glmm_p_srasymp <- glmmTMB(sr_asymp ~ tree + shrub + bare + infra + water_s + water_p +
                                     proximity + offset(log(n_cards)), ~1 | pentad,
                                   family = gaussian(link = 'identity'),
                                   data = data_p)
overdisp_fun <- function(model) {
  rdf <- df.residual(model)
  rp <- residuals(model,type="pearson")
  Pearson.chisq <- sum(rp^2)
  prat <- Pearson.chisq/rdf
  pval <- pchisq(Pearson.chisq, df=rdf, lower.tail=FALSE)
  c(chisq=Pearson.chisq,ratio=prat,rdf=rdf,p=pval)
}
sink('../ch.2_results/glmm_p_srasymp.txt') # here we create a text file to write the model results to
summary(glmm_p_srasymp)
overdisp_fun(glmm_p_srasymp)
ps  <- transform(data_p,
                 tree = scale(tree, center = FALSE),
                 shrub = scale(shrub, center = FALSE),
                 grass = scale(grass, center = FALSE),
                 bare = scale(bare, center = FALSE),
                 infra = scale(infra, center = FALSE),
                 water_s = scale(water_s, center = FALSE),
                 water_p = scale(water_p, center = FALSE),
                 proximity = scale(proximity, center = FALSE))
glmm_p_srasymp_scaled <- update(glmm_p_srasymp, data = ps)# model with scaled predictors that produced no warnings
ss <- c(1,
        tree <- 1/attr(ps$tree,"scaled:scale"),
        shrub <- 1/attr(ps$shrub,"scaled:scale"),
        grass <- 1/attr(ps$grass,"scaled:scale"),
        bare <- 1/attr(ps$bare,"scaled:scale"),
        infra <- 1/attr(ps$infra,"scaled:scale"),
        water_s <- 1/attr(ps$water_s,"scaled:scale"),
        water_p <- 1/attr(ps$water_p,"scaled:scale"),
        proximity <- 1/attr(ps$proximity,"scaled:scale"),
        tree + shrub + bare + infra + water_s + water_p + proximity)
s_vals <- cbind(glmmTMB_unsc=suppressWarnings(sqrt(diag(vcov(glmm_p_srasymp)$cond))),
                glmmTMB_sc=sqrt(diag(vcov(glmm_p_srasymp_scaled)$cond)*ss))
print(s_vals,digits=3)
summary(glmm_p_srasymp_scaled)
overdisp_fun(glmm_p_srasymp_scaled)
closeAllConnections()