[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]

I forgot to mention, the more recent documentation also includes the
following reference

Huang A (2017). "Mean-parametrized Conway–Maxwell–Poisson regression models
for dispersed counts. " Statistical Modelling 17(6), 1-22.

This paper has a thorough explanation of the parameterization. We chose the
mean parameterization so that the coefficients are comparable to other
distributions such as the Poisson.

cheers,
Mollie

On Tue, Apr 16, 2019 at 9:00 AM Mollie Brooks <mollieebrooks using gmail.com>
wrote:

> 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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>>
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