SEM analysis
To construct the SEM, we used generalized linear mixed models with a
negative binomial distribution to model overdispersion, using the
Bayesian brms package (Bürkner, 2017) in R version 3.6.1 (R-Core-Team,
2019). We used the number of species encounters (number of days in which
an animal was detected by a camera per year and season) as the response
variable, with the log-transformed number of active camera trap days as
an offset. Depending on the species, explanatory variables included: i)
large carnivores (wolf and lynx) encounters and human disturbance, and
ii) land cover variables (proportion of agricultural land and EVI). We
allowed the model to estimate different values for each pathway for
winter and summer by adding the interaction of season with all pathways.
We also included a varying intercept by study site and another by camera
location by including these two variables as random effects.
We included the default flat priors of brms and fitted the models using
3000 iterations on 3 chains. We used LOO values as indicators of
goodness of fit, and for model selection. We checked convergence by
looking at the trace plots of the MCMC chains, and with the Gelman and
Rubin convergence diagnostic Ȓ (Gelman and Rubin, 1992). We also
calculated a Bayesian R 2 (Gelman et al., 2018)
for the best fitting model using the bayes_R2 function in the brms
package (Bürkner, 2017) to assess the variance explained by the main
factors. Below, we present the posterior median and associated 90%
credible interval (CRI) for all parameters, which we discuss in terms of
non-overlapping CRI for convenience. The whole posterior distributions
can be found in Appendix 1 and 2. We also present the Probability of
Direction (pd ) as defined in the bayestestR package (Makowski et
al., 2019), which represents the (un)certainty with which an effect is
either positive or negative, as well as the Region of Practical
Equivalence (ROPE; e.g. Kruschke, 2014), which assesses the magnitude
and importance of an effect (i.e., its “significance”) (Makowski et
al., 2019). These values are in Appendix 3.