Message/Author 

Yue Yin posted on Monday, November 26, 2018  1:44 pm



Hi, Some articles proved that HGLM is algebraically equivalent to Rasch model. And it has been proved that we can use HGLM to detect DIF in person level. However, those articles only provided how to use HGLM to detect DIF in software like SAS, and HLM. And I checked the UG, I did not find how to use HGLM to examine DIF in Mplus. So I am wondering that is that possible to detect DIF using HGLM in Mplus? If it does, could you show me the code how to do it?? Thank you so much! 


I assume you are referring to 2level Rasch. I am not familiar with that DIF topic  can you give me a reference? 

Yue Yin posted on Monday, November 26, 2018  4:12 pm



I think it is still HGLM, but probably we can call it 2level Rasch HGLM. Yes, the reference is below: Kamata, A., Chaimongkol, S., Genc, E., & Bilir, K. (2005). Randomeffect differential item functioning across group unites by the hierarchical generalized linear model. This paper was presented at the annual meeting of the American Educational Research Association, Montreal, Canada. 


Has it been published? 

Yue Yin posted on Monday, November 26, 2018  4:46 pm



No, it was presented at the conference. But I have some empirical study articles about using HGLM detecting DIF if you want. And below is the dissertation about it. Wen, Y. (2014). DIF analyses in multilevel data: Identification and effects on ability estimates (Doctoral dissertation). Retrieved from UWM Digital Commons. And below is the article talking about how HGLM is algebraically equivalent to Rasch, but the author did not talk about how to use it to detect DIF until he presented it in the conference which I posted before. It is the same author. Kamata, A. (2001). Item analysis by the hierarchical generalized linear model. Journal of Educational Measurement, 38(1), 7993. 

Yue Yin posted on Tuesday, November 27, 2018  12:39 pm



And actually the firstlevel is itemlevel, and the secondlevel is personlevel. So if I want to detect gender DIF using HGLM, that would be secondlevel Rasch HGLM. And I want to try to use Mplus to run HGLM, because I use Mplus to run other models. Using Mplus to make the comparison fairly. But I do not know how to manipulate the syntax. 


In the Wen dissertation, equations (2.5)  (2.7) can be done in Mplus using twolevel modeling with categorical items. There are several UG examples of this. 

Yue Yin posted on Wednesday, November 28, 2018  2:38 pm



Alright, thank you! So I will use twolevel modeling with categorical items to model the equations. But how could I identify the DIF for interested group? Does it similar to MIMIC code? If I interested in gender DIF, so I put like item1 on gender; like this? 


I can't help you with that but I assume the Wen dissertation can guide you. 

Yue Yin posted on Monday, December 17, 2018  12:11 pm



So I have a question, since itemlevel is level one, and interested group is in leveltwo which is personlevel, I want the crosslevel interaction between itemlevel (difficulty) and personlevel(interested group), but the itemlevel does not vary in the personlevel, which means there is no random slope. So I can't use: %within% sY on X; %between% s Y on M; to make the interaction. Is there a way to express this crosslevel interaction? Thank you! 


Itemlevel difficulty sounds like it would be handled by a random intercept so Y ON M. I don't know what you mean by "itemlevel does not vary in the personlevel". 

Yue Yin posted on Tuesday, December 18, 2018  7:35 am



So the "itemlevel does not vary in the personlevel" means item effect does not vary across persons randomly, there is no random slope. But if I put within=X between=M how can I manage the crosslevel interaction, like Y ON x*m? The equation is 3.4 in Wen's paper:like pie*Group*item where Group is interested group in the personlevel, and item is item effect in the item level. Thank you. 


You mention Y, X, M and Group. How is Group related to Y, X, M? Is M=Group? 

Yue Yin posted on Thursday, December 20, 2018  11:38 am



Yes, and I treated X as the item. So is there a way to express it? 


What is your Y? What is Wen's "pie" in your terms? I am asking these questions because you are not describing your situation clearly enough for me to understand what you want to do. I don't want to take the time to read Wen's disseration  if you are going to apply Wen's ideas you need to be able to explain what you want to do. 

Yue Yin posted on Tuesday, January 01, 2019  2:32 pm



Happy New Year! I am sorry, that I did not explain it very well. So according to the dataset in her paper, the Y is the item response for each item which is either 0 or 1 since it is dichotomous. Basically, in the level one which is the item level equation is: Y=beta0+betaq*X beta0 indicates ability and betaq indicates difficulty, X indicates item. In the level two which is the student level, the equation is: beta0=pie0+e, betaq=pie10+pie11*G here pie11 is the DIF magnitude for each item, G is the group. And since item can't vary across person randomly which means there is no random slope. So if we combine level one and two to detect dif, the equation simply is:pie*G*X, pie is the DIF magnitude of the item in this group. But in Mplus, if I set within =X, and between=G, how should I express this equation since there is no random slope? Thank you! 


You say: the item level equation is: Y=beta0+betaq*X (1) level two which is the student level, the equation is: beta0=pie0+e, (2a) betaq=pie10+pie11*G (2b) Then you say that when you combine (1) and (2) you get pie*G*X (3) I don't see how you get (3) from (1) and (2). Anyway, if you want an interaction term without a random slope, why not use Define to create an interaction variable: Define: GX = G*X 

Yue Yin posted on Tuesday, January 01, 2019  7:42 pm



Yeah, I just highlight the important part of the (3), I thought about the define part, so it is OK to define GX=G*X even though I put %within% X %between% G right? Thank you. 


Perhaps you want X and GX on Within and G on Between. 

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