Abstract
In the first two chapters of this volume, models for binary or dichotomous variables have been discussed. However, in a wide range of psychological and sociological applications it is very common to have data that are polytomous or multicategorical. For instance, the response scale in the verbal aggression data set (see Chapters 1 and 2) originally consisted of three categories (“yes,” “perhaps,” “no”), but it was dichotomized to illustrate the application of models for binary data. In aptitude testing, the response is often classified into one of several categories (e.g., wrong, partially correct, fully correct). In attitude research, frequent use is made of rating scales with more than two categories (e.g., “strongly agree,” “agree,” “disagree,” “strongly disagree”). Other examples are multiple-choice items, for which each separate choice option represents another category. In a typical discrete choice experiment, the subject is faced with a choice between several options (e.g., several brands of a product in a marketing study).
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References
Adams, R.J., & Wilson, M. (1996). Formulating the Rasch model as a mixed coefficients multinomial logit. In G. Engelhard & M. Wilson (Eds), Objective Measurement: Theory and Practice. Vol 3 (pp. 143–166). Norwood, NJ: Ablex.
Adams, R.J., Wilson, M., & Wang, W.C. (1997). The multidimensional random coefficients multinomial logit model. Applied Psychological Measurement, 21, 1–23.
Agresti, A. (1999). Modeling ordered categorical data: Recent advances and future challenges. Statistics in Medicine, 18, 2191–2207.
Agresti, A. (2002). Categorical Data Analysis (2nd ed.). New York: Wiley.
Agresti, A., & Liu, I. (2001). Strategies for modelling a categorical variable allowing multiple category choices. Sociological Methods & Research, 29, 403–434.
Andersen, E.B. (1995). Polytomous Rasch models and their estimation. In G.H. Fischer & I.W. Molenaar (Eds), Rasch Models: Foundations, Recent Developments, and Applications (pp. 271–291). New York: Springer.
Andrich, D. (1978). A rating formulation for ordered response categories. Psychometrika, 43, 561–573.
Andrich, D. (1982). An extension of the Rasch model to ratings providing both location and dispersion parameters. Psychometrika, 47, 105–113.
Bartholomew, D.J., Steel, F., Moustaki, I., & Galbraith, J.I. (2002). The Analysis and Interpretation of Multivariate Data for Social Scientists. London: CRC Press.
Bock, R.D. (1972). Estimating item parameters and latent ability when responses are scored in two or more nominal categories. Psychometrika, 37, 29–51.
Boyd, J., & Mellman, J. (1980). The effect of fuel economy standards on the U.S. automotive market: A hedonic demand analysis. Transportation Research A, 14, 367–378.
Cardell, S., & Dunbar, F. (1980). Measuring the societal impacts of automobile downsizing. Transportation Research A, 14, 423–434.
Ezzet, F., & Whitehead, J. (1991). A random effects model for ordinal responses from a crossover trial. Statistics in Medicine, 10, 901–907.
Fahrmeir, L., & Tutz, G. (2001). Multivariate Statistical Modelling Based on Generalized Linear Models (2nd ed.). New York: Springer.
Fischer, G.H., & Parzer, P. (1991). An extension of the rating scale model with an application to the measurement of treatment effects. Psychometrika, 56, 637–651.
Fischer, G.H., & Ponocny, I. (1994). An extension of the partial credit model with an application to the measurement of change. Psychometrika, 59, 177–192.
Glas, C.A.W., & Verhelst, N.D. (1989). Extensions of the partial credit model. Psychometrika, 54, 635–659.
Hartzel, J., Agresti, A., & Caffo, B. (2001). Multinomial logit random effects. Statistical Modelling, 1, 81–102.
Harville, D.A., & Mee, R.W. (1984). A mixed-model procedure for analysing ordered categorical data. Biometrics, 40, 393–408.
Hedeker, D., & Gibbons, R.D. (1994). A random-effects ordinal regression model for multilevel analysis. Biometrics, 50, 933–944.
Jansen, J. (1990). On the statistical analysis of ordinal data when extravariation is present. Applied Statistics, 39, 74–85.
Jansen, P.G.W., & Roskam, E.E. (1986). Latent trait models and dichoto-mization of graded responses. Psychometrika, 51, 69–91.
Linacre, J.M. (1989). Many-faceted Rasch Measurement. Chicago: MESA Press.
Luce, R.D. (1959). Individual Choice Behavior. New York: Wiley.
Masters, G.N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47, 149–174.
McCullagh, P. (1980). Regression models for ordinal data (with discussion). Journal of the Royal Statistical Society, Series B, 42, 109–142.
McCullagh, P., & Neider, J.A. (1989). Generalized Linear Models (2nd ed.). London: Chapman & Hall.
McCulloch, C.E., & Searle, S. (2001). Generalized, Linear, and Mixed Models. New York: Wiley.
McFadden, D. (1974). Conditional logit analysis of qualitative choice behavior. In P. Zarembka (Ed.), Frontiers in Econometrics (pp. 105–142). New York: Academic Press.
Molenaar, I.W. (1983). Item steps (Heymans Bulletin 83–630-EX). Groningen, The Netherlands: Heymans Bulletins Psychologische Instituten, R.U. Groningen.
Muraki, E. (1992). A generalized partial credit model: Application of an EM algorithm. Applied Psychological Measurement, 16, 159–176.
Ramsey, F.L. & Schafer, D.W. (2001). The Statistical Sleuth: A Course in Methods of Data Analysis. Pacific Grove, CA: Duxbury Press.
Rasch, G. (1961). On the general laws and the meaning of measurement in psychology. In J. Neyman (Ed.), Proceedings of the IV Berkeley Symposium on Mathematical Statistics and Probability, Vol. IV (pp. 321–333). Berkeley: University of California Press.
Samejima, F. (1969). Estimation of ability using a response pattern of graded scores. Psychometrika Monograph, No. 17.
Thissen, D., & Steinberg, L. (1986). A taxonomy of item response models. Psychometrika, 51, 567–577.
Thurstone, L. (1927). A law of comparative judgment. Psychological Review, 34, 273–286.
Train, K.E. (2003). Discrete Choice Models with Simulation. Cambridge: Cambridge University Press.
Tutz, G. (1990). Sequential item response models with an ordered response. British Journal of Mathematical and Statistical Psychology, 43, 39–55.
Tutz, G. (1997). Sequential models for ordered responses. In W.J. van der Linden & R.K. Hambleton (Eds), Handbook of Modern Item Response Theory (pp. 139–152). New York: Springer.
Tutz, G., & Hennevogl, W. (1996). Random effects in ordinal regression models. Computational Statistics & Data Analysis, 22, 537–557.
Wilson, M., & Adams, R.J. (1993). Marginal maximum likelihood estimation for the ordered partition model. Journal of Educational Statistics, 18, 69–90.
Wilson, M., & Masters, G.N. (1993). The partial credit model and null categories. Psychometrika, 58, 87–99.
Wu, M.L., Adams, R.J., & Wilson, M. (1998). ACERConquest Hawthorn, Australia: ACER Press.
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Tuerlinckx, F., Wang, WC. (2004). Models for polytomous data. In: De Boeck, P., Wilson, M. (eds) Explanatory Item Response Models. Statistics for Social Science and Public Policy. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3990-9_3
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DOI: https://doi.org/10.1007/978-1-4757-3990-9_3
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