http://spssx-discussion.165.s1.nabble.com/Multiple-Imputation-tp4994372p5723123.html
About DVs.
If you have 3 or more responses that cannot be put into
a meaningful order, THEN you have a categorical variable.
I suggest - Browse a book on psychometrics, for this and other
background.
"Fisher's z-transformation" is the wrong name, since that name
refers to the inverse arc-tan transformation that Fisher applied
to correlations. See http://en.wikipedia.org/wiki/Fisher_transformation .
Perhaps your supervisor used that term; Fisher's z distribution could
be relevant to the approach you should be using, as I show, below.
39 dichotomies; one item with likert-type anchors and a 7-point rang;
and one numerical count. If you develop something called a *scale*,
you develop it from the 39 items alone.
One simple and direct approach is to assume that you have 3 DVs, not one.
There are ways to work with 3 outcomes -- either by choice of analysis, or
by Bonferroni correction, or creating a "composite score" as criterion.
If you want a composite score that represents a single outcome, then
you combine that 39-item scale with the two other, rather-independent
outcomes: There are at least 3 obvious ways to do this.
1) Count the likert-type item and the count as being merely equivalent,
each, to *one* of the dichotomous items. To the extent that they seem to
cover a part of the "universe" that is different from what is covered by
the items, that is a foolish way to under-rate them. ("universe" is a term
you should learn from psychometrics.) Since this is a bad approach, I won't
describe it further. You seemed to have had in mind one version of doing this.
2) Count the likert-type item and the count as being equivalent to the
scale developed from the dichotomies. Do you want to use raw counts,
or do you transform them, for instance, by taking the square root, or by
drawing in some large outlier or two (so 10= "10 and above")? Anyway,
for this, you could z-score the 39-item scale, the likert-item, and the count
(means now 0, SDs= 1); add them together (mean still 0; SD greater) to
get a composite score. - You might look at this and think that it gives
too much weight to those two items ... See "validity" comment in (3).
For convenience of reading and interpreting, I take another step with a
composite formed this way, to create a T-score with mean of 50 and SD
of 10: Divide by the SD (to make new SD=1); multiply by 10 (to make
new SD=10); add 50 (to make new mean=50).
3) From another aspect of psychometric theory, one might prefer that
the parts of a composite should be weighted by their reliability, or, even
better (but less accessible) by their validity. - That is, if equal weights
give too little weight to the 39 items (which would be my guess), you
can assign (slightly) differing weights to these 3 parts of the composite,
like (2,1,1) and not (4,1,1). COMPOSITE= 2*SCALE39 + LIKERT + COUNT.
(Follow this by T-scoring.)
I put in the "(slightly)" because even a statistician can be lulled into
forgetting that the *effective* weighting is by variance, which increases
with the square of the weight. Thus, if you use (2,1,1), you are already
saying the first one is 4 times as important as each of the others. If you
want more emphasis than that, then you might consider that your hypothesis
testing is neater to describe if you ignore the other two entirely, for the
purpose of your main test.
--
Rich Ulrich
Date: Sun, 17 Nov 2013 02:45:13 -0800
From:
[hidden email]Subject: Re: Multiple Imputation
To:
[hidden email]
Thank you again for your comments and advice!
To make sure i understood you correctly:
IV - questionnaire
Since I'm using an established questionnaire as my IV, I don't have
to impute missing values and just sum the items by mean.n. As far as
I know this procedure requires that at least 2/3, or better 3/4, of
the items i use for summing are complete, which is not the case in
my questionnaire, i.e. one scale has 11 items and i have missings on
4 of them (->only 63.3% are complete). Can I still use the mean.n
fuction or do I have to drop this scale?
Can you advice me on literature for that procedure (since the
analysis is for my thesis and I have to justify my procedure)? Also,
are you implying that I don't have to check MCAR or MAR for that
questionnaire?
Indeed, without imputation, I could replicate the factor structure
of that questionnaire.
DVs - behavioral measures
I was a little confused by Rich's comment that I don't mention
categorical items. Most of my DV items have a response format, i.e.
"not prejudiced behavior" vs. " prejudiced behavior". Doesn't that
make them categorical? By z-transform I meant Fisher's
z-transformation (my supervisor suggested that) because I will have
to build scales, and 39 are categorical, one is answered on a
7-point liker scale, one is the amount of leaflets participants take
with them (interval). I understand that I don't have to use
Z-transformation for correlational analyses and factor analysis,
right?
So your advice, Art, is that I check the factor structure with CFA
with listwise deletion and mean imputation and compare them. But
before using the summative score or listwise deletion, don't I have
to check if the data is MCAR or MAR? I understand from the
literature that every method of imputation or deletion of cases
assumes that data is MCAR/MAR.
Thank you so much for your help!!
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