Function glmer() uses by default the Laplace approximation, which is not optimal for dichotomous data. A better alternative is the adaptive Gaussian quadrature. You can use this method by setting argument nAGQ of glmer() to a higher number (e.g., 11 or 15) or alternatively using the GLMMadaptive package. In your example, it gives:
library("GLMMadaptive")
helpmeobiwan <- list(NestPlot = c(1, 0, 0, 0, 0 ,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0, 0, 0, 0, 0, 0, 0, 0, 0),NumDeadJun = c( 0.1409216, -0.1932639,-0.5274494,-0.5274494, 0.1409216, -0.5274494, -0.5274494 , 0.4751071, -0.5274494 , 2.1460347 ,-0.5274494, -0.1932639, 0.8092926, -0.5274494, -0.5274494 ,-0.5274494 ,-0.1932639, 0.1409216, -0.5274494, -0.5274494 ,-0.5274494, -0.5274494 ,-0.5274494, 0.1409216,-0.5274494, -0.5274494 ,-0.5274494, 0.1409216, -0.5274494, 0.1409216, -0.5274494, -0.5274494, -0.5274494, -0.1932639, -0.1932639, -0.5274494, 0.4751071 , 0.1409216 ,-0.5274494, -0.5274494, -0.5274494, -0.5274494, -0.5274494, -0.5274494, -0.5274494, -0.5274494, -0.1932639, -0.5274494, -0.5274494 ,-0.5274494 ,-0.5274494, 0.1409216, -0.5274494, -0.5274494, -0.1932639, -0.5274494, -0.5274494, -0.5274494, 0.1409216, -0.5274494, -0.5274494 ,3.1485912 , 2.4802202, 1.4776637, -0.5274494 , 2.8144057, -0.5274494, -0.5274494, 1.1434781, 3.8169623, 3.8169623 ,-0.1932639, -0.5274494 ,1.4776637 , 1.8118492, -0.5274494),RandomPair = c( "Madera2" , "Starfire1", "Madera2" , "Madera3" , "Starfire1" ,"Starfire1", "Starfire2", "Madera1" , "Madera3" ,"Starfire2" ,"Starfire2", "Madera1", "Madera2", "Starfire1", "Starfire1" ,"Starfire1", "Madera1", "Madera2" , "Starfire1", "Starfire1", "Starfire1", "Madera1" , "Starfire1", "Starfire1", "Madera1", "Madera1" , "Starfire1", "Madera2" , "Madera1", "Madera2" , "Madera1" , "Madera1" , "Starfire1" ,"Starfire1", "Starfire1" ,"Starfire1" ,"Madera2" , "Madera2", "Starfire2" ,"Starfire2", "Starfire2" ,"Madera3" , "Madera3" , "Madera3" , "Madera3" , "Madera3" , "Starfire2", "Starfire2", "Starfire2", "Starfire2" ,"Starfire2", "Madera3", "Madera3" , "Starfire2", "Madera3" , "Madera1" , "Starfire2" ,"Starfire1", "Madera2" , "Madera3" , "Madera3" , "Madera2" , "Madera3" ,"Starfire2", "Madera3", "Starfire1", "Madera3" , "Starfire2", "Starfire1", "Madera3", "Starfire1", "Starfire2" ,"Madera1" , "Starfire2", "Starfire2", "Madera1" ))
helpmeobiwan <- as.data.frame(helpmeobiwan)
fm <- mixed_model(NestPlot ~ NumDeadJun, random = ~ 1 | RandomPair,
family = binomial(), data = helpmeobiwan)
summary(fm)
#>
#> Call:
#> mixed_model(fixed = NestPlot ~ NumDeadJun, random = ~1 | RandomPair,
#> data = helpmeobiwan, family = binomial())
#>
#> Data Descriptives:
#> Number of Observations: 76
#> Number of Groups: 5
#>
#> Model:
#> family: binomial
#> link: logit
#>
#> Fit statistics:
#> log.Lik AIC BIC
#> -46.2248 98.44959 97.27791
#>
#> Random effects covariance matrix:
#> StdDev
#> (Intercept) 0.0477673
#>
#> Fixed effects:
#> Estimate Std.Err z-value p-value
#> (Intercept) -0.1568 0.2829 -0.5544 0.579304
#> NumDeadJun -1.2274 0.4917 -2.4961 0.012558
#>
#> Integration:
#> method: adaptive Gauss-Hermite quadrature rule
#> quadrature points: 11
#>
#> Optimization:
#> method: hybrid EM and quasi-Newton
#> converged: TRUE