When working with mixed-effects models in R, particularly with functions like `lmer()`

from the **lme4** package, you may encounter the following error:

Error: number of levels of each grouping factor must be < number of observations (problems: group)

This error occurs when your model’s grouping factor has too many levels in comparison to the number of observations. Let’s break down the cause and solution for this issue.

## Understanding the Error

In mixed-effects models, a grouping factor is often a categorical variable that defines the groups or clusters within your data (e.g., subjects, classes, regions). This error arises when the number of levels (distinct categories) of a grouping factor equals or exceeds the number of observations available for fitting the model. Essentially, R cannot fit a model because there aren’t enough observations per level to estimate variance effectively.

For example, if you have a dataset with 10 observations but a grouping factor with 10 or more levels, R throws this error because there’s not enough information within each group to estimate the model’s parameters.

**Example Code to Reproduce the Error**

Let’s consider an example using the **lme4** package.

# Load necessary package library(lme4) # Simulate data with more levels in the grouping factor than observations set.seed(123) data <- data.frame( y = rnorm(10), x = rnorm(10), group = factor(1:10) # Each observation has a unique group ) # Attempt to fit a mixed-effects model model <- lmer(y ~ x + (1|group), data = data)

Running this code will give you the following error:

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

In this case, the grouping factor `group`

has 10 levels, but there are only 10 observations, making it impossible to fit a random-effects term for each group.

### Solution

There are two primary ways to solve this issue:

#### 1. Reduce the Number of Levels in the Grouping Factor

Reducing the number of unique levels in the grouping factor avoids this error. For instance, grouping observations into fewer categories:

# Combine some groups to reduce the number of levels data$group <- factor(rep(1:5, each = 2)) # Now there are only 5 groups # Fit the model again model <- lmer(y ~ x + (1|group), data = data) summary(model)

**Output:**

Linear mixed model fit by REML ['lmerMod'] Formula: y ~ x + (1 | group) Data: data REML criterion at convergence: 23.4 Scaled residuals: Min 1Q Median 3Q Max -1.1487 -0.4868 0.1419 0.3126 1.5058 Random effects: Groups Name Variance Std.Dev. group (Intercept) 0.2796 0.5288 Residual 0.4131 0.6427 Number of obs: 10, groups: group, 5 Fixed effects: Estimate Std. Error t value (Intercept) -0.03997 0.31537 -0.127 x 0.54932 0.22610 2.430 Correlation of Fixed Effects: (Intr) x -0.150

This change reduces the number of levels in the grouping factor to 5, which is less than the number of observations (10), allowing the model to fit successfully.

#### 2. Increase the Number of Observations per Group:

Another solution is to collect or generate more observations for each level of the grouping factor. If there are more observations per group, the model will have enough information to estimate the random effects.

# Simulate more data for each group data <- data.frame( y = rnorm(20), x = rnorm(20), group = factor(rep(1:5, each = 4)) # More observations per group ) # Fit the model again model <- lmer(y ~ x + (1|group), data = data) summary(model)

**Output:**

Linear mixed model fit by REML ['lmerMod'] Formula: y ~ x + (1 | group) Data: data REML criterion at convergence: 49.7 Scaled residuals: Min 1Q Median 3Q Max -1.9950 -0.4690 0.1428 0.5531 1.6728 Random effects: Groups Name Variance Std.Dev. group (Intercept) 0.2081 0.4562 Residual 0.5453 0.7384 Number of obs: 20, groups: group, 5 Fixed effects: Estimate Std. Error t value (Intercept) -0.050625 0.263196 -0.192 x -0.005936 0.183255 -0.032 Correlation of Fixed Effects: (Intr) x -0.074

**Additional Tips:**

**Check Data Structure**: Always inspect the structure of your data, especially the grouping factors, before fitting the model. You can use functions like`str()`

or`summary()`

to examine the number of levels in each grouping factor.

str(data)

**Ensure Balanced Data**: While mixed-effects models can handle unbalanced data, it’s generally advisable to have enough observations per group to improve model stability and interpretability.

**Conclusion**

The error “number of levels of each grouping factor must be < number of observations” occurs when your data lacks enough observations per grouping level to fit a mixed-effects model. By either reducing the number of levels in the grouping factor or increasing the number of observations per level, you can resolve this error and fit your model successfully.

or further reading on R-related errors, go to the articles:

- How to Solve R Error in sort.int(x, na.last = na.last, decreasing = decreasing, …) : ‘x’ must be atomic
- How to Solve R Error: Arguments imply differing number of rows
- How to Solve R Error as.Date.numeric(x) : ‘origin’ must be supplied
- How to Solve R Error: ggplot2 doesn’t know how to deal with data of class uneval

Go to the online courses page on R to learn more about coding in R for data science and machine learning.

Have fun and happy researching!

Suf is a senior advisor in data science with deep expertise in Natural Language Processing, Complex Networks, and Anomaly Detection. Formerly a postdoctoral research fellow, he applied advanced physics techniques to tackle real-world, data-heavy industry challenges. Before that, he was a particle physicist at the ATLAS Experiment of the Large Hadron Collider. Now, he’s focused on bringing more fun and curiosity to the world of science and research online.