I have data on blue sheep density in 55 survey units which are watersheds. I want to test what factors affect blue sheep density. I used blue sheep count data in each watershed, and log(area of the watershed) as an offset. Since the 55 watersheds are distributed in 7 different sites far away from each other to represent different livestock density, I used GLMM to include site as a random effect.
library(lme4)
# Negative Binomial Regression
M1 <- glmer.nb(BS~s.AGB+log(s.DEM)+sqrt(s.VRM)+s.LS+sqrt(s.HOUSE)+sqrt(s.ROCK)+
log(s.Viewshed)+(1|Site)+offset(log(Area)),data=bs)
summary(M1)
# Poisson Regression
M2 <- glmer(BS~s.AGB+log(s.DEM)+sqrt(s.VRM)+s.LS+sqrt(s.HOUSE)+sqrt(s.ROCK)+
log(s.Viewshed)+(1|Site)+offset(log(Area)),data=bs,family=poisson)
summary(M2)
"s.coefficient" means scaled coefficients. I've re-scaled all the X variables into the range of 0-10.
The results given by the two models are very different. M1 gives no significant effects at all, and lots of convergence warning. Whereas M2 shows almost all the variables are significant.
**Summary M1:**
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
Family: Negative Binomial(0.4529) ( log )
Formula: BS ~ s.AGB + log(s.DEM) + sqrt(s.VRM) + s.LS + sqrt(s.HOUSE) + sqrt(s.ROCK) + log(s.Viewshed) + (1 | Site) + offset(log(Area))
Data: ..2
AIC BIC logLik deviance df.resid
552.7 572.8 -266.3 532.7 45
Scaled residuals:
Min 1Q Median 3Q Max
-0.7843 -0.6953 -0.3354 0.2942 4.5536
Random effects:
Groups Name Variance Std.Dev.
Site (Intercept) 2.460e-12 1.569e-06
Residual 7.353e-01 8.575e-01
Number of obs: 55, groups: Site, 7
Fixed effects:
Estimate Std. Error t value Pr(>|z|)
(Intercept) -0.4162880 19.7722023 -0.021 0.983
s.AGB 0.0043793 0.4259805 0.010 0.992
log(s.DEM) 0.1617608 8.4140466 0.019 0.985
sqrt(s.VRM) -0.0059249 0.5631603 -0.011 0.992
s.LS 0.0008908 0.1290667 0.007 0.994
sqrt(s.HOUSE) 0.0037029 0.3077675 0.012 0.990
sqrt(s.ROCK) 0.0093700 0.7265202 0.013 0.990
log(s.Viewshed) 0.0070697 0.8106204 0.009 0.993
Correlation of Fixed Effects:
(Intr) s.AGB l(.DEM s(.VRM s.LS s(.HOU s(.ROC
s.AGB -0.453
log(s.DEM) -0.973 0.250
sqrt(s.VRM) -0.410 0.180 0.392
s.LS 0.124 -0.198 -0.077 -0.317
sqr(.HOUSE) 0.071 -0.320 -0.003 -0.423 0.130
sqrt(.ROCK) 0.032 0.749 -0.239 -0.131 -0.043 -0.202
lg(s.Vwshd) -0.120 0.119 0.024 -0.091 -0.234 -0.064 0.149
**Summary M2:**
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
Family: poisson ( log )
Formula: BS ~ s.AGB + log(s.DEM) + sqrt(s.VRM) + s.LS + sqrt(s.HOUSE) + sqrt(s.ROCK) + log(s.Viewshed) + (1 | Site) + offset(log(Area))
Data: bs
AIC BIC logLik deviance df.resid
3293.1 3311.2 -1637.5 3275.1 46
Scaled residuals:
Min 1Q Median 3Q Max
-9.888 -5.417 -1.435 5.447 24.053
Random effects:
Groups Name Variance Std.Dev.
Site (Intercept) 0.6708 0.819
Number of obs: 55, groups: Site, 7
Fixed effects:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -48.22938 3.53361 -13.649 < 2e-16 ***
s.AGB -0.02396 0.03920 -0.611 0.541081
log(s.DEM) 21.36638 1.63916 13.035 < 2e-16 ***
sqrt(s.VRM) -0.20076 0.06962 -2.884 0.003929 **
s.LS -0.19084 0.01227 -15.557 < 2e-16 ***
sqrt(s.HOUSE) 0.43643 0.03284 13.290 < 2e-16 ***
sqrt(s.ROCK) -0.38330 0.10476 -3.659 0.000253 ***
log(s.Viewshed) 1.91979 0.09484 20.242 < 2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Correlation of Fixed Effects:
(Intr) s.AGB l(.DEM s(.VRM s.LS s(.HOU s(.ROC
s.AGB 0.221
log(s.DEM) -0.990 -0.322
sqrt(s.VRM) -0.318 -0.274 0.349
s.LS 0.314 0.103 -0.323 -0.231
sqr(.HOUSE) -0.570 -0.318 0.583 -0.014 -0.092
sqrt(.ROCK) 0.731 0.668 -0.795 -0.523 0.311 -0.373
lg(s.Vwshd) -0.536 -0.043 0.500 -0.225 -0.200 0.170 -0.302
The two models are nested so normally will produce quite similar results. Why in my case could the results be opposite?
