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Next, we built and compared multiple logistic regression models (LRM; i.e. GLM with binary response) fitted using: 1) true absences (as a control experiment), 2) completely random pseudo-absences, and 3) pseudo-absences selected from two-step approaches where unsuitable habitat was defined a priori from a profile method (BIOCLIM or ENFA).
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Generalized linear models were conducted with the "glm" function in the "stats" package for models with binary responses and with the "glm.nb" function in the "MASS" package for models with negative binomial responses (Venables and Ripley 2002) using the programming language and software environment, R, version 3.1.0 (R Core Team 2014).
These items were with binary responses (yes or no).
We chose to use a graded response scale based on the results of pilot studies comparing graded with binary responses, which showed that binary responses inflated positive responses and that patients had difficulty making choices on a binary scale.
Among group-discrimination techniques, logistic regression modelling (LRM), a particular branch of generalized linear models (GLM) for binary responses, remains the most widely used so far to predict the potential distributions of species [ 10].
We conducted the estimation and hypothesis testing using the SAS (version 9.1.3; SAS Institute Inc., Cary, NC) programming language (Proc mixed for continuous responses and Proc GLM mixed for binary responses).
With a binary response, either logit or probit transformation is used to convert the binary response into the probability of the positive outcome.
The analysis was carried out with the binary response being dead or survived.
With a binary response (K = 2) there obviously are no unknown threshold values.
If the items with a binary response pattern fit the Rasch model, they provide a Guttman-like response structure.
For binary response variables we used GLM with a binomial error distribution, and for discrete response variables (counts) we used GLM with a Poisson distribution controlled for overdispersion [56].
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