In the exploratory factor analysis, when the number of factors exceeds the true number of factors, the likelihood ratio test statistic no longer follows the chi-square distribution due to a problem of rank deficiency and nonidentifiability of model parameters. As a result, decisions regarding the number of factors may be incorrect. Several…

In testing factorial invariance, researchers have often used a reference variable strategy in which the factor loading for a variable (i.e., reference variable) is fixed to 1 for identification. This commonly used method can be misleading if the chosen reference variable is actually a noninvariant item. This simulation study suggests an…