[R-sig-ME] Why is glmmTMP is estimating approx half value for Zero inflated Conway maxwell poisson mixed model only for the non Zero part?

[Lokesh Arya]

Hi All,

I'm trying to estimate parameter for Zero-inflated Conway Maxwell Poisson
Mixed Model. I'm not getting why GlmmTMP function is giving approx half
value for the non zero effect part and giving nice estimates for the Zero
part and dispersion part?
E.g:- Actual value for intercept is 2.5 and I'm getting 1.21
         for "sexfemale" actual value is 1.2 and I'm getting 0.548342.
somebody, please help me out in this situation?

Thank you

#--------Simulation from ZICOMP mix lambda---------
library(COMPoissonReg)
library(glmmTMB)
set.seed(123)
n <- 100 # number of subjects
K <- 8 # number of measurements per subject
t_max <- 5 # maximum follow-up time
# we constuct a data frame with the design: # everyone has a baseline
measurment, and then measurements at random follow-up times
DF_CMP <- data.frame(id = rep(seq_len(n), each = K),
                     time = c(replicate(n, c(0, sort(runif(K - 1, 0, t_max))))),
                     sex = rep(gl(2, n/2, labels = c("male",
"female")), each = K))
# design matrices for the fixed and random effects non-zero part
X <- model.matrix(~ sex * time, data = DF_CMP)
Z <- model.matrix(~ 1, data = DF_CMP)# design matrices for the fixed
and random effects zero part
X_zi <- model.matrix(~ sex, data = DF_CMP)

betas <- c(2.5 , 1.2 , 2.3, -1.5) # fixed effects coefficients non-zero part
shape <- 2
gammas <- c(-1.5, 0.9) # fixed effects coefficients zero part
D11 <- 0.5 # variance of random intercepts non-zero part
# we simulate random effects
b <- rnorm(n, sd = sqrt(D11))# linear predictor non-zero part
eta_y <- as.vector(X %*% betas + rowSums(Z * b[DF_CMP$id,drop =
FALSE]))# linear predictor zero part
eta_zi <- as.vector(X_zi %*% gammas)
DF_CMP$CMP_y <- rzicmp(n * K, lambda = exp(eta_y), nu = shape, p =
plogis(eta_zi))
hist(DF_CMP$CMP_y)#------ estimation -------------
CMPzicmpm0 = glmmTMB(CMP_y~ sex*time + (1|id) , zi= ~ sex, data =
DF_CMP, family=compois)

summary(CMPzicmpm0)

 Family: compois  ( log )
Formula:          CMP_y ~ sex * time + (1 | id)
Zero inflation:         ~sex
Data: DF_CMP

     AIC      BIC   logLik deviance df.resid
  4586.2   4623.7  -2285.1   4570.2      792

Random effects:

Conditional model:
 Groups Name        Variance Std.Dev.
 id     (Intercept) 0.1328   0.3644
Number of obs: 800, groups:  id, 100

Overdispersion parameter for compois family (): 0.557

Conditional model:
                Estimate Std. Error z value Pr(>|z|)    (Intercept)
 1.217269   0.054297   22.42  < 2e-16 ***
sexfemale       0.548342   0.079830    6.87 6.47e-12 ***
time            1.151549   0.004384  262.70  < 2e-16 ***
sexfemale:time -0.735348   0.009247  -79.52  < 2e-16 ***---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Zero-inflation model:
            Estimate Std. Error z value Pr(>|z|)    (Intercept)
-1.6291     0.1373 -11.866  < 2e-16 ***
sexfemale     0.9977     0.1729   5.771 7.89e-09 ***---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

	[[alternative HTML version deleted]]