[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?

[Mollie Brooks]

Families are documented in the helpfile ?family_glmmTMBcompois is the
Conway-Maxwell Poisson parameterized with the exact mean which differs from
the COMPoissonReg package (Sellers & Lotze 2015)
cheers,Mollie

On Thu, Apr 11, 2019 at 7:01 PM Lokesh Arya <lokesharya.arya99 using gmail.com>
wrote:

> 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
>
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