comprise an important piece of validity evidence. Limited information test statistics are candidates for this task, including the full ($$), ordinal ($$), and mixed ($$) statistics, which differ in whether additional collapsing of univariate or bivariate contingency tables is conducted. Such collapsing makes sense when item categories are ordinal, which may not hold under the MNRM. More generally, limited information test statistics have gone unevaluated under nominal data and non-ordinal latent trait models. We present a simulation study evaluating the performance of $$ $$ and $$ with the MNRM. Manipulated conditions included sample size, presence and type of response style, and strength of item slopes on substantive and style dimensions. We found that $$ sometimes had inflated Type I error rates, $$ always had little power, and $$ lacked power under some conditions. $$ and $$ may provide complementary and valuable information regarding model fit.