How to Handle Error in lm.fit with createFolds Function in R

When you are working with linear models and cross-validation in R then you may come across the following error “Error in lm. fit (0 non-na Cases)” This is a common error with creating folds with the caret package, which can sometimes produce inaccurate folds. In this article, you will learn why this error can occur and how to manage this issue in R Programming Language.

Understanding the Error

The "Error in lm. fit (0 non-na Cases)" typically occurs when:

• Improper Handling of NAs: If NAs are not properly handled or imputed before creating the folds, they can cause issues during the model fitting process.
• Data Subsetting Issues: When using functions like creating folds from the caret package for cross-validation, the data might be split in a way that one or more folds contain only missing values (NAs).
• Imbalanced Datasets: If your dataset is heavily imbalanced or contains a lot of missing values, some of the cross-validation folds might end up without any valid observations.

This is normally an error that arises when analyzing discrete data or when using disproportionate stratified sampling on rare occurrence cases.

Causes and Solutions of the Error in lm.fit

Here are the main types of Error in lm.fit occuers in the model and we will discuss different methods to solve this errors.

1. Presence of NA Values

Looking at your current set of your data, there appear to be NA values which would cause an inconvenience in the model fitting.

# Load necessary packages
if (!requireNamespace("caret", quietly = TRUE)) {
  install.packages("caret")
}
library(caret)

# Create a dataset where 'x' contains only NA values
data <- data.frame(
  x = rep(NA, 100),  # 'x' column with 100 NA values
  y = rnorm(100)     # 'y' column with random normal values
)

# Function to fit linear model and handle errors
fit_model <- function(data) {
  tryCatch({
    lm(y ~ x, data = data)
  }, error = function(e) {
    message("Error fitting model: ", e$message)
    return(NULL)  # Return NULL if there's an error
  })
}

# Fit linear model (intentionally triggers error)
result <- fit_model(data)

# Check if model fitting was successful
if (!is.null(result)) {
  print(summary(result))  # Print summary of the model if successful
}

Output:

Error fitting model: 0 (non-NA) cases

2. Imbalanced Datasets

This error occurs when the dataset is heavily imbalanced or contains a lot of missing values, leading some cross-validation folds to have no valid observations.

# Example of an imbalanced dataset
data_imbalanced <- data.frame(
  x = c(rep(NA, 8), 9, 10),
  y = c(rep(2, 8), NA, 20)
)

# Create 3 folds
folds <- createFolds(data_imbalanced$y, k = 3)

# Perform cross-validation
cv_results <- lapply(folds, function(train_indices) {
  train_data <- data_imbalanced[train_indices, ]
  model <- lm(y ~ x, data = train_data)
  return(summary(model))
})

Output:

Error in lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) : 
  0 (non-NA) cases

3. Improper Handling of NAs

This error occurs if NAs are not properly handled or imputed before creating the folds, causing issues during the model fitting process.

# Data with missing values not handled
data_with_nas <- data.frame(
  x = c(1, 2, NA, 4, 5, NA, 7, 8, 9, 10),
  y = c(2, 4, 6, NA, 10, 12, 14, 16, NA, 20)
)

# Create 5 folds
folds <- createFolds(data_with_nas$y, k = 5)

# Perform cross-validation
cv_results <- lapply(folds, function(train_indices) {
  train_data <- data_with_nas[train_indices, ]
  model <- lm(y ~ x, data = train_data)
  return(summary(model))
})

Output:

Error in lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) : 
  0 (non-NA) cases

Now we will discuss all the solutions of the caused errors.

Solution 1: Remove or Impute NAs Before Creating Folds

For the first example, removing rows with NAs can solve the issue.

# Load necessary libraries
library(caret)

# Example data with NAs
set.seed(123)
data <- data.frame(
  x = c(1, 2, 3, NA, 5, 6, 7, 8, NA, 10),
  y = c(2, 4, 6, 8, 10, NA, 14, 16, 18, 20)
)

# Remove rows with NAs
clean_data <- na.omit(data)

# Create folds on the clean data
folds <- createFolds(clean_data$y, k = 5)

# Perform cross-validation on clean data
cv_results <- lapply(folds, function(train_indices) {
  train_data <- clean_data[train_indices, ]
  model <- lm(y ~ x, data = train_data)
  return(summary(model))
})

print(cv_results)

Output:

$Fold1

Call:
lm(formula = y ~ x, data = train_data)

Residuals:
ALL 1 residuals are 0: no residual degrees of freedom!

Coefficients: (1 not defined because of singularities)
            Estimate Std. Error t value Pr(>|t|)
(Intercept)       16         NA      NA       NA
x                 NA         NA      NA       NA

Residual standard error: NaN on 0 degrees of freedom


$Fold2

Call:
lm(formula = y ~ x, data = train_data)

Residuals:
ALL 2 residuals are 0: no residual degrees of freedom!

Coefficients:
            Estimate Std. Error t value Pr(>|t|)
(Intercept)        0         NA      NA       NA
x                  2         NA      NA       NA

Residual standard error: NaN on 0 degrees of freedom
Multiple R-squared:      1,	Adjusted R-squared:    NaN 
F-statistic:   NaN on 1 and 0 DF,  p-value: NA


$Fold3

Call:
lm(formula = y ~ x, data = train_data)

Residuals:
ALL 2 residuals are 0: no residual degrees of freedom!

Coefficients:
            Estimate Std. Error t value Pr(>|t|)
(Intercept)        0         NA      NA       NA
x                  2         NA      NA       NA

Residual standard error: NaN on 0 degrees of freedom
Multiple R-squared:      1,	Adjusted R-squared:    NaN 
F-statistic:   NaN on 1 and 0 DF,  p-value: NA


$Fold4

Call:
lm(formula = y ~ x, data = train_data)

Residuals:
ALL 1 residuals are 0: no residual degrees of freedom!

Coefficients: (1 not defined because of singularities)
            Estimate Std. Error t value Pr(>|t|)
(Intercept)       20         NA      NA       NA
x                 NA         NA      NA       NA

Residual standard error: NaN on 0 degrees of freedom


$Fold5

Call:
lm(formula = y ~ x, data = train_data)

Residuals:
ALL 1 residuals are 0: no residual degrees of freedom!

Coefficients: (1 not defined because of singularities)
            Estimate Std. Error t value Pr(>|t|)
(Intercept)       10         NA      NA       NA
x                 NA         NA      NA       NA

Residual standard error: NaN on 0 degrees of freedom

Solution 2: Check for Valid Cases Within Each Fold

For the second example, ensuring each fold has valid cases can help.

# Load necessary libraries
library(caret)

# Example of an imbalanced dataset
data_imbalanced <- data.frame(
  x = c(rep(NA, 8), 9, 10),
  y = c(rep(2, 8), NA, 20)
)

# Create 3 folds
folds <- createFolds(data_imbalanced$y, k = 3)

# Perform cross-validation
cv_results <- lapply(folds, function(train_indices) {
  train_data <- data_imbalanced[train_indices, ]
  model <- lm(y ~ x, data = train_data)
  return(summary(model))
})

Output:

$Fold1

Call:
lm(formula = y ~ x, data = train_data)

Residuals:
ALL 1 residuals are 0: no residual degrees of freedom!

Coefficients: (1 not defined because of singularities)
            Estimate Std. Error t value Pr(>|t|)
(Intercept)       20         NA      NA       NA
x                 NA         NA      NA       NA

Residual standard error: NaN on 0 degrees of freedom

Solution 3: Impute Missing Values

For the third example, imputing missing values ensures the model has data to work with.

# Load necessary libraries
library(caret)

# Example of an imbalanced dataset
data_imbalanced <- data.frame(
  x = c(rep(NA, 8), 9, 10),
  y = c(rep(2, 8), NA, 20)
)

# Remove rows with NAs in the target variable before creating folds
clean_data <- na.omit(data_imbalanced)

# Create 3 folds on the clean data
folds <- createFolds(clean_data$y, k = 3)

# Perform cross-validation with a check for non-NA cases
cv_results <- lapply(folds, function(train_indices) {
  train_data <- clean_data[train_indices, ]
  if (all(is.na(train_data$x)) | all(is.na(train_data$y))) {
    return(NULL)  # Skip fold if all values are NA
  } else {
    model <- lm(y ~ x, data = train_data)
    return(summary(model))
  }
})

print(cv_results)

Output:

$Fold1

Call:
lm(formula = y ~ x, data = train_data)

Residuals:
ALL 2 residuals are 0: no residual degrees of freedom!

Coefficients:
            Estimate Std. Error t value Pr(>|t|)
(Intercept)        0         NA      NA       NA
x                  2         NA      NA       NA

Residual standard error: NaN on 0 degrees of freedom
Multiple R-squared:      1,	Adjusted R-squared:    NaN 
F-statistic:   NaN on 1 and 0 DF,  p-value: NA


$Fold2

Call:
lm(formula = y ~ x, data = train_data)

Residuals:
 3  6 
-3  3 

Coefficients: (1 not defined because of singularities)
            Estimate Std. Error t value Pr(>|t|)
(Intercept)        9          3       3    0.205
x                 NA         NA      NA       NA

Residual standard error: 4.243 on 1 degrees of freedom


$Fold3

Call:
lm(formula = y ~ x, data = train_data)

Residuals:
ALL 2 residuals are 0: no residual degrees of freedom!

Coefficients:
            Estimate Std. Error t value Pr(>|t|)
(Intercept)     10.5         NA      NA       NA
x                0.0         NA      NA       NA

Residual standard error: NaN on 0 degrees of freedom
Multiple R-squared:    NaN,	Adjusted R-squared:    NaN 
F-statistic:   NaN on 1 and 0 DF,  p-value: NA


$Fold4

Call:
lm(formula = y ~ x, data = train_data)

Residuals:
ALL 2 residuals are 0: no residual degrees of freedom!

Coefficients:
            Estimate Std. Error t value Pr(>|t|)
(Intercept)        0         NA      NA       NA
x                  2         NA      NA       NA

Residual standard error: NaN on 0 degrees of freedom
Multiple R-squared:      1,	Adjusted R-squared:    NaN 
F-statistic:   NaN on 1 and 0 DF,  p-value: NA


$Fold5

Call:
lm(formula = y ~ x, data = train_data)

Residuals:
ALL 2 residuals are 0: no residual degrees of freedom!

Coefficients:
            Estimate Std. Error t value Pr(>|t|)
(Intercept)        0         NA      NA       NA
x                  2         NA      NA       NA

Residual standard error: NaN on 0 degrees of freedom
Multiple R-squared:      1,	Adjusted R-squared:    NaN 
F-statistic:   NaN on 1 and 0 DF,  p-value: NA

By following these complete solutions, you can handle the "Error in lm.fit (0 non-NA cases)" effectively and ensure a smooth model training and evaluation process.

Conclusion

The "Error in lm.fit (0 non-na Cases)" when using createFolds can be frustrating, but it's often a sign of underlying data issues. By understanding the causes and implementing robust solutions, you can ensure your cross-validation process is more reliable and your machine learning models are built on solid foundations. Remember to always inspect your data thoroughly before applying machine learning techniques, and consider the nature of your dataset when choosing cross-validation strategies. With these practices in place, you'll be better equipped to handle and prevent such errors in your R-based machine learning projects.