I have a 2*2*2 design, one factor is a within-subject variable, and the other two factors are between-subjects variables. The dependent measures are 19 binary variables.
Can I run mixed-design MANOVA for this data set? Thank you so much.

On Sat, 22 Jul 2017 00:02:46 -0700 (PDT), emma.fang88@gmail.com wrote:

>I have a 2*2*2 design, one factor is a within-subject variable, and the other two factors are between-subjects variables. The dependent measures are 19 binary variables.
>Can I run mixed-design MANOVA for this data set? Thank you so much.

Sure, the math is there so a MANOVA can have that design, if the N
is big enough. The d.f. for Hypotheses, in the full MANOVA model, is
about 8 time 19, or 152; for the data that I'm accustomed to, like
rating scales on individuals, I would want to have N in the 1000's if
my concern was testing.

I've rarely seen data that would justify that design. In particular,
I have seldom had 19 binary variables that I did not consider to
be inter-related in ways that I probably would want to disentangle
or clarify before further analyses.

The MANOVA context where I might consider 19 binaries would be
where I was interested in what two or three "factors" might emerge;
I would be looking at loadings rather than tests. I think it would be
exploratory work.

For the first step of data reduction, I would consider squashing the
Within factor by computing (say) the Pre-post difference, so the
design becomes 2x2 with 19 variables valued (-1,0,1). If that
ie reasonable, I would follow with a factor analysis of the 19, so
as to define pragmatic factors. If they all load in the same
direction, it may be that your primary /test/ should be on a
simple total score, so you can point to change or improvement.

--
Rich Ulrich