Implementation of Beta Regression Models on Concrete Strength Data with the Consideration of Variable Scale Parameters

Abstract

The nature of the variable in many regression usages is the response in terms of rate and ratio. As in economics, economists seek to understand the relationship between growth or unemployment rates and several other economic variables. Logistic and Probit models are usually used to model data with a variation range (0,1). However, Logistic and Probit models are not suitable for rate or ratio data modeling due to their concentration in a certain sub-range of their variation ranges. Regarding the high flexibility of the beta distribution for this type of data, a proper and efficient model is a regression based on beta distribution, which is called beta regression. This paper introduces the model and estimates its parameters. Then, we obtain an asymptotic distribution of estimators and evaluate the performance of the proposed model based on the MSE index using simulation. In the end, we will show the use of the model in a real example of concrete strength data.