Robustness of Estimators of the Squared Multiple Correlation and Squared Cross-Validity Coefficient to Violations of Multivariate Normality

摘要

A monte carlo experiment was conducted to evaluatethe robustness of two estimators of the populationsquared multiple correlation (R2p) and one estimatorof the population squared cross-validity coefficient(R2cv) to a common violation of multivariatenormality. Previous research has shown that theseestimators are approximately unbiased when independentand dependent variables follow a jointmultivariate normal distribution. The particularviolation of multivariate normality studied hereconsisted of a dependent variable that may assumeonly a few discrete values. The discrete dependentvariable was simulated by categorizing an underlyingcontinuous variable that did satisfy the multivariatenormality condition. Results illustrate theattenuating effects of categorization upon R2p and R2cv. In addition, the distributions of samplesquared multiple correlations and sample squaredcross-validity coefficients are affected by categorizationmainly through the attenuations of R2P and R2cv.Consequently, the formula estimators of R2p and R2cvwere found to be as accurate and unbiased withdiscrete dependent variables as they were with continuousdependent variables. Substantive researcherswho use categorical dependent variables,perhaps obtained by rating scale judgments, canjustifiably employ any of the three estimators examinedhere.