The Gibbs sampler applied to missing data with categorical, continuous and mixed data types.
Item
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Title
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The Gibbs sampler applied to missing data with categorical, continuous and mixed data types.
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Identifier
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AAI9630440
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identifier
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9630440
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Creator
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Boslaugh, Sarah E.
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Contributor
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Adviser: Alan Gross
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Date
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1996
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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
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Abstract
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In the present research we have investigated the problem of estimating multiple correlations for regression models containing a mix of categorical, continuous and interaction terms given a data set containing missing values. We consider the case where the model has a single binary predictor variable, a single continuous predictor variable, and a cross-product term. A Bayesian approach is used to obtain an interval estimate of the multiple correlation of Y on the predictors ({dollar}\rho\sp2{dollar}) using a Gibbs sampling procedure. Using 5,000 samples from the posterior distribution of {dollar}\rho\sp2{dollar}, we empirically construct.90 highest-density regions (HDR's) for {dollar}\rho\sp2{dollar}. To demonstrate the estimation procedure, 32 data samples were used; 18 with data missing completely at random (MCAR) and 18 with data missing at random (MAR). Within each set of 18, three sample sizes (30, 50 or 100), three population values for {dollar}\rho\sp2{dollar} (.10,.25 and.50) and two probabilities of missing data (.271 and.657) were used. In the MCAR case, 17 of the 18 HDR's contained the population {dollar}\rho\sp2{dollar}, while in the MAR cases, 16 of the 18 HDR's contained the population {dollar}\rho\sp2{dollar}. As expected, smaller sample sizes and more missing data produced wider HDR's, and MAR data produced slightly wider HDR's than MCAR data.
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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.
