glmmTMB 负二项式的置信区间 model

Question

I am trying to calculate 95% confidence intervals for model estimates in glmmTMB (family: nbinom1).

I am able to do this using a glmer.nb model and emmeans , using type = "response" to back-transform the estimates and confidence intervals.

model = glmer.nb (response ~ p1 + p2 + (1|block))
emmeans(model, ~ p1 + p2, type = "response")

I think the similar function in glmmTMB is confint(model) , but it does not back-transform the estimates.

Can anyone help me make this work using a glmmTMB model, in the way it works for glmer ?

Answer 1

This is an apples-versus-oranges situation.

The emmeans call computes predictions from the model at each combination of p1 and p2 . Those can be back-transformed.

However, confint(model) asks for inferences on the regression coefficients. Those coefficients are in essence slopes. They are not on the log scale like the EMMs are, and they cannot be back-transformed.

Answer 2

emmeans() should also work for glmmTMB models. For me, it works, and CI are also back-transformed ( from log scale):

library(glmmTMB)
data(Salamanders)

m <- glmmTMB(
  count ~ spp + mined + (1 | site),
  ziformula = ~ spp + mined,
  family = truncated_poisson,
  data = Salamanders
)

emmeans::emmeans(m, "spp", type = "response")
#>  spp    rate    SE  df lower.CL upper.CL
#>  GP    1.553 0.223 627    1.171     2.06
#>  PR    0.922 0.251 627    0.540     1.57
#>  DM    1.944 0.250 627    1.511     2.50
#>  EC-A  1.277 0.246 627    0.875     1.86
#>  EC-L  2.965 0.337 627    2.372     3.71
#>  DES-L 2.844 0.321 627    2.280     3.55
#>  DF    1.626 0.222 627    1.244     2.13
#> 
#> Results are averaged over the levels of: mined 
#> Confidence level used: 0.95 
#> Intervals are back-transformed from the log scale

^{Created on 2019-08-09 by the reprex package (v0.3.0)}

In case you need predicted values ( and confidence intervals) for mixed models with zero-inflation , the computation is a bit more complicated, but implemented in the ggeffects-package . You can find more details in this vignette .

By default, both predict() and emmeans() do not return the most appropriate confidence intervals, as proposed by Brooks et al. (see https://journal.r-project.org/archive/2017/RJ-2017-066/RJ-2017-066.pdf , appendix).

See examples here:

library(glmmTMB)
data(Salamanders)

m <- glmmTMB(
  count ~ spp + mined + (1 | site),
  ziformula = ~ spp + mined,
  family = truncated_poisson,
  data = Salamanders
)

# emmeans, not taking zero-inflation component into account
emmeans::emmeans(m, "spp", type = "response")
#>  spp    rate    SE  df lower.CL upper.CL
#>  GP    1.553 0.223 627    1.171     2.06
#>  PR    0.922 0.251 627    0.540     1.57
#>  DM    1.944 0.250 627    1.511     2.50
#>  EC-A  1.277 0.246 627    0.875     1.86
#>  EC-L  2.965 0.337 627    2.372     3.71
#>  DES-L 2.844 0.321 627    2.280     3.55
#>  DF    1.626 0.222 627    1.244     2.13
#> 
#> Results are averaged over the levels of: mined 
#> Confidence level used: 0.95 
#> Intervals are back-transformed from the log scale

# ggeffects with emmeans, not taking zero-inflation 
# component into account
ggeffects::ggemmeans(m, "spp", type = "fe")
#> 
#> # Predicted counts of count
#> # x = spp
#> 
#>      x predicted conf.low conf.high
#>     GP     1.553    1.171     2.059
#>     PR     0.922    0.540     1.574
#>     DM     1.944    1.511     2.502
#>   EC-A     1.277    0.875     1.863
#>   EC-L     2.965    2.372     3.707
#>  DES-L     2.844    2.280     3.549
#>     DF     1.626    1.244     2.126

# ggeffects with emmeans, taking zero-inflation 
# component into account
ggeffects::ggemmeans(m, "spp", type = "fe.zi")
#> 
#> # Predicted counts of count
#> # x = spp
#> 
#>      x predicted conf.low conf.high
#>     GP     0.567    0.483     0.651
#>     PR     0.089    0.072     0.107
#>     DM     0.911    0.773     1.048
#>   EC-A     0.204    0.167     0.242
#>   EC-L     1.389    1.172     1.606
#>  DES-L     1.506    1.268     1.744
#>     DF     0.762    0.637     0.886

^{Created on 2019-08-09 by the reprex package (v0.3.0)}

Answer 3

The observed mean of a zero-inflated model is a product of two components: a mean structure and a probability of excess zero, each estimated on the link scale, typically giving y = exp(log_mu)*(1 - plogis(log_zi)) . Although log_mu and log_zi are each assumed to be a liner combination of coefficients with uncertainties following normal distributions, the distribution of y as a nonlinear function of these two components are unknown. Therefore, confidence intervals for predicted means in zero-inflated models are usually built via simulation.

I noticed that ggeffects::ggpredict(type = "fe.zi") and marginaleffects:predictions() are for zero inflated count models are based on a simulation of two separate draws of 1000 random observations for the mean structure and the excess zero probability, respectively, from multivariate normal distributions following (Brooks et al., 2017, pp 391-392). Therefore, they vary per run. I have not found ways to control the number of draws in either functions, but setting the seed status using set.seed() will generate reproducible results. Somehow the confidence intervals in most cases are symmetrical around the mean in my case study. On the other hand, ggeffects::ggemmeans() does not vary per run, which I have not discovered how to explain. I suspect that ggemmeans() is based on observed distribution within the sample, so exp(log_mu)*(1 - plogis(log_zi)) is calculated for each observation. It also produces symmetrical confidence intervals. These three methods give standard errors on the response scale. ggeffects::ggeffect() only generate predictions and confidence intervals for the mean structure without considering zero inflation probabilities regardless of the type = argument, and it thus can be misleading.

For count models without zero inflation, ggeffects::ggpredict(type = "fixed") , ggeffects::ggemmeans() , and marginaleffects:predictions() build confidence intervals of y = exp(log_mu) based on normal approximation of log_mu . Therefore, CI of y is approximately exp(log_mu ± 1.96 * SE(log_mu)) which is asymmetrical around mu. This holds true as long as the distributional assumption of response is in the exponential family, which includes Poisson, conventional negative binomial (NB-2), and other negative binomial variants (eg NB-1, NB-heterogeneous). Note that the {ggeffects} package gives standard errors on the link scale (log for count models), whereas the {predictions} package gives standard errors on the response scale. The relationship between these two is simple: SE(response) = y*SE(link) .

Brooks, M., E., Kristensen, K., Benthem, K., J. ,van, Magnusson, A., Berg, C., W., Nielsen, A., Skaug, H., J., Mächler, M., & Bolker, B., M. (2017). GlmmTMB balances speed and flexibility among packages for zero-inflated generalized linear mixed modeling. The R Journal, 9(2), 378. https://doi.org/10.32614/RJ-2017-066