A monte carlo experiment was used to evaluate
four procedures for estimating the population
squared cross-validity of a sample least squares regression
equation. Four levels of population
squared multiple correlation (Rp2) and three levels
of number of predictors (n) were factorially crossed
to produce 12 population covariance matrices. Random
samples at four levels of sample size (N) were
drawn from each population. The levels of N, n,
and RP2 were carefully selected to ensure relevance
of simulation results for much applied research.
The least squares regression equation from each
sample was applied in its respective population to
obtain the actual population squared
(Rcv2). Estimates of Rcv2 were computed using three
formula estimators and the double
procedure. The results of the experiment demonstrate
that two estimators which have previously
been advocated in the literature were negatively
biased and exhibited poor accuracy. The negative
bias for these two estimators increased as Rp2 decreased
and as the ratio of N to n decreased. As a
consequence, their biases were most evident in
small samples where cross-validation is imperative.
In contrast, the third estimator was quite accurate
and virtually unbiased within the scope of this
simulation. This third estimator is recommended
for applied settings which are adequately approximated
by the correlation model.
Drasgow, Fritz, Dorans, Neil J & Tucker, Ledyard R. (1979). Estimators of the squared cross-validity coefficient: A Monte Carlo investigation. Applied Psychological Measurement, 3, 387-399. doi:10.1177/014662167900300310
Drasgow, Fritz; Dorans, Neil J.; Tucker, Ledyard R..
Estimators of the squared cross-validity coefficient: A Monte Carlo investigation.
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