Tutorial on modeling ordered categorical response data.

In the past decade there has been great progress in the development of methodology for analyzing ordered categorical data. Logit and log linear model-building techniques for nominal data have been generalized for use with ordinal data. There are many advantages to using these procedures instead of the Pearson chi-square test of independence to analyze ordered categorical data. These advantages include (a) more complete description of the nature of associations and (b) greater power for detecting population associations. This article introduces logit models for categorical data and shows two ways of adapting them to model ordered categorical data. The models are used to analyze a cross-classification table relating mental impairment and parents' socioeconomic status.

[1]  Nathan Mantel,et al.  Chi-square tests with one degree of freedom , 1963 .

[2]  Marvin K. Opler,et al.  Mental Health in the Metropolis: The Midtown Manhattan Study. , 1965 .

[3]  L. A. Goodman The analysis of dependence in cross-classifications having ordered categories, using log-linear models for frequencies and log-linear models for odds. , 1983, Biometrics.

[4]  Graham J. G. Upton,et al.  The Analysis of Cross-Tabulated Data , 1979 .

[5]  A. Agresti Analysis of Ordinal Categorical Data , 1985 .

[6]  W. Dixon,et al.  BMDP statistical software , 1983 .

[7]  Ronald G. Stansfield,et al.  Sociological Methodology 1982 , 1983 .

[8]  Bhapkar Vp,et al.  On the analysis of contingency tables with a quantitative response. , 1968 .

[9]  Clifford C. Clogg,et al.  Using Association Models in Sociological Research: Some Examples , 1982, American Journal of Sociology.

[10]  G. Koch,et al.  Linear Models Methods for Some Rank Function Analyses of Ordinal Categorical Data , 1983 .

[11]  R. D. Bock,et al.  Multivariate Statistical Methods in Behavioral Research , 1978 .

[12]  Shelby J. Haberman,et al.  Log-Linear Models for Frequency Tables with Ordered Classifications , 1974 .

[13]  Michael E. Sobel,et al.  Exchange, Structure, and Symmetry in Occupational Mobility , 1985, American Journal of Sociology.

[14]  Frederick Mosteller,et al.  Association and Estimation in Contingency Tables , 1968 .

[15]  James E. Grizzle,et al.  Analysis of Contingency Tables Having Ordered Response Categories , 1972 .

[16]  L. A. Goodman,et al.  Measures of association for cross classifications , 1979 .

[17]  Mental Health in the Metropolis: The Midtown Manhattan Study , 1977 .

[18]  G. Koch,et al.  Analysis of categorical data by linear models. , 1969, Biometrics.

[19]  Stanley Wasserman,et al.  Sociological Methodology, 1987 , 1989 .

[20]  Robert G. Lehnen,et al.  Public Program Analysis: A New Categorical Data Approach , 1981 .

[21]  Manfred Kuechler,et al.  Surveying Subjective Phenomena. , 1985 .

[22]  Gary G. Koch,et al.  Average Partial Association in Three-way Contingency Tables: a Review and Discussion of Alternative Tests , 1978 .

[23]  Alan Agresti,et al.  An empirical investigation of some effects of sparseness in contingency tables , 1987 .

[24]  M. Swafford Three Parametric Techniques for Contingency Table Analysis: A Nontechnical Commentary , 1980 .

[25]  Gary Simon Alternative Analyses for the Singly-Ordered Contingency Table , 1974 .

[26]  P. Holland,et al.  Discrete Multivariate Analysis. , 1976 .

[27]  R. P. Hastings,et al.  SUGI supplemental library user's guide , 1986 .

[28]  E. Lehmann,et al.  Nonparametrics: Statistical Methods Based on Ranks , 1976 .

[29]  Stephen E. Fienberg,et al.  The analysis of cross-classified categorical data , 1980 .

[30]  Herbert L. Smith,et al.  Scaling via Models for the Analysis of Association: Social Background and Educational Careers in France , 1987 .

[31]  W. J. Dixon,et al.  BMDP statistical software : 1981 , 1982 .

[32]  A. Agresti,et al.  Statistical Methods for the Social Sciences , 1979 .