Ioannis Ntzoufras

Analysis of sports data by using bivariate Poisson models

Summary. Models based on the bivariate Poisson distribution are used for modelling sports data. Independent Poisson distributions are usually adopted to model the number of goals of two competing teams. We replace the independence assumption by considering a bivariate Poisson model and its extensions. The models proposed allow for correlation between the two scores, which is a plausible assumption in sports with two opposing teams competing against each other. The effect of introducing even slight correlation is discussed. Using just a bivariate Poisson distribution can improve model fit and prediction of the number of draws in football games. The model is extended by considering an inflation factor for diagonal terms in the bivariate joint distribution. This inflation improves in precision the estimation of draws and, at the same time, allows for overdispersed, relative to the simple Poisson distribution, marginal distributions. The properties of the models proposed as well as interpretation and estimation procedures are provided. An illustration of the models is presented by using data sets from football and water-polo.

Bayesian variable and link determination for generalised linear models

In this paper, we describe full Bayesian inference for generalised linear models where uncertainty exists about the structure of the linear predictor, the linear parameters and the link function. Choice of suitable prior distributions is discussed in detail and we propose an efficient reversible jump Markov chain Monte-Carlo algorithm for calculating posterior summaries. We illustrate our method with two data examples.

Bayesian Modelling of Outstanding Liabilities Incorporating Claim Count Uncertainty

Abstract This paper deals with the prediction of the amount of outstanding automobile claims that an insurance company will pay in the near future. We consider various competing models using Bayesian theory and Markov chain Monte Carlo methods. Claim counts are used to add a further hierarchical stage in the model with log-normally distributed claim amounts and its corresponding state space version. This way, we incorporate information from both the outstanding claim amounts and counts data resulting in new model formulations. Implementation details and illustrations with real insurance data are provided.

On the use of marginal posteriors in marginal likelihood estimation via importance sampling

The efficiency of a marginal likelihood estimator where the product of the marginal posterior distributions is used as an importance sampling function is investigated. The approach is generally applicable to multi-block parameter vector settings, does not require additional Markov Chain Monte Carlo (MCMC) sampling and is not dependent on the type of MCMC scheme used to sample from the posterior. The proposed approach is applied to normal regression models, finite normal mixtures and longitudinal Poisson models, and leads to accurate marginal likelihood estimates.

Mixed handedness is associated with the Disorganization dimension of schizotypy in a young male population

Within the ASPIS (Athens Study of Psychosis Proneness and Incidence of Schizophrenia) we sought out to examine in accordance with previous reports if a deviation from dextrality is associated with an augmented endorsement of self rated schizotypal personality traits in a large population of 1129 young male army recruits. Schizotypal traits were assessed using the Schizotypal Personality Questionnaire and hand preference membership was determined by applying stringent criteria derived from the Annett Handedness Questionnaire and the Porac-Coren questionnaire of lateral preferences. By adopting three different definitions of hand preference membership, we confirmed an association between mixed handedness and increased schizotypal personality traits, and in particular with Disorganization schizotypy that encompasses aspects of self perceived difficulties in verbal communication. Non-verbal cognitive ability, as indexed by measurement of non-verbal IQ, sustained attention and working memory was not associated with hand preference. We argue that a deviation from normal cerebral lateralization, as indexed by mixed handedness, is associated with mild sub clinical language dysfunction, rather than non-verbal cognitive ability, and this might be relevant to the expression of psychosis phenotype.

Stochastic search variable selection for log-linear models

We develop a Markov chain Monte Carlo algorithm, based on ‘stochastic search variable selection’ (George and McCuUoch, 1993), for identifying promising log-linear models. The method may be used in the analysis of multi-way contingency tables where the set of plausible models is very large.

On Bayesian lasso variable selection and the specification of the shrinkage parameter

We propose a Bayesian implementation of the lasso regression that accomplishes both shrinkage and variable selection. We focus on the appropriate specification for the shrinkage parameter λ through Bayes factors that evaluate the inclusion of each covariate in the model formulation. We associate this parameter with the values of Pearson and partial correlation at the limits between significance and insignificance as defined by Bayes factors. In this way, a meaningful interpretation of λ is achieved that leads to a simple specification of this parameter. Moreover, we use these values to specify the parameters of a gamma hyperprior for λ. The parameters of the hyperprior are elicited such that appropriate levels of practical significance of the Pearson correlation are achieved and, at the same time, the prior support of λ values that activate the Lindley-Bartlett paradox or lead to over-shrinkage of model coefficients is avoided. The proposed method is illustrated using two simulation studies and a real dataset. For the first simulation study, results for different prior values of λ are presented as well as a detailed robustness analysis concerning the parameters of the hyperprior of λ. In all examples, detailed comparisons with a variety of ordinary and Bayesian lasso methods are presented.

Factorial composition of the Aggression Questionnaire: A multi-sample study in Greek adults

The primary aim of the current article was the evaluation of the factorial composition of the Aggression Questionnaire (AQ(29)) in the Greek population. The translated questionnaire was administered to the following three heterogeneous adult samples: a general population sample from Athens, a sample of young male conscripts and a sample of individuals facing problems related to substance use. Factor analysis highlighted a structure similar to the one proposed by Buss and Perry [Buss, A.F., Perry, M., 1992. The Aggression Questionnaire. Journal of Personality and Social Psychology 63, 452-459]. However, the refined 12-item version of Bryant and Smith [Bryant, F.B., Smith, B.D., 2001. Refining the architecture of aggression: a measurement model for the Buss-Perry Aggression Questionnaire. Journal of Research in Personality 35, 138-167] provided a better fit to our data. Therefore, the refined model was implemented in further analysis. Multiple group confirmatory factor analysis was applied in order to assess the variability of the 12-item AQ across gender and samples. The percentage of factor loading invariance between males and females and across the three samples defined above was high (higher than 75%). The reliability (internal consistency) of the scale was satisfactory in all cases. Content validity of the 12-item AQ was confirmed by comparison with the Symptom Check-List 90 Revised.

BAYESIAN VARIABLE SELECTION USING COST-ADJUSTED BIC, WITH APPLICATION TO COST-EFFECTIVE MEASUREMENT OF QUALITY OF HEALTH CARE

Summary of the RJMCMC cost-benefit search results in the p=14 case. (B) Comparison of the utility and RJMCMC methods in how their best models trade off costand predictive accuracy AModel Cost Posterior probability PO 1k X 1 +X 2 +X 3 +X 4 +X 5 +X 6 +X 7 +X 12 9.0 0.453 1.00X 1 +X 2 +X 3 +X 4 +X 5 +X 7 +X 12 7.5 0.415 1.09X 1 +X 2 +X 3 +X 4 +X 5 +X 6 +X 12 8.0 0.054 8.40X 1 +X 2 +X 3 +X 4 +X 5 +X 6 +X 7 8.5 0.031 14.72Bp Method Model Cost Median devianceLS CV 14RJMCMCX 1 +X 2 +X 3 +X 4 +X 5 +X 6 +X 7 +X 12 9.0 1654 −0.329X 1 +X 2 +X 3 +X 4 +X 5 +X 7 +X 12 7.5 1676 −0.333Utility X 1 +X 3 +X 4 +X 5 5.5 1726 −0.34283RJMCMCX 1 +X 2 +X 3 +X 5 +X 12 +X 46 +X 49 +X 51 +X 70 +X 78 7.5 1645 −0.327UtilityX 1 +X 3 +X 4 +X 12 +X 46 +X 49 +X 57 6.5 ∗ 1693 −0.336 ∗ This model had a higher cost than the best model with p=14 because the utility approachwas not optimizing on cost but on a utility-based cost-benefit tradeoff. in Table 1 that all of these variables had marginal posterior probability 0in the RJMCMC method); four more variables had identical star patterns;and the other four variables were chosen by both methods as important,differing only in how many stars they received. Table 5 uses a similar starsystem: two stars in columns 4 and 5 in this table signify membership in theglobally best model found by the utility and RJMCMC methods, respec-tively; one star in column 4 means that the variable appeared frequently inthe 100 best utility models [see Fouskakis and Draper (2008) for details],with one star in column 5 signifying that a variable often occurred in thehighest-posterior-probability RJMCMC models of Table 3. With p=83, theagreement between the two methods is also strong (although not as strongas with p=14): 60 variables were ignored by both methods, eight variableshad identical star patterns, three variables were chosen as important byboth methods but with different star patterns, 10 variables were marked asimportant by the utility approach and not by RJMCMC, and two variableswere singled out by RJMCMC and not by utility (this represents substantialagreement on the importance of 85% of the variables).Table 6 gives a summary of the RJMCMC search results with p=14 andexamines the cost-benefit tradeoffs of the utility and RJMCMC methods in

Monitoring and improving Greek banking services using Bayesian Networks: An analysis of mystery shopping data

Mystery shopping is a well known marketing technique used by companies and marketing analysts to measure quality of service, and gather information about products and services. In this article, we analyse data from mystery shopping surveys via Bayesian Networks in order to examine and evaluate the quality of service offered by the loan departments of Greek Banks. We use mystery shopping visits to collect information about loan products and services and, by this way, evaluate the customer satisfaction and plan improvement strategies that will assist banks to reach their internal standards. Bayesian Networks not only provide a pictorial representation of the dependence structure between the characteristics of interest but also allow to evaluate, interpret and understand the effects of possible improvement strategies.