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Hi Linda & Bengt! I'm hoping you'll be able to help me. I am looking at the interaction between type of treatment (COND = family = 1; group = 0) on anxiety after treatment. In my model I have Estimate PValue RCMASPPO ON COND 0.444 0.471 DMARITAL 0.847 0.428 DMALE 0.516 0.460 D_ETHNIC 0.795 0.409 M_RCMAS 0.580 0.000 M_AGE 0.880 0.000 M_AGEXCOND 0.938 0.003 Intercepts RCMASPPO 7.606 0.000 COND 1=family, 0=group I'm thinking that the mean of change for group = 7.606; family = 7.606+(.444) = 7.162. As age goes up, change in anxiety goes down (i.e., anxiety changes less). I am not sure how to interpret the product term. The reason I am asking this question here is because I have an additional question about missing data. I got this finding using FIML in MPlus. However, when I imputed the data in SPSS and used other tools to test the interaction I got a nonsignificant result. I am not sure if it is okay to use FIML when testing the above. Sorry if the questions sound basic, but whoever I asked in my program did not know and I need to figure it out for my dissertation. Thank you very much. 


FIML and imputation are asymptotically equivalent but may differ in practice with small samples. You may not have the same sample size in Mplus and SPSS. Mplus may delete observations with missing on x. The interaction between age and cond is signficant in the prediction of anxiety. This means that treatment behaves differently with respect to age. For cond=1, the coefficient is .880 + .938, a small positive value. For cond=0, it is .880, a negative value. 


Thank you. I get the full sample in MPlus by bringing in the covariates xy*; as advised here. I also get the full sample in SPSS when I impute the values, but I don't get the same results. Could clustering be the reason? MPlus accounts for clustering whereas SPSS doesn't. It would be interesting to know in what way, if any, clustering makes a difference in moderation analyses. Based on the above  would it be accurate if I say that for cond = 1  for every one unit that age goes up, anxiety goes up by .06. This is a small positive value. for cond = 0  for every one unit that age goes up, anxiety goes down by .880 units. I'm not sure if the way I wrote this makes sense. I should say that I used Anxiety Post on Anxiety Pre Anxiety Post on M_Age Anxiety Post ON M_AgeXCond as the syntax. And one more thing  I'm running some analyses with categorical moderators. How can I get the simple main effects and the means so I put them in a 2X2 table? It would make it easier for me to interpret the findings. I will then be able to report simple main effect contrasts and interaction contrasts. Thanks very much! This helps me a lot toward my dissertation. 


If you do Type = Complex in your Mplus run to deal with clustering, the parameter estimates are not affected, only their SEs. So that wouldn't be the source of the difference visavis SPSS. Yes, your statements about how age affects anxiety are correct. You should also have Cond on the righthand side of your ON statements, which you did in your initial post. You ask about means in a 2 x 2 table, so you must be asking about a binary moderator with your binary Cond variable. This is regression with two binary covariates. It is straightforward to get the 4 means by plugging in the 0's/1's for the two variables as in regular regression. 

Anke Schmitz posted on Wednesday, February 19, 2014  10:17 am



I have a signifikant moderation between two observed variables (one dichotomous and one continous). Where can I see how large the effect is for students with mean values, 1SD and +1 SD? Regards Anke 


See UG ex 3.18. 

Anke Schmitz posted on Thursday, February 20, 2014  7:07 am



Dear Bengt, I have huge problems to apply ex 3.18 on my model. Here is my command: DEFINE: int1 = t*g; !Interaction between continuous observed variable an binary observed categorical variable model: LV by lv4 lv7 lv9 lv10 lv11 lv13 lv14 lv17 lv21; VW by vw2 vw3 vw5 vw6 vw7; int2  vw XWITH text; LV on VW t g int1 int2; There is a significant interaction of int1. I have to know how the effect is when the continuous varibale is 1SD, Mean and +1SD. I don't understand the command in ex. 3.18. 


The LOOP plot is described in the UG on page 696. An application is shown on slides 2124 in the V7Part1.pdf handout shown at http://www.statmodel.com/v7workshops.shtml See Part 1 under Handouts for New Developments in Mplus Version 7 The handouts for the Mplus Version 7 workshops at Utrecht University on August 2729, 2012 are posted here in 4perpage format and in regular format: Part 1: 4perpage Regular Part 2: 4perpage Regular Part 3: 4perpage Regular You also find a video of that there. 

Anke Schmitz posted on Saturday, February 22, 2014  6:35 am



Bengt, thank you very much! It worked quite well. I have one more question: How do I compare a model without interaction (just with main effects) with a model with interaction term? There are no model criteria in the output. Just those information: MODEL FIT INFORMATION Number of Free Parameters 36 Loglikelihood H0 Value 6874.044 H0 Scaling Correction Factor 1.0009 for MLR Information Criteria Akaike (AIC) 13820.088 Bayesian (BIC) 13987.030 SampleSize Adjusted BIC 13872.714 (n* = (n + 2) / 24) Can I do it with the formula on this website? http://www.ats.ucla.edu/stat/mplus/faq/s_b_chi2.htm Kind regards Anke 


Since it is only 1 parameter that differs between the 2 models you can simply use the z test that is given in the output. Using MLR, this takes the nonnormality into account. 


Thanks for your replys on feb, 22. It worked quite good. Is there any chance to compare moderationsmodels between two observed groups (1 versus 2)? I just want to know if the interaction effects differ between two groups of students or if they are similar. I tried the "grouping is" command, but it did not work. Do I have to split the data file and generate two separate models? Regards Anke 


Please send the output showing GROUPING not working and your license number to support@statmodel.com. 


Hi Dr. Muthen, I have a question. I am doing moderation analysis with latent variables using Mplus. If my main predictor and outcome is not signification but my interaction term is, can I still interpret the significant interaction term? 


Yes, but better still is looking at the CI in the moderation plot in line with UG ex 3.18. 


Thank you, Dr. Muthen. I have a quick question to ask: I am reading an article by Maslowsky et al. In this article, it is indicated that when working with latent interaction terms, one must estimate a structural model in two steps: (1). A structural model without the latent interaction term (model 0) & (2). a structural model with latent interaction term (model 1). Doing this in two steps allows for testing of model fit (Klein & Moosebrugger, 2002; Muthen, 2012). My main question is that if I am looking at B1 as my moderator in the relationship between X and Y, do I include B1 as a predictor along with X in model 0 (that is the model that does not include the interaction term)? 


I would do that. See also Section 1.2 of the FAQ on our website http://www.statmodel.com/download/LVinteractions.pdf 

Sara Namazi posted on Tuesday, June 05, 2018  11:50 am



Thank you for your reply, Dr. Muthen. I am trying to plot my latent interaction terms in excel. However, I am having a hard time trying to figure out where to find the intercept for my model. 


If not shown in the output, latent variables have zero intercepts. 


Thank you, Dr. Muthen. Does the new version of Mplus produce standardized path coefficients when including an interaction term in a structural equation model with latent variables? 

Sara Namazi posted on Wednesday, June 06, 2018  11:06 am



Hi Dr. Muthen, I wanted to followup with you. In my reading about latent interaction terms, I learned that Mplus does not produce standardized beta coefficient when including latent interaction terms in your model. However, I am able to get standardized beta coefficient using the following command in Mplus: OUTPUT: STAND TECH1 tech4 sampstat PATTERNS RESIDUAL modindices ; Not sure If I am missing something or whether my understanding is correct. Thanks, Sara 


You get standardized coefficients also with latent variable interactions in the current Mplus. This is described in the FAQ on our website: Latent variable interactions 


Dear Dr Muthen, I have a question regarding the interpretation of a moderation model output. I have 2 indipendent latent factor: a, b and a dipendent measured variable c. I ran a simple model: c on a b; and I had in the output a negative estimate for both: c on a 0.300 c on b 0.100 I decided to run a moderation model because I assumed that variable a could interact with b and produce a stronger effect on c: (high a and high b > lesser c) On the contrary I had in the output: c on a 0.348 c on b 0.108 c on ab +0.250 In the interaction a and b the estimated relation with c is reversed. That does not make any sense in theory. Am I interpreting the output in a wrong way? 


This is a good question for SEMNET. 


Hi Dr, Muthen, I have a question about latent moderated structural questions. So to test interaction terms in Mplus, Maslowsky et al. 2015 article indicates that to estimate latent moderated structural equations, you should run a model without the interaction term (called Model 0) and then add a model with the interaction term (called Model 1) to compare model fit using the XWITH Command in Mplus. So if I am looking at the relationship between a > M > b and ab so a simple mediation, would that mean that my model 0 is: M on a b on M b on a and model 1 (v is my moderator pointing to the path going from a to M): M on a M on v M on a*v b on M b on a Thanks. 


Dear Dr Muthen, I'm running a moderation model and the moderation variable is a measured variable. When I run the model it takes 10 minutes to complete. When I used a moderation variable that is a latent variable in the same model it takes 3 minutes to complete. Is that normal or am I doing in the wrong way? I write you the model with the measured moderation variable below: USEVARIABLES ARE ZAAT2 ZAAT4 ZAAT5 ZAAT8 ZAAT10 ZAAT11 ZAAT1 ZAAT3 ZAAT6 ZAAT7 ZAAT9 ZAAT12 BSI20 BSI21 BSI22 BSI42 Zalfa1; CATEGORICAL ARE BSI20 BSI21 BSI22 BSI42; ANALYSIS: TYPE =RANDOM; ALGORITHM=INTEGRATION; INTEGRATION=MONTECARLO; OUTPUT: standardized; MODEL: AATap by ZAAT2 ZAAT4 ZAAT5 ZAAT8 ZAAT10 ZAAT11; AATav by ZAAT1 ZAAT3 ZAAT6 ZAAT7 ZAAT9 ZAAT12; INT by BSI20 BSI21 BSI22 BSI42; !!!MODERATION FACTORS AATapZalfa1  AATap XWITH Zalfa1; AATavZalfa1  AATav XWITH Zalfa1; !!!MODERATION MODEL INT on AATap Zalfa1 AATapZalfa1; INT on AATav Zalfa1 AATavZalfa1; Thank you in advance 


Answer for Sarah: We describe model fitting in section 1.2 of the FAQ on our website: Latent variable interactions. 


Answer for Allessandra: We need to see the 2 outputs  send to Support along with your license number. 

Zehua Cui posted on Tuesday, January 28, 2020  12:13 pm



Dear Dr.Muthen, One of the reviewers of my paper asked about how mplus handles interaction in which one variable is latent and one is continuous. I check the Mplus manual and I found that the manual referenced a paper by Klein, A. & Moosbrugger, H. (2000) titled "Maximum likelihood estimation of latent interaction effects with the LMS method.". I am wondering if this is the paper I should get information from and cite? Thank you so much! 


You can cite that paper for the estimator, which is maximumlikelihood, but the actual algorithm Mplus uses for maximumlikelihood estimation in this case is somewhat different and its reference should be http://www.statmodel.com/download/webnotes/webnote6.pdf 

Zehua Cui posted on Tuesday, January 28, 2020  6:49 pm



Thank you so much Dr. Muthen! 

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