Em Algorithm for MLE of a Probit Model for Multiple Ordinal Outcomes

The correlated probit model is frequently used for multiple ordered data since it allows to incorporate seamlessly different correlation structures. The estimation of the probit model parameters based on direct maximization of the limited information maximum likelihood is a numerically intensive procedure. We propose an extension of the EM algorithm for obtaining maximum likelihood estimates for a correlated probit model for multiple ordinal outcomes. The algorithm is implemented in the free software environment for statistical computing and graphics R. We present two simulation studies to examine the performance of the developed algorithm. We apply the model to data on 121 women with cervical or endometrial cancer. Patients developed normal tissue reactions as a result of post-operative external beam pelvic radiotherapy. In this work we focused on modeling the effects of a genetic factor on early skin and early urogenital tissue reactions and on assessing the strength of association between the two types of reactions. We established that there was an association between skin reactions and polymorphism XRCC3 codon 241 (C>T) (rs861539) and that skin and urogenital reactions were positively correlated. ACM Computing Classification System (1998): G.3.

Anisotropic correlated electron model associated with the Temperley-Lieb algebra

We present an anisotropic correlated electron model on a periodic lattice, constructed from an R-matrix associated with the Temperley-Lieb algebra. By modification of the coupling of the first and last sites we obtain a model with quantum algebra invariance.

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.

Bayesian analysis of an inverse Gaussian correlated frailty model

In survival analysis frailty is often used to model heterogeneity between individuals or correlation within clusters. Typically frailty is taken to be a continuous random effect, yielding a continuous mixture distribution for survival times. A Bayesian analysis of a correlated frailty model is discussed in the context of inverse Gaussian frailty. An MCMC approach is adopted and the deviance information criterion is used to compare models. As an illustration of the approach a bivariate data set of corneal graft survival times is analysed. (C) 2006 Elsevier B.V. All rights reserved.

Intellectual property and competition as complementary policies: a test using an ordered probit model

Este Artigo Testa a Proposição da Teoria Econômica de que Propriedade Intelectual e Defesa da Concorrência são Políticas Complementares. um Modelo Probit Ordenado é Utilizado para Estimar os Efeitos Marginais do Uso e Qualidade do Enforcement dos Direitos de Propriedade Intelectual em uma Medida da Gravidade dos Problemas Relacionados À Concorrência. os Resultados Obtidos Reforçam a Noção de que as Políticas de Concorrência e Propriedade Intelectual não são Contraditórias.

An analysis of quit and dismissal determinants between 1988 and 1999 using the bivariate probit model

Excessive labor turnover may be considered, to a great extent, an undesirable feature of a given economy. This follows from considerations such as underinvestment in human capital by firms. Understanding the determinants and the evolution of turnover in a particular labor market is therefore of paramount importance, including policy considerations. The present paper proposes an econometric analysis of turnover in the Brazilian labor market, based on a partial observability bivariate probit model. This model considers the interdependence of decisions taken by workers and firms, helping to elucidate the causes that lead each of them to end an employment relationship. The Employment and Unemployment Survey (PED) conducted by the State System of Data Analysis (SEADE) and by the Inter-Union Department of Statistics and Socioeconomic Studies (DIEESE) provides data at the individual worker level, allowing for the estimation of the joint probabilities of decisions to quit or stay on the job on the worker’s side, and to maintain or fire the employee on the firm’s side, during a given time period. The estimated parameters relate these estimated probabilities to the characteristics of workers, job contracts, and to the potential macroeconomic determinants in different time periods. The results confirm the theoretical prediction that the probability of termination of an employment relationship tends to be smaller as the worker acquires specific skills. The results also show that the establishment of a formal employment relationship reduces the probability of a quit decision by the worker, and also the firm’s firing decision in non-industrial sectors. With regard to the evolution of quit probability over time, the results show that an increase in the unemployment rate inhibits quitting, although this tends to wane as the unemployment rate rises.

Study on Robustness of Correlated Frailty Model

2000 Mathematics Subject Classifi cation: 62J12.

Implementation of the EM Algorithm for Maximum Likelihood Estimation of a Random Effects Model for One Longitudinal Ordinal Outcome

2010 Mathematics Subject Classification: 62J99.

Application of a Bivariate Probit Model to Investigate the Intended Evacuation from Hurricane

With evidence of increasing hurricane risks in Georgia Coastal Area (GCA) and Virginia in the U.S. Southeast and elsewhere, understanding intended evacuation behavior is becoming more and more important for community planners. My research investigates intended evacuation behavior due to hurricane risks, a behavioral survey of the six counties in GCA under the direction of two social scientists with extensive experience in survey research related to citizen and household response to emergencies and disasters. Respondents gave answers whether they would evacuate under both voluntary and mandatory evacuation orders. Bivariate probit models are used to investigate the subjective belief structure of whether or not the respondents are concerned about the hurricane, and the intended probability of evacuating as a function of risk perception, and a lot of demographic and socioeconomic variables (e.g., gender, military, age, length of residence, owning vehicles).

Twisted quantum affine superalgebra U-q[sl(2/2)((2))], U-q[osp(2/2)] invariant R-matrices and a new integrable electronic model

We describe the twisted affine superalgebra sl(2\2)((2)) and its quantized version U-q[sl(2\2)((2))]. We investigate the tensor product representation of the four-dimensional grade star representation for the fixed-point sub superalgebra U-q[osp(2\2)]. We work out the tensor product decomposition explicitly and find that the decomposition is not completely reducible. Associated with this four-dimensional grade star representation we derive two U-q[osp(2\2)] invariant R-matrices: one of them corresponds to U-q [sl(2\2)(2)] and the other to U-q [osp(2\2)((1))]. Using the R-matrix for U-q[sl(2\2)((2))], we construct a new U-q[osp(2\2)] invariant strongly correlated electronic model, which is integrable in one dimension. Interestingly this model reduces in the q = 1 limit, to the one proposed by Essler et al which has a larger sl(2\2) symmetry.

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