I am having some trouble understanding the difference in use of the anova() function and summary() function. For context, here is what I am working on:
I am using GLMMs:
glmm_dogs2 <- lmer(Den.Weeks ~ Humans * Predators + (1|packseasid), data = dogs)
glmm_dogs3 <- lmer(Den.Distance ~ Humans * Predators + (1|packseasid), data = dogs)
glmm_dogs4 <- lmer(Pups.lost ~ Humans + Predators + Den.Distance + (1|packseasid), data = dogs)
The code that I based myself on then continues to plot the residuals and test for normality of residuals, and then goes on to the results, using both Anova(glmm_dogs2) and summary(glmm_dogs2). Then I get the following output:
Anova(glmm_dogs2)
Analysis of Deviance Table (Type II Wald chisquare tests)
Response: Den.Weeks
Chisq Df Pr(>Chisq)
Humans 2.1423 1 0.14329
Predators 5.5678 1 0.01829 *
Humans:Predators 5.0390 1 0.02478 *
-------------
summary(glmm_dogs2)
Linear mixed model fit by REML. t-tests use
Satterthwaite's method [lmerModLmerTest]
Formula:
Den.Weeks ~ Humans * Predators + (1 | packseasid)
Data: dogs
REML criterion at convergence: 98.4
Scaled residuals:
Min 1Q Median 3Q Max
-1.5586 -0.4267 -0.0769 0.6049 1.6837
Random effects:
Groups Name Variance Std.Dev.
packseasid (Intercept) 1.015 1.008
Residual 2.012 1.419
Number of obs: 28, groups: packseasid, 11
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 9.9312 0.4444 14.2747 22.347 1.64e-12 ***
Humans1 -2.3783 0.9541 20.1319 -2.493 0.02151 *
Predators1 -3.6509 1.1213 18.7048 -3.256 0.00422 **
Humans1:Predators1 3.9813 1.7736 21.8223 2.245 0.03526 *
---
Signif. codes:
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Correlation of Fixed Effects:
(Intr) Humns1 Prdtr1
Humans1 -0.255
Predators1 -0.179 0.126
Hmns1:Prdt1 0.099 -0.579 -0.673
Now I have Chisq and Pr(>Chisq) values, and I have t and Pr(>|t|) values. According to the Anova(), the interaction between Humans:Predators is significant, and Predators is significant, while according to the summary(), all terms including the interaction are significant.
[Side-note: I already used the dredge(global_glmm) function to compace AIC's, so my model has already been reduced, this question mainly pertains to how I should report my results and which variables I can consider to be significantly related to eachother.]
I did read that the Anova() does a Type II test, and summary() does a type III test, so if I understood it correctly, this means that in this case I should use the summary() output, because of the significant interaction Humans:Predators. However, if the summary() function gave me no significant result, I should use the Anova() results? Or did I misinterpret this?
FYI, below are the results of one of the other GLMM's I constructed, where there is no significant interaction; in this case I would then use the Anova() results in my report because the summary() didn't show any significant interactions?
Anova(glmm_dogs3)
Analysis of Deviance Table (Type II Wald chisquare tests)
Response: Den.Distance
Chisq Df Pr(>Chisq)
Humans 3.4109 1 0.06477 .
Predators 0.0976 1 0.75467
Humans:Predators 1.3987 1 0.23694
---
Signif. codes:
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> summary(glmm_dogs3)
Linear mixed model fit by REML. t-tests use
Satterthwaite's method [lmerModLmerTest]
Formula:
Den.Distance ~ Humans * Predators + (1 | packseasid)
Data: dogs
REML criterion at convergence: 108.9
Scaled residuals:
Min 1Q Median 3Q Max
-1.28514 -0.50117 -0.01259 0.56893 2.10258
Random effects:
Groups Name Variance Std.Dev.
packseasid (Intercept) 2.554 1.598
Residual 2.652 1.628
Number of obs: 28, groups: packseasid, 11
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 2.1269 0.6105 11.2745 3.484 0.00494 **
Humans1 0.9035 1.1232 17.1159 0.804 0.43221
Predators1 -0.7322 1.3067 15.6333 -0.560 0.58319
Humans1:Predators1 2.4991 2.1131 18.7481 1.183 0.25172
---
Signif. codes:
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Correlation of Fixed Effects:
(Intr) Humns1 Prdtr1
Humans1 -0.211
Predators1 -0.143 0.132
Hmns1:Prdt1 0.071 -0.586 -0.670