Significant results after intercept removal

[Carsten Preuss]

Dear Statalist users,

I have a problem concerning my regression output and I would like you for some advice.

I run a simple OLS regression where all my independent variables sum up to 1 (they are proportions). By default, Stata omits one variables and the constant coefficient takes on the value of the this reference variable.

I also tried to remove the constant with the -noconstant- option. Strangely it happens, that most of my coeffficients turn significant and the R-squared goes up from 9% to 32%.

I would like to know, what is happening, that the removing the constant seems to fit the data better, although I understood that one always should keep the constant to ensure the residual is zero mean.

This is just my second post in Statalist and I hope I provided all the information that is needed. If not, please let me know!

I really appreciate your help!

[Carlo Lazzaro]

Carl:
Example 4: Suppressing the constant term under -regress- entry, Stata .pdf manual may be enlightening.

[Clyde Schechter]

Everything you are seeing here is an artifact of changing the parameterization of your model: nothing substantive has changed.

1. When you estimate a model with a constant term, when R squared is computed, the constant term's contribution is explicitly omitted. When you use the no-constant option, Stata includes all the variables. But in this model, the constant term's effect is now represented by the newly included term for the reference value. So R squared always goes up when you do this, but it does not mean the fit of the model is improved. In fact, if you run -predict- after both models and compare the predictions, you will see that they are exactly the same.

2. When you run the model with a constant term, the coefficients of the variables estimate the difference in expected outcome between that level and the reference level. When you use the -nocons- option, the coefficients now estimate the difference in expected outcome between that level and zero. So the coefficients estimate entirely different things and are not directly comparable.

Added: Crossed with Carlo's response.

[Carsten Preuss]

Thanks a lot Carlo and Clyde for your quick and straight forward answers! Now it seems to make sense!