Manova(rm)

Manova(rm) & manova1(Responses, GroupVar) can address the same data (if 1 group variable). Yet, they give different statistics. When I run the same data, I get a different probability of rejecting null hypothesis. are there differing null hypotheses? I there a method to tform stats of one to other?

[Adam Danz]

Could you provide a minimal working example?

When I change the example shared in the documentation for maonva1() by reducing the data to just one group, the result are empty outputs (which isn't surprising).

load carbig
isUSA = strcmp(cellstr(Origin), 'USA'); % just 1 group: USA
[d,p] = manova1([MPG(isUSA) Acceleration(isUSA) Weight(isUSA) Displacement(isUSA)],...
    Origin(isUSA,:)) 

[Michael Rossen]

Adam,

thanks for the answer, sorry about the delay, I asked the question, went on vacation, then was deluged for several weeks after my return. I enclose my data file and a matlab file that produces the different p-values for the same inputs to manova1 and manova. I also enclose a txt file with the command window output.

I think I have constructed Manova to duplicate Manova1, by only using one "grouping variable" in Manova (variables after the "~" in terms of Manova syntax).

Does the "lambda" in Manova1 refer to Wilkes Lambda output in Manova? They are different values.

I understand that Manova does repeated measures. My data can be thought of as such a design, as the 10 "treatments" are each from the same subject. Is this the cause of the p-value discrepancy?

Is Manova function limited so that it can ONLY do repeated measures assumption for the treatment variables, or is there an option (or a different function that allows multiple grouping variables, unlike Manova1) that allows independent measures assumption.

Likewise, is Manova1 function limited so that ican ONLY do independent measures assumption?

Thanks for your help on this!

Regards, Mike Rossen MD PhD, (neurology, psychology)

PS: I am the uncle of one of your colleagues, Josh Knill!

[Adam Danz]

Hi Michael,

Are you related to Dave Knill? He was on my advisory committee and I admired him deeply as a scientist and an adviser.

The m-file you attached does not define the 'tD' table so I can only run the first 5 lines. Could you add the code used to produce tD?

"Does the "lambda" in Manova1 refer to Wilkes Lambda output in Manova? "

The lambda in Manova1() is a vector of values of Wilk's lambda test statistic for testing whether the means have dimension 0, 1, etc. [1,2]. Manova() also returns the Wilk's lambda statistic [3,4]. I haven't looked into how they are computed and I couldn't run your manova because of the missing table so I can only guess that there may be a different number of degrees of freedom and a different measure of error that results in different lambdas.

The manova() and manova1() functions are flexible with regard to defining the model you're fitting. Here are several examples of repeated measures models [5]. But I hesitate to say wether either of those two functions are restricted to interpreting dependent/independent variables.

If you're providing both models with the same inputs and getting different p-values, it's likely due to the explanation in my answer below but I'd be happy to look at the rm mode if the tD table is provided.

Answer 1

[Adam Danz]

Matlab's documentation is really thin when it comes to many of their statistical methods which makes it difficult to address some of these questions. I guess that's partially why many statistical questions in this forum go unanswered.

The repeated measures MANOVA can be thought of as a within-subjects version of the between subjects MANOVA which is used when groups are independent or unrelated. The repeated measures can be the same test on the same subjects over multiple periods of time or it can be multiple, different tests across the same subjects. Matlab's documentation does provide a decent example of this where 4 different measurements were taken across 3 species of flowers. In your case, if 10 measurements were taken across 2 categories of the same subjects I think a RM design fits your needs. Since the between-subject variability is separated from the within-subjects variability in RM designs, when there is an effect the p-value will be smaller than an ordinary MANOVA. You'll also notice a reduction in the degrees of freedom for RM models.

The manova1() function does not have an input that specifies the 'withinModel' design so it is not set up to perform repeated measures tests.

The manova() method for the RepeatedMeasuresModel class receives inputs from fitrm() which is designed to return a repeated measures model. Within fitrm() you can only specify the within-subject factors, if needed.

One thing to consider with your code is treating BinaryCTNYT as categorical. Fitrm() treats the input variables as continuous unless they are of type categorical, logical, char/string array, or cell array of chars. With your two groupings ([-1,1]) there is no difference in results whether BinaryCTNYT is of class double or categorical but if the groupings were to change (say, [1,2]), the difference between a continuous and categorical interpretation would have a big effect on the results. That variable can be changed to categorical by

tableMD.BinaryCTNYT = categorical(tableMD.BinaryCTNYT); 

Answer 2

[Michael Rossen]

Hi Adam,

Yes, Dave is my brother-in-law. He was my grad school office mate. Josh, of course, is his son. I am gladdened to know that he touched your life in a such a good way.

Sorry about the confusion on my previously enclosed example. I copied/pasted from other files to strip down to a simple example but did not review variable names well enough. "tD" should simply have been "tableMD." I enclose the modified code, with the one correction at line 7, tD -> tableMD.

You will see that Lambda (Wilkes Lambda as you say) is different for the two results.

When you say you "hesitate to say wither either of those two function are restricted to interpreting dependent/independent variables," do you mean:

for manova1, you are unsure whether there is an option to turn ON repeated measures statistical assumption (which should turn OFF independent measure statistical assumptions across treatments as a consequence);

for manova, you are unsure whether there is an option to turn OFF repeated measures statistical assumption (which should turn ON independent measure statistical assumption across treatments as a consequence).

I would appreciate it if you looked at the rm model, compared to the manova1 model, with an eye on this question.

My larger question is:

Is MATLAB equipped with functionality to perform MANOVA, with more that one treatment group variable (so not Manova1), without a repeated measures assumption within a treatment group?

Regards,

Mike Rossen

[Adam Danz]

Hi Mike, I had a chance today to look into these interesting queries and I updated my answer to address some of your questions. Stats questions often get overlooked in this forum but I try to take a stab at them as an excuse to learn something myself. Hopefully it's a bit helpful.

Answer 3

[Leonardo Ermini]

Hi all, mine is not an answer but instead a new question, indeed I experienced some problem when delaing with a repeated measures MANOVA. In my case I have 5 dependent variables (thus the MANOVA) measured at two distinct moment in time (thus the repeated mesure model). To explain my case i will recall an example dataset present in matlab:

load repeatedmeas

I do not have any between factors so the Age IQ Group and Gender column are not interesting for me. Anyway: the analogy rely on the fact that we can consider the 8 variables here as 2 set of 4 dependent variables, i.e. 4 dependent variables measured twice, as follows var1 = y1 and y5, var2 = y2 and y6, var3 = y3 and y7, var4 = y4 and y8. The within table semms to express such arrangement. Anyway, let's do the fitrm model:

rm = fitrm(between,'y1-y8 ~ 1','WithinDesign',within)

and run the manova, first without any within factor and the including also the within factors

manova(rm)
manova(rm,'WithinModel','w1*w2')

Then I have compare both the results, in particular the second one, with the SPSS output for a repeated measures MANOVA and the things doesn't match at all!!

Is there somethings I am doing wrong? I cannot not figure if matlab can handle a manova for repeated measure or not, and if not why there is the possibility to set within subjects factors?

Thank yuo in advance,

Leo