Alternative Strategies for Cross-Validation of Covariance Structure Models

Alternative strategies for two-sample cross-validation of covariance structure models are described and investigated. The strategies vary according to whether all (tight strategy) or some (partial strategy) of the model parameters are held constant when a calibration sample solution is re-fit to a validation sample covariance matrix. Justification is provided for three partial strategies. Conventional and alternative strategies for cross-validation are discussed as methods for evaluating overall discrepancy of a model fit to a particular sample, where overall discrepancy arises from the combined influences of discrepancy of approximation and discrepancy of estimation (Cudeck & Henly, 1991). Results of a sampling study using empirical data show that for tighter strategies simpler models are preferred in smaller samples. However, when partial cross-validation is employed, a more complex model may be supported even in a small sample. Implications for model comparison and evaluation, as well as the issues of model complexity and sample size are discussed.