In binomial regression, a link function is used to join the linear predictor variables and the expectation of the response variable. This paper proposes a flexible link function from a new class of generalized logistic distribution, namely a flexible generalized logit (glogit) link. This approach considers both symmetric and asymmetric models, including the cases of lighter and heavier tails, as compared to standard logistic. The glogit is created from the inverse cumulative distribution function of the exponentiated-exponential logistic (EEL) distribution. Using a Bayesian framework, we conduct a simulation study to investigate the model performance compared to the most commonly used link functions, e.g., logit, probit, and complementary log–log. Furthermore, we compared the proposed model with several other asymmetric models using two previously published datasets. The results show that the proposed model outperforms the existing ones and provides flexibility fitting the experimental dataset. Another attractive aspect of the model are analytically tractable and can be easily implemented under a Bayesian approach.

Classical linear regression is inadequate when the response variable is the number of success in a sequence of experiments. However, the binomial regression is considered more suitable. Binomial regression can be analyzed through the Generalized Linear Model (GLM) with a specifics link functions. Some of link functions usually used in binomial regressions are logit, probit, and complimentary log-log (cloglog). Both logit and probit are symmetrical links functions, while cloglog is asymmetrical. This study aims to compare all three link functions and evaluate them by employing the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) index. All three link function will be applied for binomial regression models using simulation and real data on school drop-out rates in East Java Indonesia. Based on the AIC and BIC index, it is evidenced that the cloglog gives the best performance than the logit and probit link function for the school drop-out rates model. Therefore, this case is considered appropriate using the asymmetrical assumptions.

General Regression Neural Network (GRNN) has been applied in a large number of forecasting/prediction problem. Generally, there are two types of GRNN: GRNN which is based on kernel density; and Mixture Based GRNN (MBGRNN) which is based on adaptive mixture model. The main problem on GRNN modeling lays on how its parameters were estimated. In this paper, we propose Bayesian approach and its computation using Markov Chain Monte Carlo (MCMC) algorithms for estimating the MBGRNN parameters. This method is applied in simulation study. In this study, its performances are measured by using MAPE, MAE and RMSE. The application of Bayesian method to estimate MBGRNN parameters using MCMC is straightforward but it needs much iteration to achieve convergence.