A Bootstrap Confidence Interval Based on a Correlation Corrected for Range Restriction

Mendoza, John E.; Hart, Darren E.; Powell, Amy Jo

doi:10.1207/s15327906mbr2602_4

Cited by 18 publications

(29 citation statements)

References 19 publications

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“…Duan and Dunlap (1997) provided a summary of these methods and evaluate their empirical performance. Rather than the asymptotic approach, Mendoza, Hart, and Powell (1991) proposed a resampling technique to obtain the bootstrap SE, and argued that a better CI could be constructed. Chan and Chan (2004) further evaluated Mendoza et al's bootstrap procedure by a more comprehensive simulation study, and found generally comparable results to those of Mendoza et al…”

Section: Discussionmentioning

confidence: 99%

Bootstrap standard error and confidence intervals for the correlations corrected for indirect range restriction

Chan

Cui

2010

Brit J Math & Statis

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The standard Pearson correlation coefficient, r, is a biased estimator of the population correlation coefficient, ρ(XY) , when predictor X and criterion Y are indirectly range-restricted by a third variable Z (or S). Two correction algorithms, Thorndike's (1949) Case III, and Schmidt, Oh, and Le's (2006) Case IV, have been proposed to correct for the bias. However, to our knowledge, the two algorithms did not provide a procedure to estimate the associated standard error and confidence intervals. This paper suggests using the bootstrap procedure as an alternative. Two Monte Carlo simulations were conducted to systematically evaluate the empirical performance of the proposed bootstrap procedure. The results indicated that the bootstrap standard error and confidence intervals were generally accurate across simulation conditions (e.g., selection ratio, sample size). The proposed bootstrap procedure can provide a useful alternative for the estimation of the standard error and confidence intervals for the correlation corrected for indirect range restriction.

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Section: Discussionmentioning

confidence: 99%

Bootstrap standard error and confidence intervals for the correlations corrected for indirect range restriction

Chan

Cui

2010

Brit J Math & Statis

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“…Finally, the statistics and economics literature considers the classical "restrictionof-range" problem (DeMets and Halperin, 1977;Duan and Dunlap, 1997;Johnson and Ree, 1994;Held and Foley, 1994;Mendoza et al 1991;Hanges et al 1991;Holmes, 1990). In this literature, correlations, or more generally regression coefficients are shown to be affected by focusing the analysis on a small slice of the population.…”

Section: Relationship To Other Literaturementioning

confidence: 99%

Data pruning in consumer choice models

Zanutto

Bradlow²

2006

Quant Market Econ

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Common, if not ubiquitous, Marketing practice when estimating models for scanner panel data is to: (a) observe the data, (b) prune the data to a “manageable” number of brands or SKUs, and (c) fit models to the remaining data. We demonstrate that such pruning practice can lead to significantly different (and potentially biased) elasticities, and hence different managerial/practical outcomes, especially in the context of model misspecification. We first justify our claims theoretically by writing the general problem in a classic missing-data framework and demonstrate that commonly used pruning mechanisms (gleaned from current academic Marketing literature) can lead to a nonignorable missing data mechanism. Secondly, we summarize an extensive set of simulations that were run to understand the driving factors of that bias. The results indicate much greater pruning bias in those cases where model fit is poor (small $$R^{2}$$ ), random utility errors are correlated with the covariates, or the model is misspecified (e.g., a homogeneous logit is specified when a mixed-logit is true). Empirically, we also demonstrate our findings on the well-cited and highly utilized fabric softener data of Fader and Hardie ( 1996 ). Our empirical findings suggest a number of estimates that vary according to the way in which the data is pruned including the magnitude of market mix and attribute elasticities, and purchase probabilities, but that the pruning effect is smaller for better fitting models. Copyright Springer Science + Business Media, LLC 2006Nonignorable missing data mechanism, Probabilistic sampling, Scanner panel data, Multinomial logit models, Mixed-logit models,

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“…Since Pearson (1903) developed the correction formulas for restriction in range and Thorndike ( 1947,1949) defined them for practical application, educational and personnel psychologists have conducted extensive research on the problem of restriction in range (Alexander, Carson, Alliger, & Barrett, 1984;Booth-Kewley, 1985;Greener & Osburn, 1979;Gross & Fleischman, 1983;Levin, 1972;Linn, 1968;Linn, Harnisch, & Dunbar, 1981;Mendoza, Hart, & Powell, 1991;Olson & Becker, 1983;Sands, Alf, & Abrahams, 1978). However, most of the research pertains to the univariate, not the multivariate, correction formulas (Lord & Novick, 1968;Novick & Thayer, 1969).…”

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confidence: 99%

Explanations for Accuracy of the General Multivariate Formulas in Correcting for Range Restriction

Held

Foley

1994

Applied Psychological Measurement

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Univariate and multivariate corrections for range restriction were compared using Navy applicant scores on the Armed Services Vocational Aptitude Battery (ASVAB). Two Navy school ASVAB selector composites were used separately and together to simulate three selection situations for nine selection ratios (SRs). The selectors then were used as predictors. Composite validities (the ASVAB Mechanical Comprehension test was the criterion) were corrected using the univariate and the general multivariate formulas. In general, multivariate corrections were more accurate than univariate corrections, notably when the univariate explicit selection variable was negatively skewed and correction violations (linearity and homoscedasticity) did not offset each other. Multivariate correction accuracy was attributed to the inclusion of variables with adequate distributional properties, the compensatory effects of regression weights, and the related psychometric principle that differentially weighting a large number of correlated predictor variables has little impact on a multiple correlation. Index terms: correction formulas, explicit selection, incidental selection, multivariate correction formulas, restriction in range, validation studies.Since Pearson (1903) developed the correction formulas for restriction in range and Thorndike

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A Bootstrap Confidence Interval Based on a Correlation Corrected for Range Restriction

Cited by 18 publications

References 19 publications

Bootstrap standard error and confidence intervals for the correlations corrected for indirect range restriction

Bootstrap standard error and confidence intervals for the correlations corrected for indirect range restriction

Data pruning in consumer choice models

Explanations for Accuracy of the General Multivariate Formulas in Correcting for Range Restriction

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