prepare a table for fitrm and manova

I am try to perform a one way repeated measure MANOVA on a set of data. In this data, I have 6 subjects. Each subject is measureed 4 times (t1-t4) for 11 different measures (m1-m11). Each subject went through all 44 measures.

I think the table should look like the table in the attached .mat file, and the model specification should be 'm1-m11~1'.

In the table, each subject has 4 rows, and each row contain the subject ID and 11 measures at a specific time point.

My goal is to see if there is any sifnificance across time witnin any measure.

I am wondering if it is the right table layout and modelspec for my goal.

[Scott MacKenzie]

What are the "measures"? Are the units the same or are they completely different properties that are being measured?

What about doing an ANOVA for each measure, to see if the measure changes over the four sample times? Seems like that's what you want to do (x11).

[Fan Yang]

@Scott MacKenzie

Sorry for the late reply. All the measure have different property but not completely. Think of them as different flavors of a same drink. My measures are different aspects of a mouse' gait, like step length, speed, symmetry, etc.

[Scott MacKenzie]

I'm not sure what to suggest other than doing the ANOVA on each measure, using time (t1-t4) as a within-subjects factor.

[Fan Yang]

@Scott MacKenzie

I still believe a one-way repeated Multivariate ANOVA is the best fit for my dataset. It predicts one indepentent measure using multiple correlated outcome measures.

One-way repeated measures MANOVA in SPSS Statistics - Step-by-step procedure with screenshots | Laerd Statistics

The link above explained the model very well even though the precedure is domonstrated in SPSS.

Answer 1

[Scott MacKenzie]

Using the example in the documentation for the manova function, here's a MANOVA for your data (attached):

load atb;
Meas = table([1 2 3 4 5 6 7 8 9 10 11]','VariableNames',{'Measurements'});
rm = fitrm(atb,'m1-m11~ID','WithinDesign',Meas);
manova(rm)

ans = 8×9 table
     Within       Between      Statistic     Value       F       RSquare    df1    df2    pValue 
    ________    ___________    _________    _______    ______    _______    ___    ___    _______

    Constant    (Intercept)    Pillai       0.45813    1.0991    0.45813    10     13     0.42785
    Constant    (Intercept)    Wilks        0.54187    1.0991    0.45813    10     13     0.42785
    Constant    (Intercept)    Hotelling    0.84545    1.0991    0.45813    10     13     0.42785
    Constant    (Intercept)    Roy          0.84545    1.0991    0.45813    10     13     0.42785
    Constant    ID             Pillai       0.50648    1.3341    0.50648    10     13     0.30768
    Constant    ID             Wilks        0.49352    1.3341    0.50648    10     13     0.30768
    Constant    ID             Hotelling     1.0262    1.3341    0.50648    10     13     0.30768
    Constant    ID             Roy           1.0262    1.3341    0.50648    10     13     0.30768

Above, Wilks' lambda = 0.49352. The corresponding F-statistic is not significant (F[10,13] = 1.3341, p = .30768) implying no significant difference between the eleven measures over the four time points with six IDs (subjects). Your data just look like random numbers, so the result is not surprising. Hopefully, you'll have more interesting results with real data.