Data analysis
Our final dataset included time series data for all weather variables
(scaled by subtracting variable means from observed values and dividing
by the standard deviation) and daily gobbling counts. With the spatially
and temporally coupled data, we used state space modeling to evaluate
the effects of weather variables on daily gobbling activity. The state
space model accounted for correlated observations and included
observation error while modeling the influences of weather variables on
gobbling activity. We used a hierarchical state space model that allowed
us to decompose temporally correlated weather data and gobbling counts
into a process variation and observation error (Kery and Schaub 2012).
With the weather variables being the parameters of interest, the state
space model allowed us to investigate the process variation in gobbling
counts relative to stochasticity in the weather variables. We calculated
Pearson’s correlation coefficients to test for collinearity between each
of our covariates and excluded covariates with a r >
0.60.We fit the state space model within the jagsUI package (Kellner
2018) in program R (R Core team 2020) to estimate the effects of weather
on daily gobbling activity.
We fit the Bayesian state space model to counts of daily gobbles (N) at
each site (K) during each year (i). We treated daily gobbling counts
like counts in a population model but we modeled the abundance of
gobbles instead of animals. The process model was:
r expected(t) = Xlog
(N[t-1],k,i) + Site(k) +
βtemperature * Xtemperature(t,k,i) +
βwind * Xwind(t,k,i) +
βbp * (Xbp(t,k,i) -Xbp(t-1,k,i) + βhumidity *
Xhumidity(t,k,i) + βprecipitation *
Xprecipitation(t,k,i) + Year + log(Units)
r t ~
Normal(r expected[t],τprocess)
Log (Nt +1) = log (Nt) +