specification for glmmPQL
On 9/4/05, Andrew R. Criswell <r-stats at arcriswell.com> wrote:
Hello Dr. Bates and group,
I understand, the attached data file did not accompany my original
message. I have listed below the code used to create that file.
data.1 <- data.frame(subject = factor(rep(c("one", "two", "three", "four",
"five", "six", "seven",
"eight"),
each = 4),
levels = c("one", "two", "three",
"four", "five", "six",
"seven", "eight")),
day = factor(rep(c("one", "two", "three", "four"),
times = 8),
levels = c("one", "two", "three",
"four")),
expt = rep(c("control", "treatment"), each = 16),
response = c(58, 63, 57, 54, 63, 59, 61, 53, 52, 62,
46, 55, 59, 63, 58, 59, 62, 59, 64, 53,
63, 75, 62, 64, 53, 58, 62, 53, 64, 72,
65, 74))
mtrx.1 <- matrix(apply(data.1[, -4], 2, function(x)
rep(x, 100 - data.1$response)), ncol = 3, byrow = F)
mtrx.2 <- matrix(apply(data.1[, -4], 2, function(x)
rep(x, data.1$response)), ncol = 3, byrow = F)
data.2 <- data.frame(subject = factor(c(mtrx.1[,1], mtrx.2[,1]),
levels = c("one", "two", "three",
"four", "five", "six",
"seven", "eight")),
day = factor(c(mtrx.1[,2], mtrx.2[,2]),
levels = c("one", "two", "three",
"four")),
expt = factor(c(mtrx.1[,3], mtrx.2[,3]),
levels = c("control", "treatment")),
response = factor(c(rep("yes", nrow(mtrx.1)),
rep("no", nrow(mtrx.2))),
levels = c("yes", "no")))
#-------------------------------------------------------------------------------#
Thanks for sending the data. In your first message you said that you got completely different results from glmmPQL when fitting the two models. When I fit these models with glmmPQL I got quite similar parameter estimates. The reported log-likelihood or AIC or BIC values are quite different but these values apply to a different model (the list weighted linear mixed model used in the PQL algorithm) and should not be used for a glmm model in any case. The fm4 results from lmer in the lme4 package (actually lmer is now in the Matrix package but that is only temporary) confirm those from glmmPQL. The model fm3 when fit by lmer provides different standard errors but that is because the weights are not being appropriately adjusted in lmer. We will fix that. In general I think it is safest to use the long form of the data as in your data.2. Here are the results from lmer applied to the long form. The results from the Adaptive Gauss-Hermite Quadrature (AGQ) method are preferred to those from the PQL method because AGQ is a more accurate approximation to the log-likelihood of the GLMM model. In this case the differences are minor. The log-likelihood reported here is an approximation to the log-likelihood of the GLMM model.
(fm.4 <- lmer(response ~ expt + (1|subject), data.2, binomial))
Generalized linear mixed model fit using PQL
Formula: response ~ expt + (1 | subject)
Data: data.2
Family: binomial(logit link)
AIC BIC logLik deviance
4298.026 4322.31 -2145.013 4290.026
Random effects:
Groups Name Variance Std.Dev.
subject (Intercept) 0.015835 0.12584
# of obs: 3200, groups: subject, 8
Estimated scale (compare to 1) 0.9990621
Fixed effects:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 0.30764 0.08075 3.8098 0.0001391
expttreatment 0.21319 0.11473 1.8582 0.0631454
(fm.4a <- lmer(response ~ expt + (1|subject), data.2, binomial, method = "AGQ"))
Generalized linear mixed model fit using AGQ
Formula: response ~ expt + (1 | subject)
Data: data.2
Family: binomial(logit link)
AIC BIC logLik deviance
4298.023 4322.306 -2145.011 4290.023
Random effects:
Groups Name Variance Std.Dev.
subject (Intercept) 0.015855 0.12592
# of obs: 3200, groups: subject, 8
Estimated scale (compare to 1) 1.007675
Fixed effects:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 0.30811 0.08075 3.8156 0.0001358
expttreatment 0.21352 0.11473 1.8611 0.0627322
Douglas Bates wrote:
On 9/4/05, Andrew R. Criswell <r-stats at arcriswell.com> wrote:
Hello All,
I have a question regarding how glmmPQL should be specified. Which of
these two is correct?
summary(fm.3 <- glmmPQL(cbind(response, 100 - response) ~ expt,
data = data.1, random = ~ 1 | subject,
family = binomial))
summary(fm.4 <- glmmPQL(response ~ expt, data = data.2,
random = ~ 1 | subject, family = binomial))
One might think it makes no difference, but it does.
I have an experiment in which 8 individuals were subjected to two types
of treatment, 100 times per day for 4 consecutive days. The response
given is binary--yes or no--for each treatment.
I constructed two types of data sets. On Rfile-01.Rdata (attached here)
are data frames, data.1 and data.2. The information is identical but the
data are arranged differently between these two data frames. Data frame,
data.1, groups frequencies by subject, day and treatment. Data frame,
data.2, is ungrouped.
I don't think your attached .Rdata file made it through the various filters on the lists or on my receiving email. Could you send me a copy in a separate email message?
Consistency of these data frames is substantiated by computing these
tables:
ftable(xtabs(response ~ expt + subject + day,
data = data.1))
ftable(xtabs(as.numeric(response) - 1 ~ expt + subject + day,
data = data.2))
If I ignore the repeated measurement aspect of the data, I get, using
glm, identical results (but for deviance and df).
summary(fm.1 <- glm(cbind(response, 100 - response) ~ expt,
data = data.1, family = binomial))
summary(fm.2 <- glm(response ~ expt, data = data.2,
family = binomial))
However, if I estimate these two equations as a mixed model using
glmPQL, I get completely different results between the two
specifications, fm.3 and fm.4. Which one is right? The example which
accompanies help(glmmPQL) suggests fm.4.
summary(fm.3 <- glmmPQL(cbind(response, 100 - response) ~ expt,
data = data.1, random = ~ 1 | subject,
family = binomial))
summary(fm.4 <- glmmPQL(response ~ expt, data = data.2,
random = ~ 1 | subject, family = binomial))
Thank you,
Andrew
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