Understanding and Addressing the “Number of Levels” Error in Linear Mixed-Effects Models

When working with linear mixed-effects models, one common error can occur when trying to fit a model that doesn’t meet the required criteria for such models. In this article, we’ll delve into what this error means, why it happens, and how to address it.

Background on Linear Mixed-Effects Models

Linear mixed-effects (LME) models are an extension of traditional linear regression models. They allow for the inclusion of random effects to account for non-independence within groups. This is particularly useful in fields such as medicine, social sciences, and animal breeding, where observations can be nested within clusters or subjects.

The core assumption underlying LMEs is that there should be fewer subjects than total observations. This assumption ensures that each subject contributes a unique observation to the dataset, which helps in estimating the variance components of the model.

The Error Message

When trying to fit an LME using the lmer function from the lme4 package in R, you might encounter an error message:

Error: number of levels of each grouping factor must be < number of observations.

This error occurs when there are more levels in a categorical variable than the total number of observations.

Example and Explanation

Consider the following example code:

library(lme4)
set.seed(123)
n <- 38
DBS_Electrode <- factor(sample(LETTERS[1:3], n, replace = TRUE))

Distal_Lead_Migration <- 10 * abs(rnorm(n))    # Distal_Lead_Migration in cm
PostOp_ICA <- 5 * abs(rnorm(n))

# amount of observations equals to amount of subjects
Subject <- paste0("X", 1:n)
DBS <- data.frame(DBS_Electrode, PostOp_ICA, Subject, Distal_Lead_Migration)

model <- lmer(Distal_Lead_Migration ~ DBS_Electrode + PostOp_ICA + (1|Subject), data = DBS)

In this example, we have a subject variable with 38 levels and two fixed effects: DBS_Electrode and PostOp_ICA. However, since there are more levels in the subject variable than observations, the model fails to fit.

Fixing the Error

To fix this error, you need to ensure that the number of levels in each categorical variable is less than or equal to the total number of observations. This can be achieved by either:

1. Reducing the number of observations per subject.
2. Increasing the number of subjects.
3. Creating a new categorical variable with fewer levels.

Here’s an updated version of the code where we increase the number of observations per subject:

library(lme4)
set.seed(123)

# amount of observations more than amount of subjects
Subject <- c(paste0("X", 1:36), "X1", "X37")
DBS_Electrode <- factor(sample(LETTERS[1:3], length(Subject), replace = TRUE))
PostOp_ICA <- 5 * abs(rnorm(length(Subject)))

Distal_Lead_Migration <- 10 * abs(rnorm(length(Subject)))    # Distal_Lead_Migration in cm

model <- lmer(Distal_Lead_Migration ~ DBS_Electrode + PostOp_ICA + (1|Subject))

In this updated code, we’ve increased the number of observations per subject and ensured that each subject contributes only one unique observation. This allows us to fit a valid linear mixed-effects model.

Conclusion

When working with linear mixed-effects models, it’s essential to ensure that the number of levels in categorical variables meets the required criteria for such models. By reducing the number of observations per subject or increasing the total number of subjects, you can address this error and fit a valid LME model.

Last modified on 2024-04-26