The effect of partial measurement invariance on prediction
Donahue, Barbara Hayes
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In education it is common to make judgments about the progress or achievement of different groups of students; it is also common to compare the mean scores of different groups and make predictions about individuals within groups. Thus, it is important to understand how underlying measurement differences, if any, affect such predictions and comparisons. Under partial measurement invariance, some model parameters are invariant while others are allowed to vary across groups. This allows the use of a scale in which there may be some difference in measurement between the groups, while still considering the overall comparison to be meaningful. The purpose of this study is to investigate the amount of partial measurement noninvariance that can be tolerated while still allowing for comparable predictions across groups. Specifically, varying degrees of size of factor loadings, model size, sample size, amount of partial measurement invariance, factor loading differences across groups, and differing levels of predictive influence across groups were examined from the standpoint of their effects on power and accuracy in prediction. The results for partial measurement invariance suggest that level of noninvariance and factor loading differences affect goodness of fit indices while the size of the factor loading has more of an effect on parameter estimates and bias. It appears that model size affects all of the dependent variables presented here.