A monte carlo experiment was conducted to evaluate
the robustness of two estimators of the population
squared multiple correlation (R2p) and one estimator
of the population squared cross-validity coefficient
(R2cv) to a common violation of multivariate
normality. Previous research has shown that these
estimators are approximately unbiased when independent
and dependent variables follow a joint
multivariate normal distribution. The particular
violation of multivariate normality studied here
consisted of a dependent variable that may assume
only a few discrete values. The discrete dependent
variable was simulated by categorizing an underlying
continuous variable that did satisfy the multivariate
normality condition. Results illustrate the
attenuating effects of categorization upon R2p and R2cv. In addition, the distributions of sample
squared multiple correlations and sample squared
cross-validity coefficients are affected by categorization
mainly through the attenuations of R2P and R2cv.
Consequently, the formula estimators of R2p and R2cv
were found to be as accurate and unbiased with
discrete dependent variables as they were with continuous
dependent variables. Substantive researchers
who use categorical dependent variables,
perhaps obtained by rating scale judgments, can
justifiably employ any of the three estimators examined
Drasgow, Fritz & Dorans, Neil J. (1982). Robustness of estimators of the squared multiple correlation and squared cross-validity coefficient to violations of multivariate normality. Applied Psychological Measurement, 6, 185-200. doi:10.1177/014662168200600205
Drasgow, Fritz; Dorans, Neil J..
Robustness of estimators of the squared multiple correlation and squared cross-validity coefficient to violations of multivariate normality.
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