Relationship between Sets of Dependent and Independent Variables

[Susan M. Sereika]

Dear Listserv members:

        A colleague is interested in examining the relationship between two
sets of variables (dependent variables and independent variables).
Additionally she would like to investigate whether the relationship varies
between men and women.  The total sample size is somewhat moderate (about
200 participants) with 70% being women. What might be a good approach to use
when analyze these data in light of the objectives?  Any suggestions are
most appreciated.

Sincerely,
Susan Sereika

[Hector Maletta]

You state your friend's goals in a very sketchy way, so it is very difficult
to give an opinion. For instance, how many variables are involved? 200 cases
may be way too few if the variables happen to be (even moderately) numerous.
Is he/she interested in bivariate or multivariate relations between these
variables? For instance, one may be interested in crossing pairs of
variables such as X BY Z BY sex, and see whether the association/correlation
of X and Z varies with sex, and this may be feasible with 200 cases (140
women, 60 men), only if one has, say, K variables there would be K*(K-1)/2
pairs of variables, which rapidly goes into the hundreds or the thousands as
K grows. For K=50, there are 1225 pairs of variables to consider. If one is
interested in models involving many variables, such as regression, the
number of possible models grows exponentially and, besides, the small number
of cases in the sample becomes rapidly a limitation.
Another consideration is whether your friend has any theory or conceptual
approach or problem-oriented goal when facing these data, or is just
exploring blindly around. What is he/she looking for? Just mining around for
any kind of non-random-looking patterns, like an astronomer searching for
signs of extra-terrestrial intelligence among random electromagnetic cosmic
noise, or like John Nash, he of the beautiful mind, parsing newspapers in
the worst of his madness? In a sample of 200 she/he may find many promising
patterns, but they may be nothing but sample flukes.

Hector

-----Mensaje original-----
De: SPSSX(r) Discussion [mailto:[hidden email]] En nombre de Susan
M. Sereika
Enviado el: Monday, August 21, 2006 10:44 AM
Para: [hidden email]
Asunto: Relationship between Sets of Dependent and Independent Variables

Dear Listserv members:

        A colleague is interested in examining the relationship between two
sets of variables (dependent variables and independent variables).
Additionally she would like to investigate whether the relationship varies
between men and women.  The total sample size is somewhat moderate (about
200 participants) with 70% being women. What might be a good approach to use
when analyze these data in light of the objectives?  Any suggestions are
most appreciated.

Sincerely,
Susan Sereika

[Hector Maletta]

It is all the same. You may use, for instance, factor analysis to derive a
scale representing the 18 variables of one of the sets, one scale for women
and another similar scale for men, but the scale for women will be built
with data from a sample of 60 women, i.e. 2.33 women per variable, and that
is hardly statistically significant. Take any other sample of 60 women from
the same population and the results are likely to be completely different.
The margin or error in the factor loadings and the regression coefficients
will be very wide, especially if some of the variables are not very highly
correlated (r>0.90 or r>0.95) with some of the others.
Data, as the old saying goes, can always be tortured till they confess. But
you better don't. There are better ways to get to the truth.
Hector

-----Mensaje original-----
De: Susan M. Sereika [mailto:[hidden email]]
Enviado el: Tuesday, August 22, 2006 1:45 PM
Para: 'Hector Maletta'
Asunto: RE: Relationship between Sets of Dependent and Independent Variables

Dear Hector:

        I agree that sample size is problematic.  Is there anything that can
be savaged from this?  Would it be reasonable to present the work as
exploratory? Or perhaps to apply principal components analysis to derive a
smaller number of derived variables and conduct the analyses with these
derived variables using regression analysis?  Thank you very much for your
thoughts on this.

Sincerely,
Susan

-----Original Message-----
From: Hector Maletta [mailto:[hidden email]]
Sent: Tuesday, August 22, 2006 12:09 PM
To: 'Susan M. Sereika'
Subject: RE: Relationship between Sets of Dependent and Independent
Variables


Now the situation is clearer, and the answer more definitely negative. The
36 variables are far too many for just 200 cases (below 6 per variable), let
alone for 30% of them, i.e. for about 60 women (which is about 1.8 cases per
variable, when the old rule of thumb, now discredited for insufficiency, was
at least 10; nowadays far more than 10 is usually required, depending on the
variance of variables and the strength of the relationship). Hector


-----Mensaje original-----
De: Susan M. Sereika [mailto:[hidden email]]
Enviado el: Tuesday, August 22, 2006 12:54 PM
Para: 'Hector Maletta'
Asunto: RE: Relationship between Sets of Dependent and Independent Variables

Dear Hector:

Thank you for your very quick and thoughtful reply.  The investigation is
theoretically driven for the most part with respect to the relationship
between the two sets of variables. The idea that the relationship may vary
by gender/sex is a little more exploratory, although there is some
literature to support some relationships. Each set of dependent and
independent variables consists of 18 variables and the variables are
subscale scores believed to measure two concepts: beliefs about depression
(18 variables) and coping (18 variables).  The initial investigation focused
on just examining the relationships between the two variables sets and given
the complexity of the data, canonical correlation analysis (CCA) was used.
Then the investigation was expanded to consider differences between men and
women and a CCA was conducted within each gender subsample. The smaller
subsample sizes are problematic, especially for the male subsample.

Sincerely,
Susan

-----Original Message-----
From: Hector Maletta [mailto:[hidden email]]
Sent: Monday, August 21, 2006 12:05 PM
To: 'Susan M. Sereika'; [hidden email]
Subject: RE: Relationship between Sets of Dependent and Independent
Variables


You state your friend's goals in a very sketchy way, so it is very difficult
to give an opinion. For instance, how many variables are involved? 200 cases
may be way too few if the variables happen to be (even moderately) numerous.
Is he/she interested in bivariate or multivariate relations between these
variables? For instance, one may be interested in crossing pairs of
variables such as X BY Z BY sex, and see whether the association/correlation
of X and Z varies with sex, and this may be feasible with 200 cases (140
women, 60 men), only if one has, say, K variables there would be K*(K-1)/2
pairs of variables, which rapidly goes into the hundreds or the thousands as
K grows. For K=50, there are 1225 pairs of variables to consider. If one is
interested in models involving many variables, such as regression, the
number of possible models grows exponentially and, besides, the small number
of cases in the sample becomes rapidly a limitation. Another consideration
is whether your friend has any theory or conceptual approach or
problem-oriented goal when facing these data, or is just exploring blindly
around. What is he/she looking for? Just mining around for any kind of
non-random-looking patterns, like an astronomer searching for signs of
extra-terrestrial intelligence among random electromagnetic cosmic noise, or
like John Nash, he of the beautiful mind, parsing newspapers in the worst of
his madness? In a sample of 200 she/he may find many promising patterns, but
they may be nothing but sample flukes.

Hector

-----Mensaje original-----
De: SPSSX(r) Discussion [mailto:[hidden email]] En nombre de Susan
M. Sereika Enviado el: Monday, August 21, 2006 10:44 AM
Para: [hidden email]
Asunto: Relationship between Sets of Dependent and Independent Variables

Dear Listserv members:

        A colleague is interested in examining the relationship between two
sets of variables (dependent variables and independent variables).
Additionally she would like to investigate whether the relationship varies
between men and women.  The total sample size is somewhat moderate (about
200 participants) with 70% being women. What might be a good approach to use
when analyze these data in light of the objectives?  Any suggestions are
most appreciated.

Sincerely,
Susan Sereika