Many previous studies investigate the unidimensionality by examining local independence in IRT, and by concentrating the goodness of fit indices in SEM in practice. This study majorly focuses on the indices reflecting the bias effect of forcing bifactor data into a unidimesnional measurement in an SEM context. The percentage of uncontaminated correlations (PUC) index was calculated by data structure. “explained common variance” (ECV) is the variance explained by general factor divided by the total common variance, and OmegaH statistic is the variance in summed scores can be attributed to the single general factor. These indices were used to indicate the bias effect in misspecification. The result shows there is a linear relationship between ECV, PUC and structure coefficient. OmegaH will be changed as the different test length and PUC (which is highly affected by test length). The traditional fit indices such as RMSEA, CFI, and SRMR cannot used to predict bias as well as ECV, OmegaH, and PUC.
I am curious the reason of the relationship between the data structure index (PUC) and the bias because this index is calculated by number of items, number of group factors, and number of items per group factor. This index is affected strongly by test length and group factors. In contrast to ECV and OmegaH function, it is easily to understand the proportion of General factor loading in total variance is related with the unidimensional assumption. However, ECV is unaffected by the number of items on a test but OmegaH is affected by PUC.
Secondly, the bifactor model structure is an important design for this investigation because the calculation for PUC. Nevertheless, I think the percentage of uncontaminated correlations could probably also used in the other structure because it is a kind of calculation of number of correlation. Do I misunderstand the meaning of PUC?