I am studying cortical thickness as a function of age (continuous) and meditation practice (categorical, level1=Normal, level2=TM). I have three separate cases of qdec, regression1, regression2 and regression3.

Regression1: Discrete (Fixed Factor) = meditation; Continuous (Covariate) = age

Regression2: Discrete (Fixed Factor) = meditation; 

Regression3: Discrete (Fixed Factor) = meditation; Nuisance Factor = age

For the question "Does the average thickness differ between Normal and TM?", Regression1 and Regression3 have identical result, which is different from Regression2, i.e., (1 = 3 !=2 ). May I infer from this result the following about qdec:

1) Regression1 and Regression3 both fit cortical thickness,y, to the model

    y  = b0 + age*b1 + meditation*b2 + err = y_hat + err

    Regression2 fits: 

    y = b0 + b2*meditation + err = y_hat + err

2)  Some function of y_hat goes into the "average thickness", hence the difference between 2 and the others.

However, what role does "Nuisance Factor" play in this case?

Thank you very much!

Sincerely,

Ye