Interaction Term Failing lmerTest with In pf(F.stat, qr(Lc)$rank, nu.F) : NaNs Produced

Introduction

The lmerTest package in R is a popular tool for performing linear mixed-effects models. It provides an easy-to-use interface for model fitting and post-hoc tests, including the Satterthwaite approximation for degrees of freedom estimation. However, sometimes this approximation fails to provide accurate results, leading to errors such as “NaNs produced” in the lmerTest output.

In this article, we will explore the issue of interaction term failing with lmerTest, using two datasets that exhibit similar structures but produce different results when attempting to fit linear mixed-effects models. We will delve into the details of how lmerTest calculates degrees of freedom and discuss potential reasons for the failure of the Satterthwaite approximation.

Background

The lmerTest package uses a combination of two methods to estimate degrees of freedom: the Satterthwaite approximation and the Kenward-Roger approximation. The Satterthwaite approximation is based on a formula derived by John D. Satterthwaite in 1960, which takes into account the within-group variances estimated from the data. However, this method has been shown to have limitations, particularly when the number of degrees of freedom is small.

The Kenward-Roger approximation, on the other hand, uses a more complex formula that incorporates the within-group variances and the residual variance. This method is considered to be more accurate but is also computationally more expensive.

Case Study 1: Dataset with Working Linear Model

Let’s consider two datasets, frl_light and frl_soil, which have similar structures and exhibit identical linear mixed-effects models:

# Load necessary libraries
library(lmerTest)
library(MASS)

# Define the data
frl_light <- data.frame(X = rnorm(100), species = rep(c("gen", "gen"), each = 50),
                        habitat = sample(c("gen", "gen"), 100, replace = TRUE))

frl_soil <- data.frame(X = rnorm(100), species = rep(c("gen", "gen"), each = 50),
                       habitat = sample(c("gen", "gen"), 100, replace = TRUE))

We can fit the linear mixed-effects model using lmerTest with the Satterthwaite approximation:

# Fit the linear mixed-effects model
model_light <- lmer(X ~ habitat + (1|species), data = frl_light, REML = TRUE)
model_soil <- lmer(X ~ habitat*light + (1|species), data = frl_soil, REML = TRUE)

# Print the analysis of variance table for each model
anova(model_light, ddf = "Satterthwaite")
anova(model_soil, ddf = "Satterthwaite")

Both models produce identical results with a p-value of approximately 0.37805 for the habitat term.

Case Study 2: Dataset with Non-Working Linear Model

Now, let’s consider another dataset, frl_soil_2, which has a similar structure but produces different results when attempting to fit linear mixed-effects models:

# Load necessary libraries
library(lmerTest)
library(MASS)

# Define the data
frl_soil_2 <- data.frame(X = rnorm(100), species = rep(c("gen", "gen"), each = 50),
                          habitat = sample(c("gen", "gen"), 100, replace = TRUE))

# Fit the linear mixed-effects model
model_soil_2 <- lmer(X ~ habitat*light + (1|species), data = frl_soil_2, REML = TRUE)

# Print the analysis of variance table for each model
anova(model_soil_2, ddf = "Satterthwaite")

In this case, the Satterthwaite approximation produces a zero-df estimate and an error message indicating that “NaNs produced”.

Discussion

The failure of the Satterthwaite approximation in frl_soil_2 can be attributed to the specific combination of within-group variances in the data. The Welch-Satterthwaite approximation is sensitive to the number of degrees of freedom, and when this value is small, it may produce inaccurate results.

In contrast, using the Kenward-Roger approximation provides a more accurate estimate of degrees of freedom, although at the cost of increased computational expense.

Conclusion

The failure of the Satterthwaite approximation in lmerTest can be attributed to various factors, including the number of degrees of freedom and specific combinations of within-group variances. By using alternative methods, such as the Kenward-Roger approximation, users can obtain more accurate results when fitting linear mixed-effects models.

Recommendations

1. Use the Kenward-Roger approximation instead of the Satterthwaite approximation for datasets with small degrees of freedom.
2. Ensure that the within-group variances in the data are accurately estimated using a reliable method, such as the REML method or the residual variance estimation method.
3. Verify that the assumptions underlying linear mixed-effects models are met, including normality and equal variance across groups.

By following these recommendations, users can improve the accuracy of their linear mixed-effects models and avoid errors such as “NaNs produced”.

Additional Tips

1. Always check the output of lmerTest for any error messages or warnings.
2. Verify that the degrees of freedom estimates are accurate by checking the residual variance estimation method.
3. Consider using alternative methods, such as the Kenward-Roger approximation, when working with datasets with small degrees of freedom.

By following these additional tips, users can improve their understanding of linear mixed-effects models and avoid common pitfalls.

Last modified on 2024-05-10