MATLAB: How to correctly specify WithinDesign for fitrm

fitrmMATLABstatistics

I am trying to use matlab function fitrm. But the input 'WithinDesign' does not seem to make any sense to me. It seems as anything with the same length as the number of repeated measures is acceptable and the final output seem independent of the this WithinDesign. Take for instance:
load repeatedmeas
rm = fitrm(between,'y1-y8 ~ Group*Gender','WithinDesign',within)
ranova(rm)
and
    load repeatedmeas
    rm = fitrm(between,'y1-y8 ~ Group*Gender','WithinDesign',[1:8])
    ranova(rm)
and
load repeatedmeas
  rm = fitrm(between,'y1-y8 ~ Group*Gender','WithinDesign',zeros(8,1))
  ranova(rm)
all produces the exact same output, as shown in the attached image.
Could someone please explain to me why they are all the same. Since its all the same what is the point of specifying it?. Also could some explain the design matrix 'within', What is it really telling the program to do, any reference to SPSS would be great.
Thanks.

Best Answer

WithinDesign lets you store specific numeric values associated with the levels of the within-Ss factors in the RepeatedMeasuresModel object that fitlm produces as output. For example, these values might be the exact dosages of some drug if you were comparing 8 dosages. As you have noted, these don't affect the ANOVA output per se, but they can affect subsequent things you do with the output object.
For example, you get different plots with:
rm8 = fitrm(between,'y1-y8 ~ Group*Gender','WithinDesign',[1:8])
plot(rm8)
rm0 = fitrm(between,'y1-y8 ~ Group*Gender','WithinDesign',zeros(8,1))
plot(rm0)
The ANOVA model doesn't care what numerical values are associated with those 8 dosages, but it is still nice to show them in the plot. As another example, you would also need the dosage values if you wanted to compute a linear trend across the 8 dosages.
As far as I know, SPSS doesn't integrate the X values into its repeated measures ANOVAs in this way (but I don't know SPSS that well).
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