Basically tau-equivalent confirmatory factor analysis considering item particularities

We propose a basically tau-equivalent measurement model for confirmatory factor analysis that differs from the original tau-equivalent measurement model through the replacement of strict tau equivalence by basic tau equivalence, enabling the accounting of item particularities. Considered in the framework of linear regression analysis, basic tau equivalence means a slope of zero across the set of factor loadings, but without their restriction to exact correspondence. Allowing for deviations from correspondence enables the account of item particularities, whereas a zero slope keeps away systematic influences unrelated to the attribute of interest. This measurement model is illustrated using an example matrix and data from two simulation studies. The fit results of the two described methods for realizing basic tau equivalence are highly correlated.