A response function is an essential part of any generalized linear model, but its choice
\nis rarely questioned. In particular, if the modeled expected value is restricted to be
\ngreater than zero, the choice often falls on the exponential function. Even for a response
\nvariable, for which the exponential function corresponds to the canonical link, there is
\nno indication that this is the true response function in general. Therefore, we propose to
\ntake the softplus function as response function into consideration. The softplus function,
\nwhich is technically used in the context of neural networks, enables the modeling of the
\nconditional mean in an additive way and therefore ensures a linear interpretation of the
\nregression coefficients while respecting the positivity boundary of the conditional mean
\nat the same time. The central research question to be discussed in this study is: Does
\nthe softplus activating function represent an adequate substitute of the commonly used
\nlog-link with an application to infectious diseases? In the first step, a simulation study
\ngives insight into the robustness of the estimated coefficients under various circumstances.
\nFurthermore, the framework for the analysis of multivariate infection disease data yield
\nby Held et al. (2005) is self-implemented via the open source software R. By doing so,
\nthe softplus function is introduced to the model class applied. The estimation results
\nfrom Held et al. (2005) are reproduced and compared to those concerning the softplus
\nlink function with respect to the predictive quality. One-step-ahead-predictions build the
\nbasis for mean-squared prediction errors and coverage frequencies of the upper prediction
\nlimits. The results have been obtained using general optimisation routines via maximum
\nlikelihood estimation.<\/p>\n","protected":false},"excerpt":{"rendered":"
Challenging the commonly used log-link in statistical models for count data with an application to infectious disease data A response function is an essential part of any generalized linear model, […]<\/p>\n","protected":false},"author":335,"featured_media":0,"template":"","meta":{"_tribe_events_status":"","_tribe_events_status_reason":"","footnotes":""},"tags":[],"tribe_events_cat":[44],"class_list":["post-727","tribe_events","type-tribe_events","status-publish","hentry","tribe_events_cat-kolloquium-de","cat_kolloquium-de"],"_links":{"self":[{"href":"https:\/\/www.hsu-hh.de\/statistik\/wp-json\/wp\/v2\/tribe_events\/727","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.hsu-hh.de\/statistik\/wp-json\/wp\/v2\/tribe_events"}],"about":[{"href":"https:\/\/www.hsu-hh.de\/statistik\/wp-json\/wp\/v2\/types\/tribe_events"}],"author":[{"embeddable":true,"href":"https:\/\/www.hsu-hh.de\/statistik\/wp-json\/wp\/v2\/users\/335"}],"version-history":[{"count":1,"href":"https:\/\/www.hsu-hh.de\/statistik\/wp-json\/wp\/v2\/tribe_events\/727\/revisions"}],"predecessor-version":[{"id":728,"href":"https:\/\/www.hsu-hh.de\/statistik\/wp-json\/wp\/v2\/tribe_events\/727\/revisions\/728"}],"wp:attachment":[{"href":"https:\/\/www.hsu-hh.de\/statistik\/wp-json\/wp\/v2\/media?parent=727"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.hsu-hh.de\/statistik\/wp-json\/wp\/v2\/tags?post=727"},{"taxonomy":"tribe_events_cat","embeddable":true,"href":"https:\/\/www.hsu-hh.de\/statistik\/wp-json\/wp\/v2\/tribe_events_cat?post=727"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}