Limited and Censored Dependent Variable Models

Abstract

In regional science, many attributes, either social or natural, can be categorical. For example, choices of travel mode, presidential election outcomes, or quality of life can all be measured (and/or coded) as discrete responses, dependent on various influential factors. Some attributes, although continuous, are subject to truncation or censoring. For example, household income, when reported, tends to be censored, and only boundary values of a range are obtained. Such categorical and censored variables can be analyzed using econometric models that are established based on the concept of “unobserved/latent dependent variable.”

The previous examples also share another common feature: when data is collected in a spatial setting, they are all inevitably influenced by spatial effects, either spatial variation or spatial interaction. In contrast to panel data or time-series data, such variation or dependencies are two-dimensional, making it even more complicated. The need for investigating such limited and censored variables in a spatial context compels the quest for rigorous statistical methods.

This chapter introduces existing methods that are developed to analyze limited and censored dependent variables while considering the spatial effects. Different model specifications are discussed, with an emphasis on discrete response models and censored data models. Different types of spatial effects and corresponding ways to address them are then discussed. In general, when the spatial variation is of major concern, geographically weighted regression is preferred. When the spatial dependency is the primary interest, spatial filtering and spatial regression should be chosen. Techniques popularly used to estimate spatial limited variable models, including maximum simulated likelihood estimation, composite marginal likelihood estimation, and Bayesian approach, are also introduced and briefly compared.