A comparison of the accuracy of ad hoc and Bayesian estimates of the population squared multiple correlation computed from incomplete data.
Item
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Title
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A comparison of the accuracy of ad hoc and Bayesian estimates of the population squared multiple correlation computed from incomplete data.
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Identifier
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AAI9924834
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identifier
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9924834
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Creator
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Onubogu, Joseph Onyekwelu.
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Contributor
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Adviser: Alan Gross
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Date
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1999
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Language
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English
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Publisher
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City University of New York.
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Subject
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Education, Educational Psychology | Statistics | Psychology, Psychometrics
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Abstract
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The accuracy of interval estimates for the population squared multiple correlation (rho2) computed from incomplete data was assessed using three ad hoc methods and the Bayesian procedure based on the Gibbs sampler. Listwise deletion, pairwise deletion, and unconditional fill-in were the three ad hoc methods used.;A multivariate normal distribution for q > 1 predictor variables and one dependent variable, with a variance-covariance matrix Sigma for the distribution, and a value for population squared multiple correlation rho 2 was specified. A random sample of size n was then drawn from this distribution and data deleted on both the dependent variable and independent variables using a MCAR and MAR processes. The incomplete data set was analyzed using the four methods, and a sample interval estimate of rho2 for each method was computed. This analysis was repeated by varying the sample size (n = 50, 100, 250) the number of predictors (2, 5, 7) the value of the squared multiple correlation rho2 (.1, .25, .50) and the amount of the missing data (.10, .40). 95% confidence intervals (CI) for rho 2 estimates from the three ad hoc methods were computed and 95% central posterior intervals were calculated for the Bayesian approach based on the Gibbs sampler.;The results indicate that listwise deletion has the most accurate interval estimates for rho2 among the three ad hoc methods and fill-in has the least. Our overall result indicated that the Bayesian interval estimates for rho2 covered the parameter values fewer times than interval estimates from the ad hoc methods for sample sizes less than or equal to 100 and {dollar}2 less than .5. The prior for rho2 was the main reason for the Bayesian relative poor performance.
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Type
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dissertation
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Source
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PQT Legacy CUNY.xlsx
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degree
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Ph.D.
