> I'm realizing that `y ~ someFactor+0` where someFactor has more than two levels can't mean
> what I thought it did; what does it mean?

Typically a model contains an intercept, and that's why a factor of n levels is usually represented by (n-1) dummy variables. There are many (actually infinite) ways to dummy code a factor, but there are a few popular ones (see discussion here: [www.ats.ucla.edu]). When an intercept is present in the model, the intercept is usually associated with a specific effect depending the coding strategy. For example, the intercept is the effect estimate for the reference level for dummy coding, and the average across all the levels for deviation coding.

When there is only one factor (and no other explanatory variables) in the model, we can adopt a special coding method: no intercept. In doing so, we can code each level of the factor as a separate regressor, resulting n instead of (n-1) regressors. That is, in a model with a factor of n levels as an explanatory variable (e.g., the n effect estimates from the multiple basis functions such as TENT), this special coding allows us to directly test the desired hypothesis

b_1 = b_2 = ... = b_n = 0

Unfortunately we cannot do this when there are other variables in the model because the special coding would not work.

Gang