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 Seán Delaney posted on Tuesday, February 05, 2008 - 9:57 pm
I have a question in relation to testlets. I wish to do EFA and CFA on some data where several of the variables are testlets (common stem and between 3 and 7 parts related to the stem). I have been told that testlets can affect the factor analyses but that Mplus can take the potential effect of testlets into account. I would be grateful if you can tell me how to go about this or else if you could direct me to this information elsewhere in the discussion forum (if it exists. I searched and could not find it).

Thank you.
 Seán Delaney posted on Tuesday, February 05, 2008 - 10:00 pm
I want to add one thing to my previous question about testlets and factor analysis. My data are categorical (binary). Thanks.
 Linda K. Muthen posted on Wednesday, February 06, 2008 - 10:26 am
It sounds like you have testlets made up of sets of binary items. The choice of items is crucial in creating testlets. Mplus cannot help with that. Mplus can take measurement error into account when using testlets as factor indicators in factor analysis. You can also use the original binary items as factor indicators in Mplus.
 Seán Delaney posted on Wednesday, February 06, 2008 - 3:48 pm
Thanks for this reply Linda.

Can you direct me to information on how to take measurement error into account when using testlets as factor indicators in factor analysis and when entering such data into the data file?

Thank you.
 Linda K. Muthen posted on Wednesday, February 06, 2008 - 5:22 pm
The estimation of a factor model takes measurement error into account. You do not need to do anything.
 Sigbert Klinke posted on Tuesday, December 21, 2010 - 4:56 am
Hello,

since the messages in 'Testlets and Factor Analysis' are already from 2008, I would like to know if it is possible to estimate a testlet model with Mplus.

Thanks in advance Sigbert
 Linda K. Muthen posted on Tuesday, December 21, 2010 - 6:10 am
You can use testlets as factor indicators in a factor analysis model.
 Sigbert Klinke posted on Tuesday, December 21, 2010 - 8:29 am
Hello, I'am not sure that I understand you correctly, do you mean something like:

testlet1 BY item1 item2;
testlet2 BY item3 item4;
factor BY testlet1 testlet2 item1-4;

(and maybe some constraints on the loadings)?

Thanks Sigbert
 Bengt O. Muthen posted on Tuesday, December 21, 2010 - 2:56 pm
I don't know what a "testlet model" is.
 Sigbert Klinke posted on Saturday, December 25, 2010 - 1:49 am
A 2-PL Testlet model would be:

P(Y_ij=c|...) = G(a_j (theta_i - gamma_ik - b_j)),

so the probability of getting response c in item j and from person i depends on some appropriate link function G, item parameters a_j and b_j and a person parameter theta_i and the testlet effect gamma_ik (where item j belongs to testlet k).

Happy christmas Sigbert
 Bengt O. Muthen posted on Sunday, December 26, 2010 - 1:25 pm
So it looks like a bi-factor model, also called a general-factor, specific-factor model. The Mplus course Topic 1 gives the input for that with continuous items, but it is the same idea for categorical items. Except, your model imposes equality of the slope for the general factor (theta) and the specific factor (gamma).
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