Maximum Likelihood Estimation of Endogenous Switching and Sample Selection Models for Binary, Ordinal, and Count Variables

Abstract

Studying behavior in economics, sociology, and statistics often involves fitting models in which the response variable depends on a dummy variable-also known as a regime-switch variable-or in which the response variable is observed only if a particular selection condition is met. In either case, standard regression techniques deliver inconsistent estimators if unobserved factors that affect the response are correlated with unobserved factors that affect the switching or selection variable. Consistent estimators can be obtained by maximum likelihood estimation of a joint model of the outcome and switching or selection variable. This article describes a "wrapper" program, ssm, that calls gllamm (Rabe-Hesketh, Skrondal, and Pickles, GLLAMM Manual [University of California-Berkeley, Division of Biostatistics, Working Paper Series, Paper No. 160]) to fit such models. The wrapper accepts data in a simple structure, has a straightforward syntax, and reports output that is easily interpretable. One important feature of ssm is that the log likelihood can be evaluated using adaptive quadrature (

Multilevel Poisson sample selection models and alternative methods for estimating hospital effects on long-term outcomes

“…The selection equation estimates the probability of observing the outcome event with a probit serving as the link. A logit link can be used in the selection equation, but a probit link has been recommended due to its simplicity in constructing the outcome and selection equations' error variance-covariance matrix (Miranda and Rabe-Hesketh 2006). The outcome equation is modeled to the values of the outcome conditioned on selection.…”

“…Also, the parameter r 2 ''determines the amount of overdispersion in the counts'' (Miranda and Rabe-Hesketh 2006).…”

“…Still, the long-term morbidity-in the case of severe sepsis, a count of hospital readmissions in the first year after hospital discharge-can only be observed if a patient survives the initial sample selection process of in-hospital mortality. Heckman (1978) showed that applying traditional regression techniques to data with a selection process will result in biased and inconsistent estimators if the unobserved error factors in the selection process are correlated with unobserved error factors in the response (Miranda and Rabe-Hesketh 2006). Further, we are interested in the application of a ranking scheme for hospitals based on their long-term morbidity effects and the extent to which hospital processes that improve short-term mortality are correlated with hospital processes that improve long-term morbidity.…”

The psychological impact of prosthodontic treatment—a discrete response modelling approach

“…In particular, two categories measure psychological components of oral health-related quality of life. The according 11 questions detect psychological discomfort (items [19][20][21][22][23] and psychological disability (items 33-38).…”

“…Hence, the use of ML or simulated ML techniques appears superior. For instance, generalised linear latent and mixed models (gllamm) follow the ML approach by performing two sequential estimation procedures [19].…”