I am currently running a generalized linear mixed effect model using glmer and
I want to estimate how much of the variance is explained by my random factor.
summary(glmer(cbind(female,male)~date+(1|dam),family=binomial,data= liz3"))
Generalized linear mixed model fit by the Laplace approximation
Formula: cbind(female, male) ~ date + (1 | dam)
Data: liz3
AIC BIC logLik deviance
241.3 258.2 -117.7 235.3
Random effects:
Groups Name Variance Std.Dev.
dam (Intercept) 0 0
Number of obs: 2068, groups: dam, 47
Fixed effects:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 1.480576 1.778648 0.8324 0.405
date -0.005481 0.007323 -0.7484 0.454
Correlation of Fixed Effects:
(Intr)
date2 -0.997
summary(glm(cbind(female,male)~date,family=binomial,data= liz3"))
Call:
glm(formula = cbind(female, male) ~ date, family = binomial,
data = liz3")
Deviance Residuals:
Min 1Q Median 3Q Max
-1.678 0.000 0.000 0.000 1.668
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 1.484429 1.778674 0.835 0.404
date -0.005497 0.007324 -0.751 0.453
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 235.90 on 174 degrees of freedom
Residual deviance: 235.34 on 173 degrees of freedom
AIC: 255.97
Number of Fisher Scoring iterations: 3
Based on a discussion found on the R mailing list but dating back to 2008, I
have compared the log-likelihoods of the glm model and of the glmer model as
follows:
lrt <- function (obj1, obj2){
L0 <- logLik(obj1)
L1 <- logLik(obj2)
L01 <- as.vector(- 2 * (L0 - L1))
df <- attr(L1, "df") - attr(L0, "df")
list(L01 = L01, df = df, "p-value" = pchisq(L01, df, lower.tail = FALSE)) }
gm0 <- glm(cbind(female,male)~date,family = binomial, data = liz3)
gm1 <- glmer(cbind(female,male)~date+(1|dam),family=binomial,data= liz3)
lrt(gm0, gm1)
and I have compared the deviances as follows:
(d0 <- deviance(gm0))
(d1 <- deviance(gm1))
(LR <- d0 - d1)
pchisq(LR, 1, lower.tail = FALSE)
As in some of the examples posted, although the variance of my random effect is
zero, the p-value obtained by comparing the logLik is highly significant
$L01
[1] 16.63553
$df
p
1
$`p-value`
[1] 4.529459e-05
while comparing the deviances gives me the following output that I don't quite
understand but which seems (to the best of my understanding) to indicate that
the random effect explains none of the variance.
(LR <- d0 - d1)
ML
-4.739449e-06
pchisq(LR, 1, lower = FALSE)
ML
1
I would be very thankful if someone could clarify my mind about how to estimate
the variance explained by my random factor and also when to use lower = FALSE
versus TRUE.
Many thanks in advance
Davnah Urbach
Post-doctoral researcher
Dartmouth College
Department of Biological Sciences
401 Gilman Hall
Hanover, NH 03755 (USA)
lab/office: (603) 646-9916
davnah.urb...@dartmouth.edu
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