Measuring Effect Size in Regression: Partial R2, Partial Correlation

In summary, the conversation discusses the use of partial r-squared and partial correlation to compare explanatory variables in linear regression models. While they both provide information about the relationship between a specific variable and the outcome, they measure different aspects of that relationship. Partial r-squared can be interpreted as a measure of effect size, but the ranking of variables by their partial r-squared values may not necessarily be the same as their ranking by standardized coefficients.
  • #1
wvguy8258
50
0
Hi all,

I have run a few linear regression models predicting water quality for watersheds using explanatory variables such as mean impervious surface within watersheds and others suggested by theory and the research of others. I would like to be able to compare explanatory variables measured on different scales to determine their relative strengths of effect. The standard approach I see is to multiply the slope coefficients by standard deviation of the corresponding explanatory variable. I've also seen multiplying by some range based upon percentiles (such as the difference between the 75th and 25th percentile value for the variable) to deal with outliers, etc that call using standard deviation into question. I understand what partial r-squared and partial correlation are from text descriptions.

First question are partial r2 and partial correlation equivalent to each other? They are described in separate places and with different language so I have not gotten the mathematical relationship yet. Is one just the square of the other?

Second, I know that partial r2 is related to the increase in the amount of variance in the response explained by adding a variable of interest, given that all other variables are in the model. Is this a measure of effect size similar to a standardized coefficient? Will they necessarily rank variables by "importance" the same? I am trying to decide how to compare variables and partial r2 has intuitive appeal to people used to looking at multiple r2.

Thanks,
Seth
 
Physics news on Phys.org
  • #2


Hello Seth,

Thank you for sharing your research and questions regarding comparing explanatory variables in linear regression models. It is important to consider the relative strengths of different variables when interpreting the results of a regression analysis.

To answer your first question, partial r-squared and partial correlation are not equivalent to each other. Partial r-squared is a measure of the proportion of variance in the dependent variable that is explained by a specific independent variable, while partial correlation is a measure of the strength and direction of the linear relationship between two variables while controlling for the effects of other variables. So, while they both provide information about the relationship between a specific variable and the outcome, they are measuring different aspects of that relationship.

In terms of your second question, partial r-squared can be interpreted as a measure of effect size, similar to a standardized coefficient. It tells you how much of the variation in the dependent variable is explained by a specific independent variable, while controlling for the effects of other variables in the model. However, it is important to note that the ranking of variables by their partial r-squared values may not necessarily be the same as their ranking by standardized coefficients. This is because partial r-squared takes into account the effects of other variables, while standardized coefficients do not.

I hope this helps clarify some of your questions about comparing explanatory variables in linear regression models. Best of luck with your research!
 

1. What is effect size in regression?

Effect size in regression refers to the strength of the relationship between two variables. It is a measure of how much one variable (the independent variable) affects or predicts the other variable (the dependent variable).

2. What is partial R2?

Partial R2 is a measure of effect size in regression that quantifies the amount of variance in the dependent variable that is explained by a specific independent variable. It is also known as the coefficient of determination and can range from 0 to 1.

3. How is partial R2 calculated?

Partial R2 is calculated by taking the squared value of the partial correlation coefficient, which measures the relationship between the independent variable and the dependent variable while controlling for the effects of other variables. It is then divided by the total R2, which represents the variance in the dependent variable explained by all the independent variables in the model.

4. What is the difference between partial R2 and partial correlation?

Partial R2 and partial correlation are both measures of effect size in regression, but they differ in their interpretation. Partial R2 is an absolute measure that represents the proportion of variance in the dependent variable explained by a specific independent variable, while partial correlation is a relative measure that represents the strength of the relationship between the independent and dependent variable while controlling for other variables.

5. Why is it important to measure effect size in regression?

Measuring effect size in regression is important because it helps to determine the practical significance of the relationship between variables. It allows researchers to understand the strength and direction of the relationship, as well as to compare the relative importance of different independent variables in predicting the dependent variable.

Similar threads

  • Set Theory, Logic, Probability, Statistics
Replies
13
Views
2K
  • Set Theory, Logic, Probability, Statistics
Replies
8
Views
1K
  • Set Theory, Logic, Probability, Statistics
Replies
4
Views
2K
  • Set Theory, Logic, Probability, Statistics
Replies
1
Views
732
  • Set Theory, Logic, Probability, Statistics
Replies
4
Views
5K
  • Set Theory, Logic, Probability, Statistics
Replies
9
Views
986
  • Set Theory, Logic, Probability, Statistics
Replies
3
Views
1K
Replies
67
Views
5K
  • Set Theory, Logic, Probability, Statistics
Replies
7
Views
3K
  • Set Theory, Logic, Probability, Statistics
Replies
7
Views
2K
Back
Top