Multilevel IRT Model in Mplus PreviousNext
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 June Zhou posted on Tuesday, January 29, 2013 - 8:57 pm
I am trying to run multilevel IRT Rasch models in Mplus and I have some questions listing as below:

1. In the 2-level 1PL IRT model, items (level-1) were nested in students (level-2), can I use Ex.7.27 and constrain all of loadings to be 1? How to add student-level predictors in the model?

2. In the 3-level 1PL IRT model, items (level-1) were nested in students (level-2) and students were nested in schools (level-3), should I use EX.10.5 and constrain all of loadings to be 1? How to add school-level predictors in the model?

Thank you in advance.
 Linda K. Muthen posted on Wednesday, January 30, 2013 - 10:55 am
1. This is not a multilevel model in Mplus. See Example 5.2 and 5.5.

2. This is a two-level model in Mplus. See Example 9.7 which includes a between-level covariate.
 June Zhou posted on Wednesday, January 30, 2013 - 12:03 pm
Thank you very much for your advice, Dr. Muthen. I really appreciate your help.
 June Zhou posted on Monday, April 01, 2013 - 4:15 pm
I am trying to run an MCMC Rasch model in Mplus. I have two questions:

1. When I tried to constrain item discrimination parameters (factor loading) to be 1, I found I only got identical loadings but they were not 1. Why?

2. In MCEX5.5, is the code "[u1$1-u10$1*-.5 u11$1-u20$1*.5]" meant to fix item difficulty parameters of the first 10 items to be -.5 and the last 10 items .5? If yes, can I change the values to -2.5, -0.5, 0, 0.5, and 2.5 since the range of item difficulty parameter is (-3, 3)?

Thank you in advance!
 Bengt O. Muthen posted on Monday, April 01, 2013 - 4:53 pm
1. If you hold them equal, one parameter will be estimated. That won't happen if you fix them @1.

2. Yes. The range of difficulty parameters depend on the variance of the factor. Using 3 implies variance one.
 June Zhou posted on Wednesday, April 03, 2013 - 3:36 pm
Thank you so much for your prompt reply, Dr. Muthen! I really appreciate your help.

This time I am going to do a Monte Carlo study for a 2-level Rasch model with within and between-level variables in Mplus. Below are my codes. Compared with mcex10.5. I am not sure whether I defined my thresholds (item difficulty) accurately or not. Would you please give me some advice? Thank you for your time in advance.

montecarlo:
names = u1-u5 x1 x2;
generate = u1-u5(1);
categorical = u1-u5;
nobs = 200;
ncsizes = 2;
csizes = 6 (20) 2 (40);
seed = 48459;
nreps = 500;
repsave=all;
save=con1*.dat;
within = x1;
between = x2;

ANALYSIS: TYPE IS TWOLEVEL;

model population:

%Within%
[x1*0]; x1@1;
fw by u1@1 u2-u5*1;
fw*1;
fw ON x1*.25;

%Between%
[x2*0]; x2@1;
fb by u1@1 u2-u5*1;
fb*.1111;
fb ON x2*.25;
[u1$1*-2.5 u2$1*-1.5 u3$1*0 u4$1*1.5 u5$1*2.5];
 Bengt O. Muthen posted on Wednesday, April 03, 2013 - 4:48 pm
Looks ok. But you want more clusters than 8 in a twolevel analysis. And you want to specify MODEL as well, not only MODEL POPULATION.
 June Zhou posted on Thursday, April 04, 2013 - 2:00 pm
Thank you very much for your advice, Dr. Muthen.

Could you please tell me the reason why the thresholds of variables on the between and within levels exist only on the between level. In other words, why I couldn't define thresholds in within level?

Thanks!
 Bengt O. Muthen posted on Thursday, April 04, 2013 - 2:53 pm
Each item has just one set of thresholds (one if binary, several if polytomous) and the convention is that they are reported on the Between level. They cannot also be identified on the within level. This is in line with means/intercepts in regular multilevel analysis.
 June Zhou posted on Monday, April 08, 2013 - 8:00 am
I see. Thank you so much for your reply! Sorry, I have another question: is there a statistic estimating the latent person ability parameter in IRT model in Mplus? Thank you in advance!
 Bengt O. Muthen posted on Monday, April 08, 2013 - 5:03 pm
You request factor scores using FSCORES.
 zahra sharafi posted on Tuesday, September 23, 2014 - 10:15 pm
Dear Drs. Muthen,
I want to simulate ordinal multilevel data that has DIF. I just know I should use 2 parameter logistic IRT model. please tell information about this model and steps of my simulation.I have a little information about this problem and I do not know where I can find about it?
 Bengt O. Muthen posted on Wednesday, September 24, 2014 - 3:03 pm
This has been answered under a different thread.
 zahra sharafi posted on Saturday, September 27, 2014 - 6:07 am
Thank you for your answer.
I know about the theory of multilevel IRT
and I read and understand Samejima’s graded response model that you said in example 5.5 also I read your homepage.But I dont know how simulate multilevel IRT data?
Do you look at this model like CFA?
should I simulate from multilevel IRT or CFA?
 Linda K. Muthen posted on Saturday, September 27, 2014 - 9:20 am
Look at the Monte Carlo counterpart for Example 5.5. This was used to simulate the data for Example 5.5
 şeyma posted on Wednesday, October 22, 2014 - 12:43 pm
Dear Drs. Muthen,
I want to do multilevel mixture IRT analysis. But I am only interested in the differences across student level classes, when the data is multilevel (include school level). The diffuculty parameters are same across school level classes. I generated data in any other program and I used example 10.5 for analyse it. But I changed something in the syntax. Is that true?

VARIABLE:NAMES ARE u1-u8 dumb dum clus;
USEVARIABLES = u1-u8;
CATEGORICAL = u1-u8;
CLASSES = cb(1) c(2);
BETWEEN = cb;
CLUSTER = clus;
DATA: FILE = ex10.5.dat;
ANALYSIS: TYPE = TWOLEVEL MIXTURE;
ALGORITHM = INTEGRATION;
PROCESSORS = 2;
MODEL:
%WITHIN%
%OVERALL%
f BY u1-u8;
[f@0];
%BETWEEN%
%OVERALL%
%cb#1.c#1%
[u1$1-u8$1];
%cb#1.c#2%
[u1$1-u8$1];
OUTPUT: TECH1 TECH8;
 Bengt O. Muthen posted on Thursday, October 23, 2014 - 11:41 am
It seems like you want only one latent class variable cb which has two classes and is declared as a between-level variable. Which means that you would say

%BETWEEN%
%OVERALL%
%cb#1%
[u1$1-u8$1];
%cb#2%
[u1$1-u8$1];
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