TY - JOUR
T1 - Analysis of categorical response profiles by informative summaries
AU - Gilula, Zvi
AU - Haberman, Shelby J.
PY - 2001
Y1 - 2001
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0035740857&partnerID=8YFLogxK
U2 - 10.1111/0081-1750.00094
DO - 10.1111/0081-1750.00094
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AN - SCOPUS:0035740857
SN - 0081-1750
VL - 31
SP - 129
EP - 187
JO - Sociological Methodology
JF - Sociological Methodology
IS - 1
ER -