We discuss regression models for ordered responses, such as ratings of bonds, schooling attainment, or measures of subjective well-being. Commonly used models in this context are the ordered logit and ordered probit regression models. They are based on an underlying latent model with single index function and constant thresholds. We argue that these approaches are overly restrictive and preclude a flexible estimation of the effect of regressors on the discrete outcome probabilities. For example, the signs of the marginal probability effects can only change once when moving from the smallest category to the largest one. We then discuss several alternative models that overcome these limitations. An application illustrates the benefit of these alternatives.
KeywordsMarginal effects generalized threshold sequential model random coefficients latent class analysis happiness. JEL C25, 125
Unable to display preview. Download preview PDF.
- Boes, S., Winkelmann, R. (2004). Income and happiness: New results from generalized threshold and sequential models. IZA Discussion Paper No. 1175, SOI Working Paper No. 0407, Bonn.Google Scholar
- Clogg, C. C., Shihadeh, E. S. (1994). Statistical Models for Ordered Variables. Sage Publications, Thousand Oaks.Google Scholar
- Cox, C. (1995). Location-scale cumulative odds models for ordered data: A generalized non-linear model approach. Statistics in Medicine14 1191–1203.Google Scholar
- Easterlin, R. (1973). Does money buy happiness?. Public Interest30 3–10.Google Scholar
- Easterlin, R. (1974). Does economic growth improve the humal lot? Some empirical evidence. In Nations and Households in Economic Growth: Essays in Honor of Moses Abramowitz (P. David, M. Reder, eds.), 89–125. Academic Press, New York.Google Scholar
- Everitt, B. S., Merette, C. (1990). The clustering of mixed-mode data: A comparison of possible approaches. Journal of Applied Statistics17 283–297.Google Scholar
- Fienberg, S. E. (1980). The Analysis of Cross-Clasisfication Categorical Data. MIT Press, Cambridge.Google Scholar
- Frey, B. S., Luechinger, S., Stutzer, A. (2004). Valuing public goods: The life satisfaction approach. CESifo Working Paper No. 1158, München.Google Scholar
- Frey, B. S., Stutzer, A. (2002). Happiness and Economics: How the Economy and Institutions Affect Human Well-Being. Princeton University Press, Princeton and Oxford.Google Scholar
- Ronning, G. (1990). The informational content of responses from business surveys. In Microeconometrics. Surveys and Applications (J. P. Florens, M. Ivaldi, J. J. Laffont, F. Laisney, eds.), 123–144. Basil Blackwell, Oxford.Google Scholar
- Scitovsky, T. (1975). Income and happiness. Acta Oeconomica15 45–53.Google Scholar
- Terza, J. (1985). Ordered probit: A generalization. Communications in Statistics—Theory and Methods14 1–11.Google Scholar