Ridge estimation strategies for the simplex regression model with different link functions: simulation and applications

When the response variable is in the form of ratios and proportions, then the simplex regression model (SRM) is used. The unknown parameters of the SRM are estimated using the maximum likelihood estimation (MLE) method. In the SRM, when the explanatory variables are correlated, the MLE does not provide accurate results. So, we need an alternative method to the MLE to cope with the problem of multicollinearity. The most popular alternative method is the ridge regression (RR). So, we propose the RR method for the SRM called the simplex ridge regression estimator (SRRE). Moreover, this study also compares the performance of different link functions for the estimation of the SRM with correlated regressors. Furthermore, we propose different ridge parameters for the SRRE and compare the SRRE with these ridge parameters and the MLE under different link functions. To assess the performance of these estimators, we use the mean squared error (MSE) as an evaluation criterion. For numerical evaluation, we consider the simulation study and real-life examples. The results show that the SRRE with proposed ridge parameters outperforms the MLE in the presence of multicollinearity. Furthermore, the SRRE with probit link and neglog link function provides better results as compared to other link functions.