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June Zhou posted on Wednesday, January 30, 2013  2:57 am



I am trying to run multilevel IRT Rasch models in Mplus and I have some questions listing as below: 1. In the 2level 1PL IRT model, items (level1) were nested in students (level2), can I use Ex.7.27 and constrain all of loadings to be 1? How to add studentlevel predictors in the model? 2. In the 3level 1PL IRT model, items (level1) were nested in students (level2) and students were nested in schools (level3), should I use EX.10.5 and constrain all of loadings to be 1? How to add schoollevel predictors in the model? Thank you in advance. 


1. This is not a multilevel model in Mplus. See Example 5.2 and 5.5. 2. This is a twolevel model in Mplus. See Example 9.7 which includes a betweenlevel covariate. 

June Zhou posted on Wednesday, January 30, 2013  6:03 pm



Thank you very much for your advice, Dr. Muthen. I really appreciate your help. 

June Zhou posted on Monday, April 01, 2013  10:15 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$1u10$1*.5 u11$1u20$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! 


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  9:36 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 2level Rasch model with within and betweenlevel 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 = u1u5 x1 x2; generate = u1u5(1); categorical = u1u5; 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 u2u5*1; fw*1; fw ON x1*.25; %Between% [x2*0]; x2@1; fb by u1@1 u2u5*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]; 


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  8:00 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! 


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  2:00 pm



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! 


You request factor scores using FSCORES. 


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? 


This has been answered under a different thread. 


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? 


Look at the Monte Carlo counterpart for Example 5.5. This was used to simulate the data for Example 5.5 

þeyma posted on Wednesday, October 22, 2014  6:43 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 u1u8 dumb dum clus; USEVARIABLES = u1u8; CATEGORICAL = u1u8; 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 u1u8; [f@0]; %BETWEEN% %OVERALL% %cb#1.c#1% [u1$1u8$1]; %cb#1.c#2% [u1$1u8$1]; OUTPUT: TECH1 TECH8; 


It seems like you want only one latent class variable cb which has two classes and is declared as a betweenlevel variable. Which means that you would say %BETWEEN% %OVERALL% %cb#1% [u1$1u8$1]; %cb#2% [u1$1u8$1]; 


Dear Drs. Muthen, I want to use multilevel ordinal logistic regression for determining DIF. How can I do it with Mplus? Can Mplus draw figures for uniform and nonuniform DIF? how can I do it? Thank you. 


See UG ex 9.7, where you add direct effects from the covariates to factor indicators to capture DIF with respect to difficulty parameters/thresholds. You can do the plot as a function of the covariate values using an Adjusted probability plot option in the plot menu. 


Dear Drs. Muthen, I follow your suggestion about finding DIF and logistic regression. I want to find DIF with logistic regression my response are ordinal and multilevel how I can do it? example 9.7 find DIF with CCFA but I want to do with logistic regression. Thanks 


You can do ex9.7 with logistic link using ML. The direct effects on within or between are indications of DIF. 


Dear Drs. Muthen, thanks for your answer.I wrote following program.x1(dependent variable) is peoples' answer to my first question(1,2,3,4,5),theta(independent variable)is ability and wv (independent variable)is the group indicator(1or2). I want to know this program is true for detection of DIF with ordinal logstic regression? and also when I run this program x1 and wv both are considered dependent variable? TITLE: this is an example of a twolevel ordinal logistic regression , a random intercept, and covariates DATA: FILE = "F:/Mplus.dat"; VARIABLE: NAMES = s clus per wv bv theta X1 X2 X3 X4 X5 s1 clus1 per1 wv1 bv1theta1 y1 y2 y3 y4 y5; usevariables X1 wv theta; CATEGORICAL = X1 wv ; WITHIN =wv theta; CLUSTER = clus; MISSING = ALL (999); ANALYSIS:TYPE = TWOLEVEL random; Estimator is MLR; Link=logit; MODEL: %WITHIN% X1 on wv theta; OUTPUT:Sampstat TECH1 TECH8; 


Dear Drs. Muthen, I think I get it. is this program true? TITLE: this is an example of a twolevel ordinal logistic regression , a random intercept, and covariates DATA: FILE = "F:/Mplus.dat"; VARIABLE: NAMES = s clus per wv bv theta X1 X2 X3 X4 X5 s1 clus1 per1 wv1 bv1theta1 y1 y2 y3 y4 y5; usevariables X1 wv theta; MISSING=.; CATEGORICAL = X1 ; WITHIN =wv theta; CLUSTER = clus; MISSING = ALL (999); ANALYSIS: TYPE = TWOLEVEL random; Estimator is MLR; Link=logit; MODEL: %WITHIN% X1 on wv theta; %BETWEEN% X1 OUTPUT:Sampstat TECH1 TECH8; regards 


This looks ok. 

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