Analysis of Categorical Response Profiles By Informative Summaries

Autor: Shelby J. Haberman, Zvi Gilula
Rok vydání: 2001
Předmět:
Zdroj: Sociological Methodology. 31:129-187
ISSN: 1467-9531
0081-1750
DOI: 10.1111/0081-1750.00094
Popis: A categorical profile is a vector of observed values of several categorical variables that share a common context. Statistical analysis of categorical profiles may involve study of the joint distribution of the profiles or study of the relationship of the profiles to explanatory variables. Such analysis entails special difficulties due to the very large number of possible categorical profiles and due to the very strong relationships among the responses. Given the complex nature of the relationships among the variables, large samples are required for analysis. These large samples generally render useless traditional methods of model fitting based on tests of goodness of fit. Alternatively, model quality may be assessed in terms of descriptive power, as measured by information-theoretic criteria. A useful method of data description involves summary statistics derived from the data. A new approach combining log-linear models and summary statistics results in insightful and parsimonious description of categorical profiles. The analysis of summary statistics results in the use of log-linear models that differ substantially from those commonly employed in the analysis of profile data. Special measures are introduced for comparison of the descriptive power associated with different choices of summary statistics and for comparison of the number of parameters required for each model. Estimates for these special measures are proposed, and large-sample properties are considered in order to find asymptotic confidence intervals, providing an added inferential value to the proposed methods of analysis. Through use of an empirical example of responses to questions concerning legal abortions, it is shown that models based on very succinct summaries of responses involve remarkably little information loss, thus describing the data relatively accurately and parsimoniously.
Databáze: OpenAIRE
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