Cross-Validation in Regression and Covariance Structure Analysis

This article gives an overview of cross-validation techniques in regression and covariance structure analysis. The method of cross-validation offers a means for checking the accuracy or reliability of results that were obtained by an exploratory analysis of the data. Cross-validation provides the possibility to select, from a set of alternative models, the model with the greatest predictive validity, that is, the model that cross-validates best. The disadvantage of cross-validation is that the data need to be split in two or more parts. This can be a serious problem when sample size is small. Various authors have therefore tried to find single sample criteria that provide the same kind of information as the cross-validation criteria but that do not require the use of a validation sample. Several of these criteria will be discussed, along with some results from studies comparing cross-validation and single sample criteria in covariance structure analysis.