A Comparison of Bayesian and Sampling Theory Inferences in a Probit Model

HE PROBIT MODEL IS A POPULAR DEVICE for explaining binary choice decisions in econometrics. It has been used to describe choices such as labor force participation, travel mode, home ownership, and type of education. These and many more examples can be found in papers by Amemiya (1981) and Maddala (1983). Given the contribution of economics towards explaining such choices, and given the nature of data that are collected, prior information on the relationship between a choice probability and several explanatory variables frequently exists. Bayesian inference is a convenient vehicle for including such prior information. Given the increasing popularity of Bayesian inference it is useful to ask whether inferences from a probit model are sensitive to a choice between Bayesian and sampling theory techniques. Of interest is the sensitivity of inference on coefficients, probabilities, and elasticities. We consider these issues in a model designed to explain choice between fixed and variable interest rate mortgages. Two Bayesian priors are employed: a uniform prior on the coefficients, designed to be noninformative for the coefficients, and an inequality restricted prior on the signs of the coefficients. We often know, a priori, whether increasing the value of a particular explanatory variable will have a positive or negative effect on a choice probability. This knowledge can be captured by using a prior probability density function (pdf) that is truncated to be positive or negative. Thus, three sets of results are compared:those from maximum likelihood (ML) estimation, those from Bayesian estimation with an unrestricted uniform prior on the coefficients, and those from Bayesian estimation with a uniform prior truncated to accommodate inequality restrictions on the coefficients.

A bayesian spatial individual effects probit model of the 2010 UK general election

The Conservative Party emerged from the 2010 United Kingdom General Election as the largest single party, but their support was not geographically uniform. In this paper, we estimate a hierarchical Bayesian spatial probit model that tests for the presence of regional voting effects. This model allows for the estimation of individual region-specic effects on the probability of Conservative Party success, incorporating information on the spatial relationships between the regions of the mainland United Kingdom. After controlling for a range of important covariates, we find that these spatial relationships are significant and that our individual region-specic effects estimates provide additional evidence of North-South variations in Conservative Party support.

Forecasting US bond default ratings allowing for previous and initial state dependence in an ordered probit model

In this paper we investigate the ability of a number of different ordered probit models to predict ratings based on firm-specific data on business and financial risks. We investigate models based on momentum, drift and ageing and compare them against alternatives that take into account the initial rating of the firm and its previous actual rating. Using data on US bond issuing firms rated by Fitch over the years 2000 to 2007 we compare the performance of these models in predicting the rating in-sample and out-of-sample using root mean squared errors, Diebold-Mariano tests of forecast performance and contingency tables. We conclude that initial and previous states have a substantial influence on rating prediction.

Obesity and the incidence of chronic diseases: a seemingly unrelated probit approach

Western societies can reduce avoidable mortality and morbidity by better understanding the relationship between obesity and chronic disease. This paper examines the joint determinants of obesity and of heart disease, diabetes, hypertension, and elevated cholesterol. It analyzes a broadly representative Spanish dataset, the 1999 Survey on Disabilities, Impairments and Health Status, using a health production theoretical framework together with a seemingly unrelated probit model approach that controls for unobserved heterogeneity and endogeneity. Its findings provide suggestive evidence of a positive and significant, although specification-dependent, association between obesity and the prevalence of chronic illness

Obesity and the incidence of chronic diseases: a seemingly unrelated probit approach

Western societies can reduce avoidable mortality and morbidity by better understanding the relationship between obesity and chronic disease. This paper examines the joint determinants of obesity and of heart disease, diabetes, hypertension, and elevated cholesterol. It analyzes a broadly representative Spanish dataset, the 1999 Survey on Disabilities, Impairments and Health Status, using a health production theoretical framework together with a seemingly unrelated probit model approach that controls for unobserved heterogeneity and endogeneity. Its findings provide suggestive evidence of a positive and significant, although specification-dependent, association between obesity and the prevalence of chronic illness

Ordered probit regression analysis of the effect of brand name on beer acceptance by consumers

Ordered probit regression was used to analyze data of sensory acceptance tests designed to study the effect of brand name on the acceptability of beer samples. Eight different brands of Pilsen beer were evaluated by 101 consumers in two sessions of acceptance tests: blind evaluation and brand information test. Ordered probit regression, although a relatively sophisticated technique compared to others used to analyze sensory data, was chosen to enable the observation of consumers' behavior using graphical interpretations of estimated probabilities plotted against hedonic scales. It can be concluded that brands B, C, and D had a positive effect on the sensory acceptance of the product, whereas brands A, F, G, and H had a negative influence on consumers' evaluation of the samples. On the other hand, brand E had little influence on consumers' assessment.

Equacionamento da qualidade inicial de sementes de milho e soja para aplicação no modelo de probit

Objetivou-se, neste trabalho, equacionar a qualidade inicial das sementes (Ki), utilizada no modelo de probit, para a previsão da longevidade de sementes de milho (Zea mays) e soja (Glycine max), em função do resultado dos testes iniciais de germinação e vigor. Onze lotes de sementes de diferentes cultivares de milho e de soja foram submetidos aos testes de germinação (TG), envelhecimento acelerado (TEA), frio sem solo (TF), para milho, e tetrazólio (TZ), para soja, e a testes de envelhecimento acelerado, com condições constantes do grau de umidade e da temperatura das sementes, para determinar o valor de Ki. Dados da literatura contendo resultados de testes de TEA e TF para milho e TEA e TZ para soja também foram usados nesta pesquisa. Conduziram-se análises de regressão linear simples e múltipla para equacionar: a) Ki em função de TG e TEA para milho e soja, b) TEAm (envelhecimento acelerado do milho) em função de TF; c) TEAs (envelhecimento acelerado da soja) em função de TZ. As equações obtidas foram: Ki = 0,4230 + 0,4464 TG + 0,4131 TEA TEA M = - 0,4408 + 1,214 TF TEA S = - 0,1872 + 0,9875 TZ. A equação de Ki apresentou coeficiente de determinação ajustado (r²) de 0.80 (d.p. 0.18 probit e parâmetros significantes em p < 0.01, p < 0.02 e p < 0.05, respectivamente). A equação de TEAm apresentou r² de 0.80 (d.p. 0.24 probit e parâmetros significantes em p < 0.002). A equação de TEAs apresentou r² de 0.84 (d.p. 0.18 probit e parâmetros significantes em p < 0.005). O valor de Ki pode ser equacionado em função do resultado dos testes iniciais de germinação e vigor para milho e soja (TEA ou TF para milho e TEA ou TZ para soja).

Forecasting UK real estate cycle phases with leading indicators: a probit approach

This paper examines the significance of widely used leading indicators of the UK economy for predicting the cyclical pattern of commercial real estate performance. The analysis uses monthly capital value data for UK industrials, offices and retail from the Investment Property Databank (IPD). Prospective economic indicators are drawn from three sources namely, the series used by the US Conference Board to construct their UK leading indicator and the series deployed by two private organisations, Lombard Street Research and NTC Research, to predict UK economic activity. We first identify turning points in the capital value series adopting techniques employed in the classical business cycle literature. We then estimate probit models using the leading economic indicators as independent variables and forecast the probability of different phases of capital values, that is, periods of declining and rising capital values. The forecast performance of the models is tested and found to be satisfactory. The predictability of lasting directional changes in property performance represents a useful tool for real estate investment decision-making.