Hello, I have three variables (factors)... A, B and C I have one response ..let's call it Y.
I have done a full factorial DOE with 2-levels for each factor. I have established a relationship of the form Y = k0 + k1*A + k2*B + k3*C + k4*A*B + k5*A*C + k6*B*C I have evaluated the coefficients(k's) using least squares. Thus my "X" matrix is a 8x7 matrix Now I am interested in evaluating the sum of squares for each term in the equation (i.e. A, B, C, AB, AC and BC) Using Type II SS (Higher order terms omitted...HTO), I evaluate the SS for each term as follows First I evaluate the SS for whole model, then for each term in equation A -> remove columns A, AB and AC from the X matrix B -> remove columns B, AB and BC from the X matrix C -> remove columns C, AC and BC from the X matrix AB -> remove column AB AC -> remove column AC BC -> remove column BC and the evaluate the coefficients again I evaluate the difference in SS between two models This gives me the SS for that particular term. Now for Type III (Higher order terms included ..HTI) I do everything same as above except how i choose terms for my model A -> remove column A B -> remove column B C -> remove column C AB -> remove column AB AC -> remove column AC BC -> remove column BC For a balanced design (like this..a full factorial), I should get SS values from both types exactly same, but I don't...and also the total of SS for each model term should add up to the SS of the model. In my case this doesn't Is there something wrong that I am doing. Is my understanding of Type II (HTO) and Type III (HTI) somewhere flawed. I don't expect both types to give same SS for each term in case of unbalance designs. Any help is appreciated. I am not using any commercial software. I have coded this thing up myself. thanks . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
