Summary
The purpose of the present paper is to propose an analytical method for ordered categorical responses obtained from a repeated measurement/longitudinal experiment. The ordered categorical scale is assumed to be a manifestation of a latent quantitative variable. A linear model is assumed for location parameters of the underlying distributions. Weighted least square method is applied to parameter estimation and subsequent analysis. Two data sets are analyzed to show several aspects of analysis by the proposed model and to discuss comparative characteristics of analysis compared with earlier analysis. A mention is made for a computer software program for the proposed model.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Asano, C., Watanabe, M., Hosokawa, K. and Kurihara, K. (1982). A recent development in NISAN System,Bull. Inform. Cybernet.,20, 79–96.
Bhapkar, V. P. (1980). ANOVA and MANOVA: Models for categorical data, inHandbook of Statistics,1 (ed. P. R. Krishnaiah), North-Holland, 343–387.
Bishop, Y., Fienberg, S. E. and Holland, P. W. (1975).Discrete Multivariate Analysis: Theory and Practice, M.I.T. Press.
Bryant, E. and Gillings, D. (1985). Statistical analysis of longitudinal repeated measures designs,BIOSTATISTICS: Statistics in Biomedical, Public Health and Environmental Sciences (ed. P. K. Sen), Elsevier Science Publishers B. V., North-Holland 251–282.
Ghosh, M., Grizzle, J. E. and Sen, P. K. (1973). Nonparametric methods in longitudinal studies,J. Amer. Statist. Ass.,68, 29–36.
Grizzle, J. E., Starmer, C. F. and Koch, G. G. (1969). Analysis of categorical data by linear models,Biometrics,25, 489–504.
Koch, G. G., Arama, I. A., Stokes, M. E. and Gillings, D. B. (1980). Some views on parametric and non-parametric analysis for repeated measurements and selected bibliography,Int. Statist. Rev.,48, 249–265.
Koch, G. G., Landis, J. R., Freeman, J. L., Freeman, D. H. and Lehnen, R. G. (1977). A general methodology for the analysis of experiments with repeated measurement of categorical data,Biometrics,33, 133–158.
Koch, G. G. and Reinfurt, D. W. (1971). The analysis of categorical data from mixed models,Biometrics,27, 157–173.
McCullagh, P. (1977). A logistic model for paired comparisons with ordered categorical data,Biometrika,63, 449–453.
Plackett, R. L. (1980).Analysis of Categorical Data, 2nd ed., Griffin, London.
Thurstone, L. L. (1959).The Measurement of Values, the University of Chicago Press.
Timm, N. H. (1980). Multivariate analysis of variance of repeated measurements, inHandbook of Statistics,1 (ed. P. R. Krishnaiah), North-Holland, 41–87.
Uesaka, H. and Asano, C. (1984). Analytical methodology for several multivariate samples with ordered categorical responses, inProc. China-Japan Symp. Statist., Peking University Press, Beijing, China, 292–295.
Uesaka, H. and Asano, C. (1985). A latent scale linear model for ordered categorical responses,Engineering Sciences Report, Kyushu University,6, 259–265.
Uesaka, H. and Asano, C. (1986). Interactive factorial analysis of ordered categorical data using NISAN System,Research Report No. 107, Research Institute of Fundamental Information Science, Kyushu University.
Uesaka, H. and Asano, C. (1987). Latent scale linear models for multivariate ordinal responses and their analysis by the method of weighted least squares,Ann. Inst. Statist. Math.,39, 191–210.
Author information
Authors and Affiliations
About this article
Cite this article
Uesaka, H., Asano, C. Analysis of ordered categorical data from repeated measurements assuming a quantitative latent variable. Ann Inst Stat Math 39, 513–531 (1987). https://doi.org/10.1007/BF02491487
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02491487