Session 3: Multivariable#

Multivariable analysis typically involves working with multiple independent variables to understand their impact on a dependent variable. Often, we use parametric methods for this analysis as they provide a useful framework when the assumptions of these methods are met. However, in cases where the assumptions of parametric methods are not met, semi-parametric methods can be helpful. Unfortunately, non-parametric methods are not well-suited for multivariable analysis due to their limitations in handling multiple independent variables. In this chapter, we’ll focus on parametric and semi-parametric methods, exploring how they can be used in Stata

Session 3: Multivariable Regression Analysis

  1. Introduction to Multivariable Regression Analysis:

    • Overview of multivariable regression and its applications

    • Understanding the concept of multiple independent variables and a dependent variable

  2. Parametric Methods:

    • Review of simple linear regression from Session 2

    • Extending to multiple independent variables: multiple linear regression

    • Interpretation of regression coefficients, adjusted R-squared, and significance testing

  3. Assumptions of Multivariable Regression:

    • Discussing the assumptions of multivariable regression: linearity, independence, homoscedasticity, and normality

    • Techniques for checking and addressing violations of these assumptions in Stata

  4. Model Building:

    • Strategies for model building: forward selection, backward elimination, and stepwise regression

    • Introduction to techniques such as AIC and BIC for model selection

    • Applying these techniques in Stata to construct a multivariable regression model

  5. Interactions and Non-Linear Relationships:

    • Incorporating interactions between independent variables in the regression model

    • Examining and interpreting interaction effects using Stata

    • Handling non-linear relationships through polynomial terms or splines

  6. Semi-Parametric Methods:

    • Introduction to semi-parametric regression models, such as generalized additive models (GAMs)

    • Overview of the advantages and limitations of semi-parametric methods in multivariable analysis

    • Demonstrating the use of semi-parametric methods in Stata

  7. Model Evaluation and Interpretation:

    • Assessing model fit, goodness of fit measures, and residual analysis in multivariable regression

    • Interpretation of regression coefficients, p-values, and confidence intervals in a multivariable context

    • Discussing the challenges and considerations in interpreting complex regression models

  8. Case Study and Practice:

    • Applying multivariable regression techniques to a real-world dataset

    • Building and interpreting a comprehensive regression model

    • Discussing the implications and limitations of the findings

Ensure that the session includes practical examples, hands-on exercises, and opportunities for students to apply the concepts in Stata. Emphasize the importance of model interpretation, addressing assumptions, and selecting appropriate variables to build robust multivariable regression models.