Change Reference (Baseline) Category in Regression with R | R Tutorial 5.6 | MarinStatsLectures

MarinStatsLectures-R Programming & Statistics
10 Mar 201404:19
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TLDRIn this educational video, Mike Marin explains the concept of changing the reference category in a linear regression model. He demonstrates using R and the Lung Capacity dataset, showing how the intercept and coefficients change when the baseline category for the 'smoking' variable is altered. The tutorial highlights the use of the 'relevel' command in R to redefine the reference category and emphasizes that this change does not affect the model's overall fit, illustrating the process of re-parameterizing a model.

Takeaways
  • 📊 In a linear regression model, the intercept represents the estimated mean Y-value for the reference or baseline group.
  • 🧮 Model coefficients indicate expected changes in the mean Y-value relative to the reference group.
  • 📁 Understanding dummy or indicator variables is essential for interpreting regression models.
  • 📋 The Lung Capacity data set is used for demonstration in this video.
  • 🔍 The 'relevel' command in R is used to change the reference category for a categorical variable.
  • 📈 By default, R chooses the first category alphabetically or numerically as the reference category.
  • ✅ The video demonstrates fitting a regression model with Lung Capacity related to Age and Smoking.
  • 📉 The coefficient for Age represents the expected change in mean Lung Capacity for a one-unit increase in Age, holding Smoking constant.
  • 🚬 The coefficient for Smoking indicates the expected change in mean Lung Capacity for smokers relative to non-smokers, holding Age constant.
  • 🔄 Re-parameterizing a model by changing the reference category does not alter important statistics like R-squared or residual standard error.
Q & A

  • What is the purpose of the video by Mike Marin?

    -The purpose of the video is to explain how to change the reference or baseline category for a categorical variable in a linear regression model.

  • What does the intercept in a linear regression model represent?

    -The intercept represents the estimated mean Y-value for the reference or baseline group in a linear regression model.

  • What is the role of the model coefficients in a linear regression model?

    -The model coefficients represent the expected changes in the mean Y-value relative to the reference group for each unit change in the independent variable.

  • What is a dummy or indicator variable in the context of regression analysis?

    -A dummy or indicator variable is a binary variable used in regression analysis to represent the presence or absence of a categorical variable.

  • What data set does Mike Marin use in his video?

    -Mike Marin uses the Lung Capacity data set in his video.

  • What command does Mike Marin demonstrate for changing the reference category in R?

    -Mike Marin demonstrates the use of the 'relevel' command in R to change the reference category.

  • How does the 'relevel' command work in R?

    -The 'relevel' command in R allows you to change the reference category by storing a re-leveled version of the variable with the desired category as the reference.

  • What is the default reference category chosen by R in a categorical variable?

    -By default, R chooses the reference category to be the first category that appears alphabetically or numerically if categories are coded using 0, 1, 2.

  • How does changing the reference category affect the model's R-squared and residual standard error?

    -Changing the reference category does not affect the R-squared, residual standard error, or other summaries of the model; it only changes the interpretation of the coefficients.

  • What is the estimated mean Lung Capacity for a non-smoker of age 0 in the original model?

    -In the original model, the estimated mean Lung Capacity for a non-smoker of age 0 is 1.09.

  • What is the expected change in mean Lung Capacity for a smoker relative to a non-smoker in the original model?

    -In the original model, the expected change in mean Lung Capacity for a smoker relative to a non-smoker, adjusting for age, is a decrease of 0.65.

  • What is re-parameterizing a model and why is it done?

    -Re-parameterizing a model involves changing the reference category to alter the interpretation of the coefficients without affecting the model's overall fit. It is done to provide a more meaningful or relevant perspective on the data.

Outlines
00:00
📊 Changing the Baseline Category in Linear Regression

In this section, Mike Marin introduces the concept of altering the reference or baseline category for a categorical variable within a linear regression model. He explains the significance of the intercept as the estimated mean Y-value for the baseline group and how coefficients represent changes relative to this group. The video utilizes the Lung Capacity dataset and demonstrates the use of the 'relevel' command in R to adjust the baseline category from 'No' to 'Yes' for the smoking variable. The summary of the initial model, 'mod1', is provided, showing the estimated mean Lung Capacity for the reference group and the expected changes in mean Y-value associated with age and smoking status.

Mindmap
Keywords
💡Linear Regression Model
A linear regression model is a statistical method used to predict the value of a dependent variable (Y) based on the value of one or more independent variables (X). In the video, the model is used to analyze the relationship between lung capacity and factors such as age and smoking. The intercept and coefficients in the model represent the estimated mean lung capacity for a baseline group and the expected changes in lung capacity relative to this group.
💡Intercept
The intercept in a linear regression model is the constant term that represents the estimated mean value of the dependent variable when all the independent variables are zero. In the context of the video, the initial intercept of 1.09 indicates the mean lung capacity for a group with age equal to 0 and who do not smoke.
💡Coefficient
In the linear regression model discussed in the video, coefficients are the parameters that represent the expected change in the mean value of the dependent variable for a one-unit change in an independent variable. For example, the coefficient for age (0.56) suggests that for each additional year of age, the mean lung capacity is expected to increase by 0.56 units, assuming all other variables are held constant.
💡Dummy Variable
A dummy variable, also known as an indicator variable, is used in regression analysis to represent categorical data. In the video, the smoking status is represented as a dummy variable where 1 indicates smoking and 0 indicates not smoking. This allows the model to account for the impact of smoking on lung capacity.
💡Reference Category
The reference category, also known as the baseline category, is the category of a categorical variable that serves as a comparison point for other categories in a regression model. In the video, the default reference category for smoking is 'No', but it is changed to 'Yes' using the 'relevel' command to make smokers the baseline for comparison.
💡Relevel Command
The 'relevel' command in R is used to change the reference category of a factor variable. In the video, this command is demonstrated to change the reference category of smoking from 'No' to 'Yes', which alters the interpretation of the coefficients in the regression model.
💡Lung Capacity Data
The Lung Capacity data set mentioned in the video is the dataset used for the regression analysis. It contains variables such as age and smoking status, which are used to predict lung capacity. The data is imported into R and serves as the basis for demonstrating how to change the reference category.
💡R-squared
R-squared is a statistical measure that represents the proportion of the variance for a dependent variable that's explained by an independent variable or variables in a regression model. In the video, R-squared remains the same after changing the reference category, indicating that the model's explanatory power is unchanged.
💡Residual Standard Error
The residual standard error is a measure of the average difference between the observed values and the values predicted by the regression model. In the video, the residual standard error is mentioned as one of the summary statistics that remains unchanged when the reference category is altered.
💡Re-parameterizing a Model
Re-parameterizing a model involves changing the reference category or the way parameters are interpreted without altering the fundamental relationships within the model. In the video, changing the reference category from 'No' to 'Yes' for smoking is an example of re-parameterizing the model, which changes the interpretation of the coefficients but not the overall model fit.
Highlights

Introduction to changing the reference category in a linear regression model.

Explanation of the intercept as the estimated mean Y-value for the baseline group.

Clarification on model coefficients representing expected changes in mean Y-value relative to the reference group.

Reference to a video explaining the concept of dummy or indicator variables.

Introduction of the Lung Capacity data set used for demonstration.

Demonstration of the 'relevel' command in R for changing the reference category.

Instructions on accessing help in R for the 'relevel' command.

Fitting the initial regression model 'mod1' with Lung Capacity related to Age and Smoking.

Summary of the initial model output showing the estimated mean Lung Capacity for non-smokers of age 0.

Interpretation of the age coefficient indicating the expected change in Lung Capacity per year.

Interpretation of the smoking coefficient as the expected difference in Lung Capacity between smokers and non-smokers.

Default behavior of R in choosing the reference category based on alphabetical or numerical order.

Method to change the reference category to 'Yes' for smokers using the 'relevel' command.

Verification of the new reference category through a frequency table.

Fitting a new model with the re-leveled smoking variable and its summary.

Interpretation of the new intercept as the estimated mean Lung Capacity for smokers of age 0.

Interpretation of the non-smoking coefficient in the context of the new reference category.

Comparison of the two models to illustrate the unchanged R-squared and residual standard error despite the change in reference group.

Concept of re-parameterizing a model by changing the reference group.

Closing remarks and invitation to watch other instructional videos.

Transcripts

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Related Tags
Linear RegressionR ProgrammingData AnalysisCategorical VariablesDummy VariablesModel FittingStatistical ModelingReference CategoryBaseline GroupRegression AnalysisData Science