Check the model assumptions

Oct 13, 2025 by wbrum.org 104 views

Calculating 95% Confidence Intervals on Negative-Binomial Marginal Coefficients: A Guide to GLMMadaptive

When working with count data in a repeated measures setting, it's essential to consider the complexities of the data and the models used to analyze them. One such model is the negative-binomial model, which is commonly used to account for overdispersion in count data. However, when it comes to calculating marginal coefficients and confidence intervals, things can get tricky. In this article, we'll explore how to calculate 95% confidence intervals on negative-binomial marginal coefficients using the GLMMadaptive package in R.

When working with mixed-effects models, such as the negative-binomial model, it's common to encounter issues with calculating marginal coefficients and confidence intervals. The GLMMadaptive package provides a convenient way to estimate marginal effects and confidence intervals, but sometimes, the results may not be what you expect. In this article, we'll focus on the specific issue of calculating 95% confidence intervals on negative-binomial marginal coefficients using the GLMMadaptive::confint and GLMMadaptive::marginal_coef functions.

The GLMMadaptive package is a powerful tool for estimating generalized linear mixed models (GLMMs) in R. It provides a range of functions for estimating marginal effects, confidence intervals, and other model diagnostics. In this article, we'll focus on the GLMMadaptive::confint and GLMMadaptive::marginal_coef functions, which are used to calculate confidence intervals and marginal coefficients, respectively.

Before we dive into the details of calculating 95% confidence intervals on negative-binomial marginal coefficients, let's take a look at a simple example of a negative-binomial model for count data in a repeated measures setting.

library(GLMMadaptive)
library(ggplot2)
dat <- structure(
list(
subjectId = c("1", "1", "2", "2", "3", "3"),
time = c(1, 2, 1, 2, 1, 2),
count = c(5, 3, 2, 4, 6, 5)
),
class = "data.frame",
row.names = c(NA, -6L)
)
model <- mixed(count ~ time, random = ~ 1 | subjectId, data = dat, family = negbin())

Once we've fit the negative-binomial model, we can use the GLMMadaptive::marginal_coef function to calculate the marginal coefficients.

# Calculate marginal coefficients
marginal_coef <- marginal_coef(model)

Now that we have the marginal coefficients, we can use the GLMMadaptive::confint function to calculate the 95% confidence intervals.

# Calculate 95% confidence intervals
confint <- confint(model)

However, when we run the GLMMadaptive::confint and GLMMadaptive::marginal_coef functions, we may encounter strange results. The confidence intervals may not be what we expect, and the marginal coefficients may not be accurate. This can be due to a range of issues, including:

Overdispersion: The negative-binomial model assumes that the data are overdispersed, but the degree of overdispersion may not be accurately captured by the model.
Correlated data: The repeated measures design may introduce correlations between the data points, which can affect the accuracy of the confidence intervals and marginal coefficients.
Model misspecification: The model may not be correctly specified, leading to inaccurate estimates of the marginal coefficients and confidence intervals.

So, what can we do to troubleshoot these issues? Here are a few suggestions:

Check the model assumptions: Make sure that the model assumptions are met, including the assumption of overdispersion and the assumption of correlated data.
Check the model specification: Make sure that the model is correctly specified, including the inclusion of all relevant predictors and the correct specification of the random effects.
Use alternative methods: Consider using alternative methods for calculating marginal coefficients and confidence intervals, such as the emmeans package or the marginaleffects package.

Calculating 95% confidence intervals on negative-binomial marginal coefficients can be a complex task, especially when working with count data in a repeated measures setting. The GLMMadaptive package provides a convenient way to estimate marginal effects and confidence intervals, but sometimes, the results may not be what you expect. By understanding the potential issues and troubleshooting techniques, we can improve the accuracy of our estimates and make more informed decisions about our data.

Bates, D., Mächler, M., Bolker, B., & Walker, S. (2015). Fitting linear mixed-effects models using lme4. Journal of Statistical Software, 67(1), 1-48.
Harrison, X. A. (2014). Using observation-level random effects to model overdispersion in count data in ecology. Methods in Ecology and Evolution, 5(5), 442-445.
Rizopoulos, D. (2012). Joint models for longitudinal and time-to-event data: with applications in R. CRC Press.
Q&A: Calculating 95% Confidence Intervals on Negative-Binomial Marginal Coefficients

In our previous article, we explored how to calculate 95% confidence intervals on negative-binomial marginal coefficients using the GLMMadaptive package in R. However, we also encountered some issues with the GLMMadaptive::confint and GLMMadaptive::marginal_coef functions. In this article, we'll answer some of the most frequently asked questions about calculating 95% confidence intervals on negative-binomial marginal coefficients.

A: The GLMMadaptive::confint function is used to calculate the confidence intervals for the fixed effects in the model, while the GLMMadaptive::marginal_coef function is used to calculate the marginal coefficients, which represent the change in the response variable for a one-unit change in the predictor variable, while holding all other variables constant.

A: There are several reasons why your confidence intervals may be wide. One reason is that the model may not be correctly specified, leading to inaccurate estimates of the marginal coefficients and confidence intervals. Another reason is that the data may be overdispersed, which can lead to wider confidence intervals. Finally, the model may not be able to capture the complexity of the data, leading to wider confidence intervals.

A: There are several steps you can take to troubleshoot issues with your confidence intervals. First, check the model assumptions, including the assumption of overdispersion and the assumption of correlated data. Next, check the model specification, including the inclusion of all relevant predictors and the correct specification of the random effects. Finally, consider using alternative methods for calculating marginal coefficients and confidence intervals, such as the emmeans package or the marginaleffects package.

A: Yes, you can use the GLMMadaptive::confint function with other types of models, including linear mixed-effects models and generalized linear mixed models. However, the function may not work as expected with all types of models, so be sure to check the documentation and the output carefully.

A: To calculate marginal coefficients for a model with multiple predictors, you can use the GLMMadaptive::marginal_coef function with the predict argument set to TRUE. This will allow you to calculate the marginal coefficients for each predictor variable, while holding all other variables constant.

A: Yes, you can use the GLMMadaptive::confint function with a model that has a non-linear relationship between the response variable and the predictor variable. However, the function may not work as expected with all types of non-linear relationships, so be sure to check the documentation and the output carefully.

A: To calculate confidence intervals for a model with a random effect, you can use the GLMMadaptive::confint function with the random argument set to TRUE. This will allow you to calculate the confidence intervals for the random effect, while holding all other variables constant.

Calculating 95% confidence intervals on negative-binomial marginal coefficients can be a complex task, especially when working with count data in a repeated measures setting. By understanding the potential issues and troubleshooting techniques, we can improve the accuracy of our estimates and make more informed decisions about our data. We hope this Q&A article has been helpful in answering some of the most frequently asked questions about calculating 95% confidence intervals on negative-binomial marginal coefficients.