Testlets and Factor Analysis PreviousNext
Mplus Discussion > Exploratory Factor Analysis >
Message/Author
 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).
 Jing Davis posted on Wednesday, August 29, 2018 - 9:39 am
Dear Dr. Muthen,


I was running an analysis, which has two testlets in the data. The structure I set up is:
MODEL: T1 BY V4 V5 V6 V7 V8 V18;
T2 BY V13 V14 V15 V16 V17 V19;
G BY V1-V22;
G WITH T1@0 T2@0;
T1 WITH T2@0;

My question is: As for a testlet model, whether I should put T1 T2 as factor indicators in the Command line, such as: G BY T1 T2 V1-V22.

Thank you,
Jing
 Bengt O. Muthen posted on Wednesday, August 29, 2018 - 1:19 pm
No.
 Ryan Veal posted on Wednesday, January 16, 2019 - 6:06 pm
Hi Prof. Muthen,

I'm trying to work out the syntax for a CFA model using testlets and latent variables, and the above discussion thread doesn't answer my question.

I can't quite work out how to include testlets as factor indicators in a factor analysis model. For the model in question, each testlet would load on the latent factor, as would another separate item. I have provided the below syntax as a guide for the model i am referring to:

MODEL:
F1 BY ITEM1 (TESTLET BY ITEM2 AND ITEM3);
F2 BY ITEM5 (TESTLET BY ITEM4 AND ITEM6);
F3 BY ITEM9 (TESTLET BY ITEM7 AND ITEM10);
G BY F1 F2 F3;

I have tried to create separet indicators using the testlets as indicators without success. Are you able to provide a brief answer?
 Bengt O. Muthen posted on Thursday, January 17, 2019 - 4:28 pm
I assume the testlets are sums of items. If so, you can create them in Define. And then you simply refer to these new variables on the Usevariable list and in your BY statements (together with other items loading on the factor). I am not sure if that is what you are asking, however.
 Ryan Veal posted on Thursday, March 07, 2019 - 10:08 pm
Hello Prof. Muthen,

Thanks for your reply. No, I am not referring to sums of items (I believe sums of items are referred to as parcels).

Testlets developed from Item Response Theory: local dependence occurs when two or more items are more highly associated than can be explained by their relationships with the underlying latent trait. Local dependence can occur because the same information is used to score more than one item, and thus, a pair of items may actually represent somewhere between one and two items. Testlets, therefore, are essentially a "sub-factor" for a pair of items, that act as indicators for a latent factor and alongside other indicators/items for that latent factor. I hope this is clear.

On 21/12/10, Prof. Linda K Muthen in the thread above wrote: 'You can use testlets as factor indicators in a factor analysis model.' I am trying to run a model that includes both a testlet and separate test items as factor indicators for the same latent factor, yet am unsure of the input to do this.

When I attempt to run testlets as factor indicators, i receive the following:
*** ERROR in MODEL command
The metric for the following factor cannot be determined because the factor has both observed and latent indicators.

Does this make sense? I am seeking the input to do so.
 Bengt O. Muthen posted on Friday, March 08, 2019 - 10:07 am
Don't you want to handle that by a bi-factor approach

G by all items

f1 by first set of testlet items
f2 by second set of testlet items
etc

Typically, G is fixed to be uncorrelated with the testlet factors.
 Ryan Veal posted on Thursday, March 14, 2019 - 8:20 pm
Hi Professor Muthen,

Thanks again for your reply - I appreciate your assistance. Unfortunately, the testlet model I have been discussing (which I want to analyse using CFA) is not a bi-factor model. I have included the reference of the original article proposing the model for your reference below (the model diagram is on page 181):

Cooke, D. J., & Michie, C. (2001). Refining the construct of psychopathy: Towards a hierarchical model. Psychological Assessment, 13(2), 171-188. doi:10.1037//1040-3590.13.2.171

This model has been validated in a number of different studies (using the EQS program), yet I do not believe it has ever been researched using Mplus. I have now tried a number of different ways to run the model without success. I now presume the problem may be that Mplus simply cannot compute this type of hierarchical model because it contains factors that have both observed and latent indicators. Would you agree?

Kind regards,
Ryan
 Bengt O. Muthen posted on Friday, March 15, 2019 - 1:36 pm
Mplus will have no problem estimating this model with observed and latent indicators. You can for instance say

factor1 by testlet1 pclvs3;
testlet1 by pclsv1 pclsv2;
psychop by factor 1 etc;

If this doesn't help, send your output to Support along with your license number.
 Ryan Veal posted on Saturday, March 16, 2019 - 11:03 pm
Thanks Professor Muthen. I figured out the problem was that the factor loading default setting needed to be overridden to allow the testlets to be freely estimated (not fixed to 1, as is the default setting) because there is only a single latent indicator alongside the observed indicator. Hence the following syntax:

testlet1 BY pcl1 pcl2;
F1 BY testlet1* pcl3;

Models are now estimating normally. Thank you again for your help on this.
Back to top
Add Your Message Here
Post:
Username: Posting Information:
This is a private posting area. Only registered users and moderators may post messages here.
Password:
Options: Enable HTML code in message
Automatically activate URLs in message
Action: