Modeling Ordered Choices: A Primer and Recent Developments

Abstract

We survey the literature on models for ordered choices, including ordered logit and probit specifications. The contemporary form of the model is presented and analyzed in detail. The historical development of the model is presented as well. We detail a number of generalizations that have appeared in the recent literature. Finally, we propose a new form of the model that accommodates in a natural, internally consistent form, functional form flexibility and individual heterogeneity. Much of this study is pedagogical. However, the last few sections propose new model formulations, and illustrate them with an application to self reported health satisfaction.

Willingness to pay for wholesome canteen takeaway

“…a multinomial logit model 8 , is that the model account for the natural order of the alternatives in the estimation of the probabilities (see e.g. Greene 2008 or Greene andHensher 2010). The ordered probability model is built around the latent regression:…”

“…The marginal effects of a change in an explanatory variable are therefore analysed via the change in the cell probabilities. The formulae used to calculate the change in cell probability for continuous and dummy variables can be found in Greene (2008, Ch22) and Greene and Hensher (2010).…”

A latent variable representation of count data models to accommodate spatial and temporal dependence: Application to predicting crash frequency at intersections

“…In the standard ordered probit (SORP) model of Equation (1), the thresholds ψ are assumed to be fixed across individuals, though this need not be the case (see Terza, 1985, Pudney and Shields, 2000, King et al, 2004, Kapteyn et al, 2007, Eluru et al, 2008, and King, 2009; see also Greene and Hensher, 2010, Chapter 7 for a discussion). Following these earlier studies, consider that the thresholds are parameterized as a non-linear function of a set of 1 The exclusion of a constant in the vector x q of Equation (1) is an innocuous normalization as long as all the intermediate thresholds (ψ 0 through ψ K-1 ) are left free for estimation.…”

“…Following these earlier studies, consider that the thresholds are parameterized as a non-linear function of a set of 1 The exclusion of a constant in the vector x q of Equation (1) is an innocuous normalization as long as all the intermediate thresholds (ψ 0 through ψ K-1 ) are left free for estimation. Similarly, the use of the standard normal distribution rather than a non-standard normal distribution for the error term is also an innocuous normalization (see Zavoina and McKelvey, 1975;Greene and Hensher, 2010). Note also that any other proper continuous error distribution may be assumed for the error terms, such as the logistic distribution or the extreme value distribution.…”

Attitudes of Germans towards distributive issues in the German health system

“…Hence all equations can be estimated separately as single probit models but this might be inefficient as it ignores the correlation between the disturbances (cf. Greene and Hensher 2010;Maddala 1983). …”