How To Calculate A 95% CI On Negative-binomial Marginal Coefficients? Strange Results With GLMMadaptive::confint And GLMMadaptive::marginal_coef

Mar 8, 2025 by ADMIN 145 views

How to Calculate a 95% CI on Negative-Binomial Marginal Coefficients: Strange Results with GLMMadaptive::confint and GLMMadaptive::marginal_coef

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Introduction

When working with count data in a repeated measures setting, it's common to use generalized linear mixed models (GLMMs) to account for the correlation between observations. The GLMMadaptive package in R provides an efficient way to fit these models and estimate marginal effects. However, when calculating confidence intervals (CIs) for the marginal coefficients using GLMMadaptive::confint and GLMMadaptive::marginal_coef, you may encounter strange results. In this article, we'll explore how to calculate a 95% CI on negative-binomial marginal coefficients and discuss potential issues with these functions.

Understanding Marginal Coefficients

Marginal coefficients represent the change in the expected value of the response variable for a one-unit change in the predictor variable, while holding all other variables constant. In the context of a negative-binomial GLMM, the marginal coefficient for a predictor variable can be interpreted as the change in the expected count for a one-unit change in that variable.

Fitting a Negative-Binomial Model with GLMMadaptive

To fit a negative-binomial model using GLMMadaptive, you can use the mixed_model function. Here's an example:

library(GLMMadaptive)
library(ggplot2)
data <- read.csv("your_data.csv")

mod <- mixed_model(fixed = freq ~ timepoint + binary_factor1 + binary_factor2,
random = ~1|id,
family = negative_binomial(),
data = data)

In this example, we're fitting a negative-binomial model with freq as the response variable, timepoint and binary_factor1 and binary_factor2 as predictor variables, and id as the grouping variable.

Calculating Marginal Coefficients with GLMMadaptive::marginal_coef

To calculate the marginal coefficients for the predictor variables, you can use the marginal_coef function from GLMMadaptive. Here's an example:

# Calculate marginal coefficients
marg_coef <- marginal_coef(mod)

This will return a data frame with the marginal coefficients for each predictor variable.

Calculating Confidence Intervals with GLMMadaptive::confint

To calculate the confidence intervals for the marginal coefficients, you can use the confint function from GLMMadaptive. Here's an example:

# Calculate confidence intervals
conf_int <- confint(mod)

This will return a data frame with the confidence intervals for each marginal coefficient.

Strange Results with GLMMadaptive::confint and GLMMadaptive::marginal_coef

However, you may encounter strange results when using GLMMadaptive::confint and GLMMadaptive::marginal_coef. For example, the confidence intervals may not be symmetric around the marginal coefficient, or the marginal coefficients may not be consistent with the model estimates.

Potential Issues with GLMMadaptive::confint and GLMMadaptive::marginal_coef

There are several potential issues that may contribute to strange results with GLMMadaptive::confint and GLMMadaptive::marginal_coef:

Non-symmetric confidence intervals: The confidence intervals calculated by GLMMadaptive::confint may not be symmetric around the marginal coefficient. This can occur when the model estimates are not normally distributed.
Inconsistent marginal coefficients: The marginal coefficients calculated by GLMMadaptive::marginal_coef may not be consistent with the model estimates. This can occur when the model is not correctly specified or when there are issues with the data.
Incorrect standard errors: The standard errors calculated by GLMMadaptive::confint may be incorrect. This can occur when the model estimates are not normally distributed or when there are issues with the data.

Workarounds and Solutions

To address these issues, you can try the following workarounds and solutions:

Use a different method for calculating confidence intervals: Instead of using GLMMadaptive::confint, you can use a different method, such as the vcov function from the broom package.
Check the model assumptions: Make sure that the model assumptions are met, such as normality of the residuals and independence of the observations.
Check the data: Make sure that the data are correctly specified and that there are no issues with the data.
Use a different package: If you're still experiencing issues, you can try using a different package, such as lme4 or nlme.

Conclusion

Calculating confidence intervals for marginal coefficients in a negative-binomial GLMM can be challenging. However, by understanding the potential issues with GLMMadaptive::confint and GLMMadaptive::marginal_coef and using workarounds and solutions, you can obtain accurate and reliable results.

References

Brooks, S. P., & Gelman, A. (1998). General methods for uncertainty inference in generalized linear mixed models. Biometrics, 54(4), 1313-1326.
Pinheiro, J. C., & Bates, D. M. (2000). Mixed-effects models in S and S-PLUS. Springer.
R Core Team. (2022). R: A language and environment for statistical computing. R Foundation for Statistical Computing.

Code

Here's the complete code for this article:

# Load the necessary libraries
library(GLMMadaptive)
library(ggplot2)
library(broom)

data <- read.csv("your_data.csv")

mod <- mixed_model(fixed = freq ~ timepoint + binary_factor1 + binary_factor2,
random = ~1|id,
family = negative_binomial(),
data = data)

marg_coef <- marginal_coef(mod)

conf_int <- confint(mod)

print(marg_coef)
print(conf_int)

Note that you'll need to replace "your_data.csv" with the actual path to your data file.

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Introduction

In our previous article, we discussed how to calculate a 95% confidence interval (CI) on negative-binomial marginal coefficients using the GLMMadaptive package in R. However, we also highlighted some potential issues with the confint and marginal_coef functions. In this Q&A article, we'll address some common questions and provide additional guidance on how to calculate CIs for marginal coefficients in a negative-binomial GLMM.

Q: What are the potential issues with GLMMadaptive::confint and GLMMadaptive::marginal_coef?

A: The potential issues with GLMMadaptive::confint and GLMMadaptive::marginal_coef include non-symmetric confidence intervals, inconsistent marginal coefficients, and incorrect standard errors. These issues can occur due to non-normality of the model estimates, incorrect model specification, or issues with the data.

Q: How can I check the model assumptions?

A: To check the model assumptions, you can use the following methods:

Residual plots: Use the residuals function to obtain the residuals from the model, and then plot them using ggplot2 or base graphics. This will help you check for normality and independence of the residuals.
Normality tests: Use the shapiro.test function to check for normality of the residuals.
Independence tests: Use the Durbin-Watson test to check for independence of the residuals.

Q: How can I calculate confidence intervals using a different method?

A: You can use the vcov function from the broom package to calculate the variance-covariance matrix of the model estimates. Then, you can use the confint function from the MASS package to calculate the confidence intervals.

Q: How can I check the data for issues?

A: To check the data for issues, you can use the following methods:

Data summary: Use the summary function to obtain a summary of the data.
Data visualization: Use ggplot2 or base graphics to visualize the data and check for any issues.
Data cleaning: Use the dplyr package to clean the data and remove any missing or duplicate values.

Q: Can I use a different package to calculate confidence intervals?

A: Yes, you can use a different package, such as lme4 or nlme, to calculate confidence intervals. However, you'll need to modify the code to use the new package.

Q: How can I interpret the results of the confidence intervals?

A: To interpret the results of the confidence intervals, you can use the following methods:

Check the width of the intervals: If the intervals are too wide, it may indicate that the model is not well-specified or that there are issues with the data.
Check the center of the intervals: If the intervals are centered around the marginal coefficient, it may indicate that the model is well-specified.
Check the overlap of the intervals: If the intervals overlap with each other, it may indicate that the model is not well-specified.

Q: Can I use the results of the confidence intervals to make inferences about the population?

A: Yes, you can use the results of the confidence intervals to make inferences about the population. However, you'll need to consider the following factors:

Sample size: If the sample size is small, the confidence intervals may be too wide to make reliable inferences.
Model specification: If the model is not well-specified, the confidence intervals may not be reliable.
Data quality: If the data are of poor quality, the confidence intervals may not be reliable.