Hey Buddy, Hope you have been doing well since last contact.
If you have the answer to the following question, please let me know. If you have chance to travel up north. let me know. best, -Sean ---------- Forwarded message ---------- From: Sean Zhang <seane...@gmail.com> Date: Sat, Apr 11, 2009 at 12:12 PM Subject: question related to fitting overdispersion count data using lmer quasipoisson To: r-help@r-project.org Cc: seane...@gmail.com Dear R-helpers: I have a question related to fitting overdispersed count data using lmer. Basically, I simulate an overdispsed data set by adding an observation-level normal random shock into exp(....+rnorm()). Then I fit a lmer quasipoisson model. The estimation results are very off (see model output of fit.lmer.over.quasi below). Can someone kindly explain to me what went wrong? Many thanks in advance. -Sean #data simulation (modified from code at http://markmail.org/message/j3zmgrklihe73p4p) set.seed(100) m <- 5 n <- 100 N <- n*m #X <- cbind(1,runif(N)) X <- cbind(1,rnorm(N)) X <- cbind(runif(N),rnorm(N)) id <- rep(1:n,each=m) # Z <- kronecker(diag(n),rep(1,m)) #Possion with group level heterogeneity z <- rpois(N, exp(X%*%matrix(c(1,2)) + Z%*%matrix(rnorm(n)))) #2*rnorm(n*m) is added to each observation to create overdispersion z.overdis <- rpois(N, exp(X%*%matrix(c(1,2)) + Z%*%matrix(rnorm(n)) + 2*rnorm(n*m))) #without observation-level random shock i.e., 2*rnorm(n*m), estimate results are very accurate (fit.lmer <- lmer(z ~ X + (1|id), family="poisson",verbose=F)) #Generalized linear mixed model fit by the Laplace approximation #Formula: z ~ X + (1 | id) # AIC BIC logLik deviance # 851 868 -422 843 #Random effects: # Groups Name Variance Std.Dev. # id (Intercept) 0.977 0.988 #Number of obs: 500, groups: id, 100 # #Fixed effects: # Estimate Std. Error z value Pr(>|z|) #(Intercept) -0.0128 0.1116 -0.1 0.9 #X1 1.0615 0.0601 17.7 <2e-16 *** #X2 2.0236 0.0214 94.7 <2e-16 *** #--- #Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1 # #Correlation of Fixed Effects: # (Intr) X1 #X1 -0.349 #X2 -0.270 0.258 #Now you can see the results are very off (fit.lmer.over.quasi <- lmer(z.overdis ~ X + (1|id), family=quasipoisson(link="log"),verbose=F)) #Generalized linear mixed model fit by the Laplace approximation #Formula: z.overdis ~ X + (1 | id) # AIC BIC logLik deviance # 41867 41888 -20929 41857 #Random effects: # Groups Name Variance Std.Dev. # id (Intercept) 175.8 13.26 # Residual 72.9 8.54 #Number of obs: 500, groups: id, 100 # #Fixed effects: # Estimate Std. Error t value #(Intercept) 1.3530 1.3492 1.00 #X1 1.0834 0.2273 4.77 #X2 1.3501 0.0783 17.25 # #Correlation of Fixed Effects: # (Intr) X1 #X1 -0.099 #X2 -0.055 0.070 [[alternative HTML version deleted]]
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