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Browsing by Author "Bobko, Philip"

Now showing 1 - 3 of 3
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    Appropriate moderated regression and inappropriate research strategy: A demonstration of information loss due to scale coarseness
    (1991) Russell, Craig J.; Pinto, Jeffrey K.; Bobko, Philip
    Paunonen and Jackson (1988) demonstrated that stepwise moderated regression provides a test of interaction effects that protects the nominal Type I error rate. However, the stepwise procedure has also been characterized as failing to detect interaction effects in empirical studies. This issue has led to questions regarding the method’s statistical power (Bobko, 1986; Zedeck, 1971) in applied research. It is demonstrated that, because of a research strategy frequently used in empirical investigations, the probability of Type II error in detecting a true interaction effect is unknown. Specifically, the number of scale steps used in measuring the dependent variable is shown to result in a form of systematic error that can spuriously increase or decrease the expected effect size of the interaction. The problem is also discussed in the context of testing more complex models. Recommendations for eliminating this problem in future research designs are provided. Index terms: information loss, interaction effects, Likert scales, moderated regression, response transformation.
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    Eigenvalue shrinkage in principal components based factor analysis
    (1984) Bobko, Philip; Schemmer, F. Mark
    The concept of shrinkage, as (1) a statistical phenomenon of estimator bias, and (2) a reduction in explained variance resulting from cross-validation, is explored for statistics based on sample eigenvalues. Analytic solutions and previous research imply that the magnitude of eigenvalue shrinkage is a function of the type of shrinkage, sample size, the number of variables in the correlation matrix, the ordinal root position, the population eigenstructure, and the choice of principal components analysis or principal factors analysis. Hypotheses relating these specific independent variables to the magnitude of shrinkage were tested by means of a monte carlo simulation. In particular, the independent variable of population eigenstructure is shown to have an important effect on shrinkage. Finally, regression equations are derived that describe the linear relation of population and cross-validated eigenvalues to the original eigenvalues, sample size, ordinal position, and the number of variables factored. These equations are a valuable tool that allows researchers to accurately predict eigenvalue shrinkage based on available sample information.
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    Large sample estimators for standard errors of functions of correlation coefficients
    (1980) Bobko, Philip; Rieck, Angela
    Standard errors of estimators that are functions of correlation coefficients are shown to be quite different in magnitude than standard errors of the initial correlations. A general large-sample methodology, based upon Taylor series expansions and asymptotic correlational results, is developed for the computation of such standard errors. Three exemplary analyses are conducted on a correction for attenuation, a correction for range restriction, and an indirect effect in path analysis. Derived formulae are consistent with several previously proposed estimators and provide excellent approximations to the standard errors obtained in computer simulations, even for moderate sample size (n = 100). It is shown that functions of correlations can be considerably more variable than product-moment correlations. Additionally, appropriate hypothesis tests are derived for these corrected coefficients and the indirect effect. It is shown that in the range restriction situation, the appropriate hypothesis test based on the corrected coefficient is asymptotically more powerful than the test utilizing the uncorrected coefficient. Bias is also discussed as a by-product of the methodology.