fitting glmm under lme4 and Gauss Hermite integration
On 10-10-30 01:07 PM, Jie Li wrote:
Dear colleagues,
Happy Halloween.
When I try fitting glmm under lme4 using the following code:
x=as.factor(rep(c("1","2","3", "4", "5", "6"),each=2))
y=c(14, 18, 10, 47, 13, 24, 10, 12, 1, 0, 6, 6)
offset=c(5.505332,5.645447, 5.549076, 5.886104, 6.023448, 6.177944, 6.077642,
6.186209,
5.030438, 5.117994, 5.170484, 5.493061)
eu=gl(12,1)
try=data.frame(x,y,eu,offset)
fit <- glmer(y ~ x + (1 | eu) + offset(log(adjust)),
family = poisson, data =try)
A message pops up, saying "Number of levels of a grouping factor for the random
effects
is *equal* to n, the number of observations".
Question1: can I still use the fit statistics? (Should the levels be less than
the number of observations? But I can't help it. My data are like that)
In principle, yes. 1. You're essentially using the random effects here to account for individual-level variance (i.e. a lognormal-Poisson model), rather than accounting for grouping/correlation. 2. This is a very small dataset. In particular, fitting k=6 fixed-effect parameters to n=12 data points means that you will be far from reliable asymptotic rules of thumb (we would generally prefer n/k >= 10 ...). I would strongly recommend bootstrapped confidence intervals, or some other reasonably robust small-sample procedure (permutation test, parametric bootstrap ...)
Question2: When running the glmm function under the repeated package written by James Lindsey, I encountered the problem of trying to decide on the value of points, ie. Gauss Hermite integration numbers. Different points resulted in quite different fit statistics. Here is my code: fit2<-glmm(y~x, family=poisson, offset=offset, nest=gl(12,1),points=4,data=try) Is it true that the more points, the better? A book says points=20 entails decent approximation, but there???s an error msg when I increased my point number to 10. It says ???Product of probabilities is too small to calculate.??? May I seek your advice on this issue (what point should I be using)? Are there good references you would recommend so that I can understand better understand Gauss Hermite integration? BTW, glmer under lme4 uses adapted Gauss-Hermite integration too.
glmer uses the Laplace approximation (aGH with 1 quadrature point) unless you set nAGQ>1. I might recommend [Jiang, Jiming. 2007. Linear and generalized linear mixed models and their applications. Springer]. <http://lme4.r-forge.r-project.org/book/Ch5.pdf> is Bates's draft of his new book, but it only goes as far as defining the Laplace approximation. If you already have "a book" that talks about GH, does it give any more information? I would suggest comparing the results of glmer() and glmm() for different numbers of quadrature points; see if the two packages give similar estimates, and see whether the estimates seem to be behaving reasonably/converging to something sensible as you increase the number of quadrature points. (For "extra credit" :-) or if this is really important you could also try comparing the results with the glmmML package.) good luck, Ben Bolker