Lecture_20Video_20W10D2_20-_20Categorical_20predictors_20in_20MLR_20-_20part_202

Collecting Midterm Exams

• Midterm exams returned for face-to-face students.

• Online students should collect their original exams via email to avoid scanning.

• Scanning and posting on Canvas will be done if necessary.

Categorical Predictors Overview

• Focus on categorical predictors previously discussed.

• Importance of defining dummy variables.

• Mechanism explained for coding with categorical predictors.

Dummy Variables

• Categorical predictors (e.g., race) often require multiple dummy variables based on the number of categories.

• Example: Race as a predictor with 3 categories requires 2 dummy variables (for hypothesis testing).

• Hypotheses:

  • Null Hypothesis: Both beta coefficients are zero (no effect).

  • Alternative Hypothesis: At least one beta is non-zero (some effect).

Factor Function in R

• Use of the factor() function is crucial for defining categorical variables:

  • Wrap categorical predictors with factor() in regression models.

  • Automatically handles dummy variable creation.

Example of the Factor Function

• Given a vector with numerics (1, 2, 3):

  • Using factor helps R treat them as categories instead of numerics.

  • levels showcase the categories defined.

Modifying Categorical Variables

• Use labels in the factor() function to change category names.

• Verifying categorical conversion with is.numeric() and is.factor().

Analyzing Categorical Data

• Using the table() function summarizes frequencies of each category.

• Example with gender: Shows counts of males and females.

Visualization

• Bar plots and table functions provide visual representation of frequencies.

• Using cross-tabulation with table() allows for joint distributions (e.g., gender vs. blood pressure group).

Summary Functions

• summary() function provides insights into numeric predictors and frequencies for categorical ones.

• Ensure categorical variables like BP groups are properly defined as factors to avoid misleading summaries.

Box Plots and Residuals

• Box plots are effective for displaying distributions of a continuous variable against a categorical variable.

• Useful in assumption checking after model fitting—e.g., residuals vs. categorical predictors.

Fitting Models in R

• Fitting multiple linear regression models:

  • Example: Model comparisons using ANOVA (Analysis of Variance).

  • Models may differ in predictors for hypothesis testing.

ANOVA for Nested Models

• Valid for testing effects across multiple variables:

  • Null Hypothesis: No significant model difference (e.g., certain beta coefficients are zero).

  • Framework: Fit two models and compare them, paying attention to missing values and handling them accordingly.

Missing Values Handling

• Removing incomplete observations to ensure same dataset size for models to avoid errors in ANOVA.

• Utilization of sub-databases focusing only on necessary columns to simplify analysis without missing values.

Conclusion of Hypothesis Testing

• ANOVA p-values determine whether to reject the null hypothesis.

• Beta coefficients allow for interpretation of average differences between categorical groups (e.g., BMI groups).

• The significance of outcomes must be contextualized with other variables held constant.