The analysis of data involving ordinal variables in which some of the data are missing.
Item
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Title
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The analysis of data involving ordinal variables in which some of the data are missing.
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Identifier
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AAI9630512
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identifier
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9630512
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Creator
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Strauss, Shiela Maiman.
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Contributor
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Adviser: David Rindskopf
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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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Sociology, Theory and Methods | Statistics
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Abstract
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The current work explores the analysis of categorical data in which some of the values are missing. For a given data set, each missing data point is viewed as only partially categorized, having an unknown value on at least one, but not all of the variables. It is not necessarily assumed that the data are missing at random. Hypothesized associations among the variables in a data set and the hypothesized nature (random or nonrandom) of the missing data mechanism are represented using loglinear models. Expected values of cell frequencies and sums of expected frequencies (marginals) are expressed by using an extension of the generalized linear model with composite links.;For each of three kinds of data set structures, models which hypothesize nonignorable nonresponse are first explored for their identification status. Then, for each of these three kinds of data set structures, a specific example is chosen from the literature for a determination of the adequacy of fit of a variety of loglinear models. Models proposed to represent relationships among the data for each of these specific data sets include both those which postulate ignorable nonresponse and those for which the missingness is hypothesized to be nonrandom. Maximum likelihood estimates for parameters and expected cell frequencies and marginals are obtained for each of the models using the EM algorithm. Chi square goodness of fit tests are performed, and for each of the three data sets, comparisons of predicted cell frequencies are made for those models which adequately fit the data.;All data sets analyzed in the current work contain at least one ordinal variable. Statistical modeling involving ordinal variables allows for the consideration of a greater number of patterns of association among the variables than if all the variables are nominal, and often requires fewer model parameters. More parameters can then be used to represent the missing data mechanism, and the possibility of nonignorable nonresponse can be investigated. The current work adds to the small body of literature in which a nonrandom missing data mechanism is considered in modeling data with missing values.
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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.
