Linear regression with special coefficient features attained via parameterization in exponential, logistic, and multinomial–logit forms

Multiple linear regression with special properties of its coefficients parameterized by exponent, logit, and multinomial functions is considered. To obtain always positive coefficients the exponential parameterization is applied. To get coefficients in an assigned range, the logistic parameterization is used. Such coefficients permit us to evaluate the impact of individual predictors in the model. The coefficients obtained by the multinomial–logit parameterization equal the shares of the predictors, which is useful for interpretation of their influence. The considered regression models are constructed by nonlinear optimization techniques, have stable solutions and good quality of fit, have simple structure of the linear aggregates, demonstrate high predictive ability, and suggest a convenient way to identify the main predictors.