What is a no intercept model?
Regression through the origin is when you force the intercept of a regression model to equal zero. It’s also known as fitting a model without an intercept (e.g., the intercept-free linear model y=bx is equivalent to the model y=a+bx with a=0).
Does the intercept have a useful interpretation here?
In market research, there is usually more interest in prediction, so the intercept is more important here. When X never equals 0 is one reason for centering X. If you re-scale X so that the mean or some other meaningful value = 0 (just subtract a constant from X), now the intercept has a meaning.
Can you test a model with no intercept?
It is NOT the same F test that will appear on either output. The idea is that because the no-intercept model is nested within the full model (nested b/c it contains only a subset of the parameters), you can test the fit of the model with an F test. citation: p. 80 of Neter, Kutner, Nachtsheim, & Wasserman’s Applied Linear Regression Models, 3rd Ed.
When is it better not to assume the intercept is zero?
Observation: In general, it is better not to assume that the intercept is zero. In fact, as mentioned earlier, the only time you should use this type of model is when on theoretical grounds you expect that the intercept is zero. Some examples of this are:
Why is a zero intercept linear regression model predicts?
Second, there should be a reasonable subject matter knowledge expection for the regression line to remain a straight line as you approach zero. Even if both conditions are satisfied, it is wise to run an analysis with an intercept term and verify that the intercept is not significantly different from zero.
When to remove the intercept from a meta regression model?
When the model only includes continuous (i.e., numeric) predictors/moderators, then removing the intercept does just that: it removes the intercept. Hence, the model above forces the intercept to be 0, that is, it assumes that at the equator, the (average) log risk ratio is exactly zero.