Running ANCOVA Tests with lm() in R: A Comprehensive Guide

ANCOVA (Analysis of Covariance) is a statistical technique used to analyze the effect of one or more covariates on the response variable, while controlling for their effects. In this article, we will explore how to run ANCOVA tests using the lm() function in R.

Introduction to ANCOVA

ANCOVA includes both factor and continuous variables as independent variables in a linear model. This approach allows us to examine the effect of one or more covariates on the response variable while controlling for their effects. In essence, ANCOVA provides a way to analyze the interaction between the covariate(s) and the response variable.

Running ANCOVA with lm() in R

For the iris dataset, we can run the following code:

lm(Sepal.Length ~ Sepal.Width + Species, data = iris)

This code runs a linear regression model that includes both Sepal.Width and Species as independent variables. The Sepal.Length variable is the response variable.

Understanding the Model

The output of this code will provide us with the estimated coefficients for each independent variable. However, we must understand that the intercept represents the factor level that’s not listed in the output, and the other factor levels are interpreted as differences relative to the species represented by the intercept.

For example, since Setosa is not listed in the regression coefficients list, it is represented by the intercept term. Therefore, the other species coefficients (e.g., Versicolor) are interpreted as “the effect of Species = Virginica on sepal length is x relative to Setosa, net of sepal width.”

Making Predictions

To make predictions with this model, we can save the model object and use it with the predict() function. This function allows us to predict values of Sepal.Length based on specific combinations of independent variables.

Let’s consider an example:

fit <- lm(Sepal.Length ~ Sepal.Width + Species, data = iris)

# predict some values
Species <- c("setosa", "setosa", "virginica", "versicolor", "setosa")
Sepal.Width <- c(3.1, 3.2, 3.8, 2.9, 3.25)

data <- data.frame(Species, Sepal.Width)
data$predicted <- predict(fit, data)
data

In this code, we first create a new dataframe data with the specified combinations of independent variables. We then use the predict() function to compute the predicted values of Sepal.Length. The output is:

  Species Sepal.Width predicted
1     setosa        3.10      4.742432
2     setosa        3.20      4.822788
3  virginica        3.80      7.251741
4 versicolor        2.90      6.040463
5     setosa        3.25      4.862966

Using lm() with Multiple Covariates

In some cases, we may want to include multiple covariates in our linear model. To do this, we can simply add more independent variables to the lm() function.

For example:

fit <- lm(Sepal.Length ~ Sepal.Width + Petals.Length + Species, data = iris)

This code runs a linear regression model that includes both Sepal.Width, Petals.Length, and Species as independent variables.

Conclusion

In this article, we have explored how to run ANCOVA tests using the lm() function in R. We covered the basics of ANCOVA, including how to specify the model and interpret the output. We also demonstrated how to make predictions with the model using the predict() function. With these skills, you can now apply ANCOVA techniques to your own research projects.

Additional Tips

• Make sure to check the assumptions of ANCOVA before running a test.
• Consider using other R packages such as lmtest or car for more advanced ANCOVA models.
• Always explore and visualize your data before running any statistical analysis.

Last modified on 2023-11-24