Unidimensionality
Message/Author
 Tony LI posted on Tuesday, April 15, 2008 - 9:14 am
Hi all,

I was trying to use Mplus to perform IRT analysis for 5 independent constructs, each of them contains approx.20 items(categorical response: 0,1,2,3). All the items had been reviewed by subject experts. The sample size is 500+.

To assess unidimensionality, I first conducted CFA for each construct,finding that the CFA produces 2 factors, one being positive items and the other being negative items.

I further factor-analysed all items from 5 constructs together and found the similar positive-negative split pattern: the items were loaded by their direction (positive vs. negative), rather than construct relevancy.

I searched this forum but couldn't find any similar case. Could anyone advise on this? Thanks in advance.
 Bengt O. Muthen posted on Tuesday, April 15, 2008 - 9:51 am
This "methods factor" phenomenon is common. See for example the CFA book

Brown, T.A. (2006). Confirmatory factor analysis for applied researchers. New York: The Guilford Press.

It has many references on this topic as well. You can probably also Google "methods factor", or "MTMM" (multi-trait, multi-method).
 Tony LI posted on Tuesday, April 15, 2008 - 3:20 pm
Hi Bengt,

Thanks for the timely replay.

I conducted IRT analysis for the above mentioned scales. For each construct, if I put all items together (treat as unidimensional),the IRT parameters show
very low slope (<1) on negative items. However,when conducting seperate IRT for negative and positive items, all the slops for negative items appear to have significant increase. Slop for positve items have trivial change.

Would this cause a concern?
 Bengt O. Muthen posted on Tuesday, April 15, 2008 - 7:42 pm
That would seem to me to suggest that you have 2 factors behind all these items, that the factors don't correlate very highly, and that you have fewer negative items than positive ones. In that case, forcing unidimensionality gives low slopes for the negative items (the low loadings fitting the low correlations between the negative and positive items). The positive items have higher loadings because that is needed to fit the correlations among (the more plentiful) positive items. And a separate analysis of the negative items would give larger loadings because the negative items correlate rather highly among themselves.

Just guessing. So if this is the case, a unidimensional IRT for all items is not suitable. Hope I am understanding what you meant.
 Keivn Linares posted on Monday, November 22, 2010 - 5:44 pm
Hello Drs. Muthen,
I am trying the new Bayes estimator using a correlated uniqueness model but I get a warning that the psi matrix is not positive definite. Is there a problem with my syntax or is this not possible?

ANALYSIS:
ESTIMATOR = BAYES;
PROCESS = 2;
FBITER = 100000;
STVAL = ML;
COVERAGE = 0.10;

MODEL:
EmoDys BY mf1* KF1;
Narc BY mf2* kf2;
Imp BY mf3* kf3;
EmoDys@1.0; narc@1.0; Imp@1.0;
mf1 mf2 WITH mf3; mf1 WITH mf2;
kf1 kf2 WITH kf3; kf1 WITH kf2;
EmoDys Narc WITH Imp; EmoDys WITH Narc;
 Bengt O. Muthen posted on Monday, November 22, 2010 - 5:46 pm
Check first if ML gives you pos def Psi. If it does and Bayes doesn't, send material to support.
 Keivn Linares posted on Monday, November 22, 2010 - 6:10 pm
Thank you so much for the quick response.
It converges in ML with pos def psi. I think the problem is that I have 2 indicators per factor. So in other words I have 3 traits, 2 methods. Is it possible to constrain factor loadings of indicator loadings are equal to the same trait. If so, how would I go about it and using Bayes. Would it look like this?

MODEL:
EmoDys BY mf1(1) KF1(1);
Narc BY mf2(2) kf2(2);
Imp BY mf3(3) kf3(3);
 Bengt O. Muthen posted on Tuesday, November 23, 2010 - 8:00 am
f BY y1-y2* (1-2);
f@1;
 Keivn Linares posted on Tuesday, November 23, 2010 - 11:46 am
Thank you so much for your quick response and help. The model converged, but I am wondering the stdyx command in the output are not available for this model. After all, isn't it the standardized parameter estimates that are reported in a CU model?
 Linda K. Muthen posted on Wednesday, November 24, 2010 - 9:26 am
Please send your output and license number to support@statmodel.com so I can see why you don't get a standardized solution.