Using the Softplus Function to Construct Alternative Link Functions in Generalized Linear Models and Beyond

11/28/2021
by   Paul F. V. Wiemann, et al.
0

Response functions linking regression predictors to properties of the response distribution are fundamental components in many statistical models. However, the choice of these functions is typically based on the domain of the modeled quantities and is not further scrutinized. For example, the exponential response function is usually assumed for parameters restricted to be positive although it implies a multiplicative model which may not necessarily be desired. Consequently, applied researchers might easily face misleading results when relying on defaults without further investigation. As an alternative to the exponential response function, we propose the use of the softplus function to construct alternative link functions for parameters restricted to be positive. As a major advantage, we can construct differentiable link functions corresponding closely to the identity function for positive values of the regression predictor, which implies an quasi-additive model and thus allows for an additive interpretation of the estimated effects by practitioners. We demonstrate the applicability of the softplus response function using both simulations and real data. In four applications featuring count data regression and Bayesian distributional regression, we contrast our approach to the commonly used exponential response function.

READ FULL TEXT

page 10

page 22

page 23

research
02/19/2020

Linear Regression Models in Epidemiology

The paper proposes to analyze epidemiological data using regression mode...
research
02/26/2021

Cholesky-based multivariate Gaussian regression

Multivariate Gaussian regression is embedded into a general distribution...
research
07/30/2020

Skewed link regression models for imbalanced binary response with applications to life insurance

For a portfolio of life insurance policies observed for a stated period ...
research
05/18/2016

Online Algorithms For Parameter Mean And Variance Estimation In Dynamic Regression Models

We study the problem of estimating the parameters of a regression model ...
research
10/05/2018

Modeling data with zero inflation and overdispersion using GAMLSSs

Count data with high frequencies of zeros are found in many areas, speci...
research
07/05/2020

Generalized additive models to capture the death rates in Canada COVID-19

To capture the death rates and strong weekly, biweekly and probably mont...
research
09/20/2020

Skewed probit regression – Identifiability, contraction and reformulation

Skewed probit regression is but one example of a statistical model that ...

Please sign up or login with your details

Forgot password? Click here to reset