Abstract
Previous studies on household poverty classification have commonly dichotomized the dependent variable into non-poor or poor, and used binary models. This way, the most extreme categories of poverty, which are usually the main targets of interventions, are not identified. Moreover, expenditure data used to describe poverty is typically collected at several locations over large geographical domains. Local disturbances introduce spatial correlation, implying that global parameters (obtained via independence assumptions of standard statistical methods) cannot adequately describe site-specific conditions of the data. The objective, therefore, is to describe an appropriate method for ordered categorical data collected at geo-referenced locations over large geographical space. To achieve this, a model named Spatial Cumulative Probit Model (SCPM) was proposed. This model classified household poverty in an ordinal spatial framework. Bayesian inference was performed on data sampled by Markov Chain Monte Carlo (MCMC) algorithms. A test of model adequacy show that the SCPM is unbiased and attains a lower misclassification rate of 14.43% than the simple Cumulative Probit (CP) model with misclassification rate of 16.5% that ignores spatial dependence in the data. Overall, ‘savannah ecological zone’, ‘polygamous marriage’ and ‘rural location’ were the most powerful predictors of extreme poverty in Ghana. The prediction map, created by this study, identified positive correlation with respect to ‘poor’ and ‘extremely poor’ categories. Results of the model in this study can be considered a category and site-specific report that identifies all levels and sites of poverty for easy targeting, thus, avoiding the blanket approach that prefers the one-fits-it-all solution to the problem of poverty. Analysis was based on the Ghana Living Standards Survey (GLSS 6) dataset.
Highlights
Generalized Linear Models (GLMs) introduced by Nelder and Wedderburn [1] have commonly been used to model non-Gaussian data
Beginning with Terza [4], analysts have questioned the adequacy of the simple zero-mean, homoscedastic CP model from this perspective. This is Richard Puurbalanta: Spatial Cumulative Probit Model: An Application to Poverty Classification and Mapping important because generally, most applications in regional science rely heavily on data collected from different locations, and over large geographical areas
A Spatial Cumulative Probit Model (SCPM) was fitted to the GLSS data in Ghana using Bayesian estimation discussed in Section 2.1 together with the simple aspatial CP model
Summary
Generalized Linear Models (GLMs) introduced by Nelder and Wedderburn [1] have commonly been used to model non-Gaussian data. GLMs assume that the response data are drawn from some statistical distribution other than the Gaussian distribution [2]. Model errors require a specific statistical distribution that is paired with a link function that relates the linear function of predictors to some function of the response. When dealing with an ordered response, the focus of this study, a probit link function is recommended. The probit approach hypothesizes the existence of a latent continuously varying trend that underlies the ranking of the ordered outcomes [2, 3]. The form of the ordered model requires the latent variable to predict class membership based on the theory of cumulative functions.
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