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 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)
> 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
