Gain Score in Item Response Theory as an Effect Size Measure

Abstract

Because of the requirement of reporting effect sizes and in the interest of measurement of change within the item response theory framework, their combination becomes a new issue. In the present study, repeated measures are decomposed as an initial ability and one or more modifiabilities (gain score) using a multidimensional Rasch model. The modifiability can be directly interpreted in terms of logit scale. The standardized mean modifiability is recommended for meta-analysis when test equating is not possible across studies. A simulation study was conducted to assess parameter recovery. It appeared that the point estimates were accurate whereas the error variances were underestimated. The bootstrap method was used and found appropriate for estimating the error variances. Implications and applications are illustrated through an empirical example.

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