English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Response functions linking regression predictors to properties of theresponse distribution are fundamental components in many statistical models.However, the choice of these functions is typically based on the domain of themodeled quantities and is not further scrutinized. For example, the exponentialresponse function is usually assumed for parameters restricted to be positivealthough it implies a multiplicative model which may not necessarily bedesired. Consequently, applied researchers might easily face misleading resultswhen relying on defaults without further investigation. As an alternative tothe exponential response function, we propose the use of the softplus functionto construct alternative link functions for parameters restricted to bepositive. As a major advantage, we can construct differentiable link functionscorresponding closely to the identity function for positive values of theregression predictor, which implies an quasi-additive model and thus allows foran additive interpretation of the estimated effects by practitioners. Wedemonstrate the applicability of the softplus response function using bothsimulations and real data. In four applications featuring count data regressionand Bayesian distributional regression, we contrast our approach to thecommonly used exponential response function.

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