A Bayesian approach to estimating a correlation with missing data.
Item
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Title
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A Bayesian approach to estimating a correlation with missing data.
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Identifier
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AAI9325157
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identifier
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9325157
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Creator
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Torres-Quevedo, Rocio.
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Contributor
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Adviser: Alan Gross
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Date
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1993
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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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Psychology, Psychometrics | Statistics
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Abstract
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A Bayesian approach was developed to estimate {dollar}\rho{dollar} (correlation between two continuous variables) for the cases where one of the variables is either missing at random or missing completely at random. A formula for the posterior distribution of {dollar}\rho{dollar} was developed, evaluated as a function of different factors (n = sample size, r* = correlation between both variables using only the complete cases, R{dollar}\sb1{dollar} = proportion of missing data, R{dollar}\sb2{dollar} = the ratio of the variance of X using only the complete cases to the variance of X using all cases), and compared to the Maximum likelihood approach for estimating {dollar}\rho{dollar}.;Maximum Likelihood based Confidence Intervals and Bayesian Highest Density Regions were computed for different values of n, r*, R{dollar}\sb1{dollar} and R{dollar}\sb2{dollar}. The Bayesian approach was most advantageous under the following conditions; the prior distribution although "non-informative", restricted {dollar}\rho{dollar} to be positive, both n and r* were small. For larger sample sizes the Highest Density Regions and the Confidence Intervals were more similar. However, when r* was small the Bayesian approach was still more precise than the Maximum Likelihood approach even for larger samples.;Maximum Likelihood Estimates (MLE's), posterior means and posterior medians were also computed for the different values of n, r*, R{dollar}\sb1{dollar} and R{dollar}\sb2{dollar}. When {dollar}\rho{dollar} was not restricted to be positive the Bayesian estimates and the MLE's were practically equal except for small sample sizes where the posterior mean was smaller than the MLE. When {dollar}\rho{dollar} was restricted to be positive, the Bayesian estimates tended to be higher than the MLE's; but as the sample size and the r* values increased, the MLE's and Bayesian estimates became more similar.;Both the posterior mean and median were analyzed in order to obtain descriptive information on how they varied as a function of n, r*, R{dollar}\sb1{dollar} and R{dollar}\sb2{dollar}. As r* increased the Bayesian estimates of {dollar}\rho{dollar} strongly increased. As n increased the estimates decreased. Similarly, as R{dollar}\sb1{dollar} increased the estimates decreased and as R{dollar}\sb2{dollar} increased the posterior mean and median decreased.
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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.
