The use of Lagrange multiplier (LM) tests in specification searches and the efforts that involve the addition of extraneous parameters to models are discussed. Presented are a rationale and strategy for conducting specification searches in two stages that involve adding parameters to LM tests to maximize fit and then deleting parameters not needed…

Examined 20 goodness-of-fit indexes based on the minimum fit function using a simulation under the 2-group situation. Results support the use of the delta comparative fit index, delta Gamma hat, and delta McDonald's Noncentrality Index to evaluation measurement invariance. These three approaches are independent of model complexity and sample size.…

Used three approaches to understand the effect of the number of variables in the model on model fit in structural equation modeling through computer simulation. Developed a simple formula for the theoretical value of the comparative fit index. (SLD)

The adequacy of "rule of thumb" conventional cutoff criteria and several alternatives for fit indices in covariance structure analysis was evaluated through simulation. Analyses suggest that, for all recommended fit indexes except one, a cutoff criterion greater than (or sometimes smaller than) the conventional rule of thumb is required…