FIPC Linking Across Multidimensional Test Forms: Effects of Confounding Difficulty within Dimensions

This study investigated the effects of linking potentially multidimensional test forms using the fixed item parameter calibration. Forms had equal or unequal total test difficulty with and without confounding difficulty. The mean square errors and bias of estimated item and ability parameters were compared across the various confounding tests. The estimated discrimination parameters were influenced by the levels of correlation between dimensions. The mean square errors (MSEs) of the average of the true discrimination parameters with the estimated value were smallest when the correlation equaled 0; however, the MSEs of the multidimensional discrimination parameter were smallest when the correlation was larger than 0. The estimated difficulty parameters were highly affected by different amount of confounding difficulty within dimensions. Furthermore, the MSEs of the average of the true ability parameters on the first and second dimensions with the estimated ability were smaller than those from the ability parameter on each dimension for all conditions. The pattern varied according to the number of common items, and the measures of MSE and squared bias were relatively consistent across forms at the same level of correlation, except for the condition where the correlation was 0 and the number of common items was 8.