The Effect of Psychometric Parallelism among Predictors on the Efficiency of Equal Weights and Least Squares Weights in Multiple Regression

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There are several conditions for applying equal weights as an alternative to least squares weights. Psychometric parallelism, one of the conditions, has been suggested as a necessary and sufficient condition for equal-weights aggregation. The purpose of this study is to investigate the effect of psychometric parallelism among predictors on the efficiency of equal weights and least squares weights. Target correlation matrices with 10,000 cases were simulated so that the matrices had varying degrees of psychometric parallelism. Five hundred samples with six ratios of observation to predictor = 5/1, 10/1, 20/1, 30/1, 40/1, and 50/1 were drawn from each population. The ... continued below

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x, 133 leaves : ill.

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Zhang, Desheng May 1996.

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  • Zhang, Desheng

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There are several conditions for applying equal weights as an alternative to least squares weights. Psychometric parallelism, one of the conditions, has been suggested as a necessary and sufficient condition for equal-weights aggregation. The purpose of this study is to investigate the effect of psychometric parallelism among predictors on the efficiency of equal weights and least squares weights. Target correlation matrices with 10,000 cases were simulated so that the matrices had varying degrees of psychometric parallelism. Five hundred samples with six ratios of observation to predictor = 5/1, 10/1, 20/1, 30/1, 40/1, and 50/1 were drawn from each population. The efficiency is interpreted as the accuracy and the predictive power estimated by the weighting methods. The accuracy is defined by the deviation between the population R² and the sample R² . The predictive power is referred to as the population cross-validated R² and the population mean square error of prediction. The findings indicate there is no statistically significant relationship between the level of psychometric parallelism and the accuracy of least squares weights. In contrast, the correlation between the level of psychometric parallelism and the accuracy of equal weights is significantly negative. Under different conditions, the minimum p value of χ² for testing psychometric parallelism among predictors is also different in order to prove equal weights more powerful than least squares weights. The higher the number of predictors is, the higher the minimum p value. The higher the ratio of observation to predictor is, the higher the minimum p value. The higher the magnitude of intercorrelations among predictors is, the lower the minimum p value. This study demonstrates that the most frequently used levels of significance, 0.05 and 0.01, are no longer the only p values for testing the null hypotheses of psychometric parallelism among predictors when replacing least squares weights with equal weights.

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x, 133 leaves : ill.

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  • May 1996

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  • March 26, 2014, 9:30 a.m.

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  • Aug. 28, 2015, 9:30 a.m.

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Zhang, Desheng. The Effect of Psychometric Parallelism among Predictors on the Efficiency of Equal Weights and Least Squares Weights in Multiple Regression, dissertation, May 1996; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc278996/: accessed December 14, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .