rt
Where rexpected(t) was the expected change in
daily gobbling activity, Site was the fixed effect for each of the 5
sites, βtemperature was the coefficient for the effect
of temperature in matrix Xtemperature,
βwind was the coefficient for the effect of wind in
matrix Xwind , βbp was the coefficient
for the effect of the change in barometric pressure in matrix
Xbp , βhumidity was the coefficient for
the effect of humidity in matrix Xhumidity ,
βprecipitation was the coefficient for the effect of
precipitation in matrix Xprecipitation , Year was
modelled as a random effect, and Units was an offset term used to
account for the number of ARUs recording. We modeled the observation
process as follows: yt,k,i ~
Poisson(log(Nt)) where yt,k,iwas the logged observed number of gobbles each day(t) at each site
during each year . We calculated 95% credible intervals for each
parameter estimate of interest. For the random effect of year and to
account for process variation, we used a gamma distribution for the
priors with a precision of 0.001. For the rest of the parameters, we
used a normal distribution with a mean of 0 and a precision of 0.001. We
used Markov chain Monte Carlo (MCMC) to estimate the posterior
distributions of the model parameters. We generated 3 MCMC chains using
a thinning rate of 10,000 iterations per chain and 2,500 burn in values.
To check for convergence, we investigated trace plots of the MCMC chains
and used Gelman-Rubin statistic to calculate R-values, with R-values
less than 1.1 indicating model convergence (Gelman et al. 2004).