MATLAB: Estimate main effects and interactions

pareto plotstandardised effects

Hi,
I'm trying to replicate Minitab functionality by creating a Pareto Chart of standardised effects.
I'm using data from the example linked here where a DOE was run with 4 inputs and the response was measured. In the link, a full effects table is calculated which has effects of each of the inputs A,B,C & D but also all of the interaction terms.
In Matlab I'm trying to use stepwiselm to fit a model to the table of data but I find that Matlab is removing terms based on their P-value. is there a way to use this function but ask for all linear and interaction terms to be retained?
Secondly, I'm looking at the functions plotEffects() and plotInteraction() to use on the model but is there a function or way to group all main & interaction effects together in a single table, as per table 2 in the link above?
Many thanks, Dan

Best Answer

I was able to replicate the effect estimates, but only via a rather odd normalization scheme of the variables:
data = [1	10	220	10	50	8	70
        2	15	220	10	50	2	60
        3	10	240	10	50	10	89
        4	15	240	10	50	4	81
        5	10	220	12	50	16	60
        6	15	220	12	50	5	49
        7	10	240	12	50	11	88
        8	15	240	12	50	14	82
        9	10	220	10	80	15	69
        10	15	220	10	80	9	62
        11	10	240	10	80	1	88
        12	15	240	10	80	13	81
        13	10	220	12	80	3	60
        14	15	220	12	80	12	52
        15	10	240	12	80	6	86
        16	15	240	12	80	7	79];
A = data(:,2);
B = data(:,3);
C = data(:,4);
D = data(:,5);
Y = data(:,7);
A = normalize(A,'zscore','robust');
B = normalize(B,'zscore','robust');
C = normalize(C,'zscore','robust');
D = normalize(D,'zscore','robust');
Y = 2*Y;
tbl = table(A,B,C,D,Y);
mdl = fitlm(tbl,'Y ~ A + B + C + D + A:B + A:C + A:D + B:C + B:D + C:D + A:B:C + A:B:D + A:C:D + B:C:D + A:B:C:D')
The normalization of the explanatory variables is a standard one, but I have no idea the reason behind needing to multiply the response variable by 2.
A slightly simpler way to specify the model in this case would be
modelMatrix = fullfact([2 2 2 2])-1;
mdl = fitlm([A B C D],Y,modelMatrix)
That's more of a Design of Experiments approach, I guess, but it boils down to the same thing.
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