Model-based clustering using Bayesian approach for binary panel Probit models

1. Researchpaper Model-Based Clustering using Bayesian Approach For Binary Panel Probit Models Tags : Statswork | Statistical Analysis | Probit Models | Regression Model | MixedModels | Cross-Validation | Posterior Distribution | Generalized Linear MixedModels ResearchPlanning| Data Collection| SemanticAnnotation| | BioStatistics |Econometrics Copyright © 2019 Statswrok. All rightsreserved

2. BayesianModelling In common Statistical Analysis, the classical estimation for various situations may be invalid, in the sense that it may be lead to misinterpretations. In Bayesian paradigm, each explanatory variable are assumed to be a random variables. With the advent of computational practice, Bayesian modelling becomes a interesting area of research in all the field ofscience. 01 03 05 02 04 It involves formulating a suitable prior distribution for the data under study and result will yield in a posteriordistribution. To deliver more appropriate results for the study, Bayesian paradigmshave emerged. ResearchPlanning| Data Collection| SemanticAnnotation| | BioStatistics |Econometrics Copyright © 2019 Statswrok. All rightsreserved

3. ProbitModel A probit model is a type of Regression Modelin which the response variable can take only binary outcomes (eg. yes or no, married or unmarried, male or female,etc.,). Generally, Probit model are considered as class of Generalized Linear Mixed Modelsespecially in the panelstudy. ResearchPlanning| Data Collection| SemanticAnnotation| | BioStatistics |Econometrics Copyright © 2019 Statswrok. All rightsreserved

4. ProbitModelIssues Endogeneity and Heterogeneity in the probit or logit models are an important issue in estimating the variables since it estimates the cumulativefunctions. Heterogeneity especially in non-linear model yields an attention to the researchers in recent years to provide better estimates to thevariables. ResearchPlanning| Data Collection| SemanticAnnotation| | BioStatistics |Econometrics Copyright © 2019 Statswrok. All rightsreserved

5. ProbitModelUsingBayesianPerspective An approach of using marginal likelihood and across-validation technique is adopted to identify the number of clusters and a simulation study is adopted to assess these approaches in Aßmann and Hogrefe(2011). Bayesian estimation can beused to estimate even smaller sample size & identifies unknown or uncertain parameters through a PosteriorDistribution. Bayesian flavour has been increasing inprobit model to provide appropriateresults. 03 01 02 04 05 Clustering approach isserved as a supporting tool for modelling the latent heterogeneity in the probit models. Literature is abundant for estimating the latent heterogeneity through clustering approachusing fixed and randomeffects. ResearchPlanning| Data Collection| SemanticAnnotation| | BioStatistics |Econometrics Copyright © 2019 Statswrok. All rightsreserved

6. ILLUSTRATIVE EXAMPLE ResearchPlanning| Data Collection| SemanticAnnotation| | BioStatistics |Econometrics Copyright © 2019 Statswrok. All rightsreserved

7. The priors are chosen withnormal and dirichlet distribution for the parameters under study and are presented in the belowtable. The non-random andrandom cluster specification priors are used for thesimulation. Random coefficient specification is used for the empiricalstudy. ResearchPlanning| Data Collection| SemanticAnnotation| | BioStatistics |Econometrics Copyright © 2019 Statswrok. All rightsreserved

8. SimulationStudy Estimation procedures adopted for the simulation study are Gibbs sampling, MCMC sampling, and Bridgesampling using maximum likelihood and Cross- Validationtechnique and conducted eleven scenarios for thispurpose. 01 02 A comparison of the log-likelihood of the marginals and the out-of-sampleprediction is presented with cluster and stratified clusteringtechnique. ResearchPlanning| Data Collection| SemanticAnnotation| | BioStatistics |Econometrics Copyright © 2019 Statswrok. All rightsreserved

9. BayesianProbitModel Two cluster specific random effects (RE) specifications with uncorrelated and correlated random effects with stratified and unconditional probabilities are considered to model the latent heterogeneity using binary probit model using Bayesian estimation and the comparison results of the models are depicted in the belowtable. The proposed stratified clustering Bayesianprobit model is illustrated with a real time dataset from Bertschek and Lechner(1998). The data involves investments of 1270 competitive firms from the years 1984 to1988. The empirical study indicated that the proposed method provides better model specifications. Contd... ResearchPlanning| Data Collection| SemanticAnnotation| | BioStatistics |Econometrics Copyright © 2019 Statswrok. All rightsreserved

10. It is clear that random coefficient specification is preferred as normally described in Jefferys’ scale. Uncorrelated random effects shows a better characterization of latentheterogeneity. ResearchPlanning| Data Collection| SemanticAnnotation| | BioStatistics |Econometrics Copyright © 2019 Statswrok. All rightsreserved

11. DeterminationOfNo.OfClusters Stratified and non-stratified probabilities are used and it yields similar results in estimating via marginallikelihood. In the out-of-sample method, AUC measure indicated the better cluster strategy to use i.e the non-stratified clusters and the Bayesian estimation for the preferred specifications are tabulated and it concludes that the firm has no positiveeffect. The variables substantiate the effect of the firm innovation is that the log scale, investment and the firm size among the othervariables. ResearchPlanning| Data Collection| SemanticAnnotation| | BioStatistics |Econometrics Copyright © 2019 Statswrok. All rightsreserved

12. Summary The proposed stratified clustering technique yields better performance in different scenarios than compared with classical non-stratified clustering method. The issue of model selection under the latent heterogeneity is analyzed using the Bayesian probit model via clustering approach and the results of the study revealed that the model selection using marginal likelihood is preferred in Bayesian point ofview. 02 01 In out of sample method, the stratified clustering doesn’t give satisfactory results because of the AUC measure and concludes that there is a need for more appropriate methodology to give consistent results in model selection process. The illustrative example revealed that the there exists a strong evidence in capturing the latent clusters using this latent heterogeneitymethods. 03 04 ResearchPlanning| Data Collection| SemanticAnnotation| | BioStatistics |Econometrics Copyright © 2019 Statswrok. All rightsreserved

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