How to Solve R Error: number of levels of each grouping factor must be < number of observations

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.

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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.

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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.

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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

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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.

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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
  

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