# Hierarchical regression

## Test a theoretical framework using regression

Hierarchical regression or hierarchical linear modeling is a subset of regression methods that attempt to generate theory driven evidence for a given effect. In hierarchical regression, predictor variables are entered into the model in pre-determined iterations to see how the change in r-squared is affected. The most important aspect of running hierarchical regression is that there is a sound methodology grounded in the empirical literature for the order of entry into the model. A theoretical, conceptual, or physiological link must exist that drives the nature of order of entry into the hierarchical linear model.

The hierarchical regression analysis occurs in iterations. The first iteration will be with the most highly correlated variable to the outcome, then subsequently add in other variables that have some sort of association or mitigating effect on the outcome to see what happens. If entry of a variable leads to a significant increase in R-squared as per the F-statistic, then evidence of its predictive ability can be noted. Other iterations of variable entry occur until the best group of variables that accounts for the most shared variance in the outcome is found. Once all iterations are run with all variables interacting or being thrown out, a much more tangible argument for multivariate associations can be made.

The hierarchical regression analysis occurs in iterations. The first iteration will be with the most highly correlated variable to the outcome, then subsequently add in other variables that have some sort of association or mitigating effect on the outcome to see what happens. If entry of a variable leads to a significant increase in R-squared as per the F-statistic, then evidence of its predictive ability can be noted. Other iterations of variable entry occur until the best group of variables that accounts for the most shared variance in the outcome is found. Once all iterations are run with all variables interacting or being thrown out, a much more tangible argument for multivariate associations can be made.

## Hire A Statistician

**DO YOU NEED TO HIRE A STATISTICIAN?**

Eric Heidel, Ph.D., PStat** **will provide the following statistical consulting services for undergraduate and graduate students at $100/hour. Secure checkout is available with Stripe, Venmo, Zelle, or PayPal.

- Statistical Analysis
- Research Design
- Sample Size Calculations
- Diagnostic Testing and Epidemiological Calculations
- Survey Design and Psychometrics