Statistical analysis of the solar diffuse fraction radiation using regression analysis of longitudinal data in India

In this study, the validity of the estimation of a single regression equation for the diffuse fraction across 22 stations in India using the two parameters: the clearness index and the sunshine ratio is tested. The homogeneity test based on Fisher's statistics was applied to test the homogeneity of the estimated parameters across all stations. The results showed that the p-value at the level of 5% for each model is smaller than 0.05, indicating that all stations were heterogeneous. The Hierarchical Cluster Analysis (HCA) was used to classify the data into homogenous clusters. The results of HCA indicated that the longitudinal data were divided into four main clusters. For each cluster, the regression analysis was applied based on the longitudinal data then, the fixed effects model (FEM) and the random-effects model (REM) were used for the evaluation. Further, the Hausman test was applied to choose between the fixed effects model and the random-effects model. Finally, the results showed that the four best regression models were found for the selected stations in the study area.