WHO Multi - Country Studies unit Working

In many social science researches and econometric applications data that arise through measurement of discrete outcomes or discrete choice among a set of alternatives are in the form of ordinal or ordered categorical data. Such examples, among others, are selfreport responses in household surveys, modeling labor force participate, or decision of which product to choose or which candidate to elect. To analyze such data a number of discrete response (choice) models have been developed in econometric theory, see Greene [,]. A simple one of these kinds of models is the class of ordered univariate response models where the number of categories of the dependent variable is greater than two, i.e. there are several possible outcomes or choices and they are ordered according to the preferences of respondent. The same data structure also arises in the analysis of repeated measurements, where the response of each respondent, experimental unit or subject is observed on multiple occasions to record the level of a specific event. Responses of this type are known as multivariate or correlated categorical responses. The theory of univariate ordered models is relatively well developed and they have been applied extensively in biostatics, economics, political science and sociology while estimations of the joint probability distribution of two or more ordered categorical variables are less common in the literature. The relatively new bivariate (multivariate) ordered probit (BIOPROBIT) models could be treated as an extension of a standard bivariate (multivariate) probit model when the number of categories of the dependent variables is greater than two. The estimation procedures and their statistical properties of BIOPROBIT model are studied in Greene [, Section 11.5.2], Sajaia [] and others. Some of the applications of BIOPROBIT models are modeling educational level of married couples (Magee et al. []), educational attainment in French and Germany (Lauer []), family size (Calhoun [,]), fertility outcome and fertility motivations of Danish twins (Kohler and Rodgers []), analyzing ownership of cats and dogs or dogs and televisions (Butler and Chatterjee [,]), and household-level decision between number of seasonal tickets and number of cars (Scott and Axhausen []).