Penalized variable selection and modeling: application of h-likelihood, joint-GLM and HGLM methods to modeling crop yield in the three Northern regions of Ghana

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September, 2015
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This study proceeded on two paths; to select signi cant crop yield physical sup-port variables among many potential ones to be included in a model via penalized methods (LASSO, SCAD, H-Likelihood) and to also propose and demonstrate the excellent performance of higher levels and very recent extensions of the Gen-eralized Linear Models (GLM); Joint Generalized Linear Models (JGLM) and Hierarchical Generalized Linear Models (HGLM) in the global quest to develop-ing Statistical Models with highest model accuracy. The analyses is be based on raw data available at the regional Monitoring and Evaluation o ce of the Linking Farmers to Markets (FtM) project in Tamale - Ghana. Physical support (Fixed e ect) variables measured include; crop type, Financial Credit, Training, Study tour, Demonstrative Practicals, Networking Events, Post harvest Equip-ment, Number of farmers in the FBO and Plot size cultivated. Dependent variable measured is Total Crop Yield whereas the regions and the particular communi-ties were treated as Random variables. After the highly rigorous processes of data analysis the study concluded that, the H-Likelihood method of penalized variable selection performs both selection of signi cant variables and estimation of their coe cients simultaneously with the least penalize cross-validated errors compared to the SCAD and the LASSO. In modelling the e ects of xed physi-cal support services given to farmer based organizations on crop yield, the GLM with assumed xed dispersion will not be recommended by this study. The study concludes that the proposed modelling of both mean and dispersion (Joint-GLM) improves the quality of the models signi cantly. In the case of both xed and random e ects, the, HGLM 2 is highly recommended. This study concludes that the HGLM 2 performs far better, gives a more tting model and improves the quality of the crop yield models signi cantly. The study recommends that delib-erate e ort be put into strengthening the Agricultural support systems as a form of strategy for increasing crop production in Northern Ghana.
A thesis submitted to The Department of Mathematics, Kwame Nkrumah University of Science And Technology in partial fulfilment of the requirement for the degree Of Doctor of Philosophy in Mathematical Statistics, 2015