003 - Course 03. Advanced Regression Modeling: A Discrete Approach

Session Submission Type: Course

Description

This research workshop is directed to experienced users of regression analysis in their research. It provides advanced regression modeling tools that will be useful in producing stronger analysis for publication. The prerequisite for the workshop is knowledge of statistics and regression analysis as taught in a one-year graduate sequence. The workshop has five main parts: 1) explanation of key regression modeling concepts, 2) examination of strengths and weaknesses of four approaches for considering the influence of control variables; 3) discussion of alternative approaches for modeling interactions involving categorical and interval variables; 4) instruction of how to use spline variables to model linearity; and 5) specification of verbal hypotheses that con be tested with each modeling technique.

There are generally four kinds of hypotheses which can be addressed with regression analysis. The simplest is whether there is an effect for an independent variable on a dependent variable. This effect is easily estimated by bivariate or multivariate regression. A second kind of hypothesis is about how other independent variables, often called control variables, explain the effect of an independent variable on a dependent variable. This hypothesis is modeled by adding control variables in some sequence to a baseline model. The third type of hypothesis is about how the effects of an independent variable on a dependent variable are contingent on the level of a second independent variable. Regression models with interaction variables address this kind of hypothesis. The fourth kind of hypothesis is about the degree to which an independent variable is linearly related to a dependent variable. Spline variables can be used to examine issues of linearity. The purpose of this methodological workshop is to expose participants to underlying conceptual issues behind using regression modeling to address the second, third, and fourth types of hypotheses.

The topics that I intend to cover are as follows:

Key Regression Modeling Concepts
- Nestedness
- Higher Order Differences
- Constraints
Control Modeling
- Small and Big Models
- Allocating Influence With Multiple Control Variables
- One-at-a-Time Without Controls
- Step Approach
- One-at-a-Time With Controls
- Hybrid Approach
Modeling Interactions
- Interactions Between Dummy Variables
- Interactions Between Dummy Variables and Interval Variable
- Three-Way Interactions
- Estimating Separate Models
Modeling Linearity With Splines
- Introduction to Knotted Spline Variables
- Spline Variables Nested in Interval Variable
- Regression Modeling Using Spline Variables
Testing Research Hypotheses
- Bivariate Hypothesis/No Controls
- Bivariate Hypothesis/Unanalyzed Controls
- Bivariate Hypothesis/Analyzed Controls
- Hypothesis Involving Interactions
- Hypothesis Involving Nonlinearity

Sub Unit

• Courses

Leader

• Roger A. Wojtkiewicz, Ball State University