The unilateral spatial autogressive process for the regular lattice two-dimensional spatial discrete data

This paper proposes a generalized framework to analyze spatial count data under a unilateral regular lattice structure based on thinning type models. We start from the simple spatial integer-valued auto-regressive model of order 1. We extend this model in certain directions. First, we consider various distributions as choices for the innovation distribution to allow for additional overdispersion. Second, we allow for use of covariate information, leading to a non-stationary model. Finally, we derive and use other models related to this simple one by considering simplification on the existing model. Inference is based on conditional maximum likelihood approach. We provide simulation results under different scenarios to understand the behaviour of the conditional maximum likelihood. A real data application is also provided. Remarks on how the results extend to other families of models are also given

Model misspecification effects in clustered count data analysis

Clustered count data are usually analysed using Poisson mixed models based on the assumptions of either gamma distributed or log-normal distributed random effects. As it is difficult to anticipate the true mixed model, the researchers tend to make an arbitrary choice between the assumption of gamma or log-normal distribution for the random effects. This arbitrary choice may not affect the estimation of the regression parameters of the model but the efficiency of the estimates of the variance component of the random effects may however be affected to a great extent. This paper addresses this issue by examining the misspecification effects of the distributional assumptions for the random effects in the clustered data.Clustered count data Mixed effects Quasi-likelihood Efficiency Regression effects Variance of the random effects

GMM versus GQL inferences for panel count data

It is well known that the likelihood inferences in dynamic mixed models for count data is extremely complicated. In this paper, we, first, develop a generalized method of moments (GMM) approach for the estimation of the parameters of such models. We then consider an alternative generalized quasi-likelihood (GQL) approach. The relative efficiency of the GQL approach to the GMM approach is examined by comparing the asymptotic variances of the GQL estimates of the parameters to the corresponding asymptotic variances of the GMM estimates.

On familial longitudinal Poisson mixed models with gamma random effects

Poisson mixed models are used to analyze a wide variety of cluster count data. These models are commonly developed based on the assumption that the random effects have either the log-normal or the gamma distribution. Obtaining consistent as well as efficient estimates for the parameters involved in such Poisson mixed models has, however, proven to be difficult. Further problem gets mounted when the data are collected repeatedly from the individuals of the same cluster or family. In this paper, we introduce a generalized quasilikelihood approach to analyze the repeated familial data based on the familial structure caused by gamma random effects. This approach provides estimates of the regression parameters and the variance component of the random effects after taking the longitudinal correlations of the data into account. The estimators are consistent as well as highly efficient.Multi-dimensional count data Mixed effects Quasilikelihood Efficiency Repeated count responses Regression effects Variance component of the random effects Longitudinal correlations

Modelling the Dependence Structure of MUR/USD and MUR/INR Exchange Rates using Copula

American Dollar (USD) and Indian Rupee (INR) play an important role in Mauritian economy. It is important to model the pattern of dependence in their co-movement with respect to Mauritian Rupee (MUR), as this may indicate the export-import behavior in Mauritius. However, it is known that distributions of exchange rates are usually non-normal and the use of linear correlation as a dependence measure is inappropriate. Moreover it is quite difficult to obtain the joint distribution of such random variables in order to specify the complete covariance matrix to measure their dependence structure. In this paper, we first identify the marginal distributions of the exchange rates of MUR against USD and INR and then select the best fitting copula model for the bivariate series. It is concluded that both the series are asymmetric and fat-tailed following hyperbolic distribution. Their dependence structure is appropriately modeled by t copula

Modelling Football Data Using a GQL Algorithm based on Higher Ordered Covariances.

The modelling of the number of goals scored by a football team has beenrarely studied in literature. This paper proposes a bivariate integer-valuedautoregressive process of order 1 (BINAR(1)) that models the first and secondhalf number of goals scored by a team in each league match. In this timeseries process, the innovations are considered to be bivariate Negative binomialssince the goals scored express some variability than its means underboth halves. However, a challenging issue is the estimation of the parametersof interest that include the vector of regression effects which influence thegoals, the over-dispersion coefficients and the cross and serial dependence parameters.As at date, the generalized quasi-likelihood equation is the mostsuitable to estimate these parameters as it does not require the likelihoodspecification while it yields equally efficient estimates as likelihood-based approaches.The estimation of the over-dispersion requires the construction ofhigh-ordered covariances which demands the working multivariate Gaussiannormality. This assumption, as proved in previous studies, is more robustthan the traditional Method of Moments. The BINAR(1) process is assessedon the Arsenal football data from the period 2005 to 2016