Comparing R^2 from log and level models

  • MHB
  • Thread starter Usagi
  • Start date
  • Tags
    Log Models
In summary, two models with known R^2 values, one with a logarithmic dependent variable and the other with a level dependent variable, cannot be directly compared in terms of goodness-of-fit. While it is possible to manipulate the log model to make a comparison, the reason for this limitation is that the dependent variable's form affects the interpretation of the R^2 values. A deeper explanation can be found in the concept of scaling effects, which explores the impact of different dependent variable forms on model comparisons.
  • #1
Usagi
45
0
Say we have 2 models:

[tex]ln(y) = \beta_0 + \beta_1 x_1 + \cdots + \beta_nx_n[/tex] with a known R^2

and

[tex]y = \beta_0 + \beta_1 x_1 + \cdots + \beta_nx_n[/tex] with a known R^2

Now I know that we can not compare the R^2's from these 2 models to determine goodness-of-fit and I am also aware of how we can manipulate the log model so that we can compare, but my question is, what is the reason for which we can't compare? Obviously the dependent variable is the natural log for the first one and the second model is level in terms of y, but is there a deeper reason? Why is it that if the dependent variable's form is different, then we cannot compare the R^2's between the models?

Thanks
 
Mathematics news on Phys.org
  • #2
Deep as you would like, I would think.

http://www.yale.edu/ciqle/Breen_Scaling%20effects.pdf
 

FAQ: Comparing R^2 from log and level models

1. What is R^2 in the context of comparing log and level models?

R^2, also known as the coefficient of determination, is a statistical measure of how well a model fits the data. It represents the proportion of variation in the dependent variable that can be explained by the independent variables in the model. In the context of comparing log and level models, R^2 is used to determine which model provides a better fit for the data.

2. How are log models and level models different?

Log models and level models differ in the way they handle the relationship between the dependent and independent variables. In a log model, the dependent variable is transformed using a logarithmic function, while in a level model, the variables are used in their original form. This can lead to different interpretations and predictions from the models.

3. Why is it important to compare R^2 from log and level models?

Comparing R^2 from log and level models allows us to determine which model provides a better fit for the data. This is important because a higher R^2 indicates a stronger relationship between the variables, and a better fit means that the model can more accurately predict the dependent variable. It also helps us understand the impact of using log transformations on the model results.

4. Can R^2 from log and level models be directly compared?

No, R^2 from log and level models cannot be directly compared. This is because the two models have different scales and interpretations of the dependent variable. In order to compare R^2, it is necessary to use a statistical test or to transform the R^2 values to a common scale.

5. How can the results of comparing R^2 from log and level models be interpreted?

The results of comparing R^2 from log and level models can be interpreted by looking at the difference in R^2 values and the significance of this difference. A higher R^2 and a significant difference between the models indicates that the log model provides a better fit for the data. On the other hand, if the difference in R^2 is not significant, it may be more appropriate to use the simpler level model.

Similar threads

I How to propagate errors through a regression & non-linear model?
Replies
8
Views
2K
I Exploring OLS and GLM Models: Understanding the Link Function and Coefficients
Replies
3
Views
2K
A Differential of Multiple Linear Regression
Replies
1
Views
1K
I Linear Models vs Nonlinear Models
Replies
22
Views
3K
MHB Levels of Measurement, Basic OLS Regression Questions
Replies
1
Views
2K
I What are the commonly used estimators in regression models?
Replies
23
Views
3K
I Handling categorical variables in R
Replies
2
Views
1K
Engineering Deriving the Cable Equation (neuroscience) from Fundamental Physics Laws
Replies
1
Views
1K
I Does the New Muon g-2 Measurement Indicate Physics Beyond the Standard Model?
Replies
2
Views
2K
I The standard model from loop quantum gravity via spinors octonions
Replies
26
Views
2K

Hot Threads

Recent Insights

Back
Top