Message/Author 

Oli Christ posted on Thursday, August 25, 2005  3:15 am



I have a multilevel example where I expect the relationship between two individuallevel variables to be moderated by a grouplevel variable (one that varies only betweengroups). Can I test this hypothesis using MPlus? The handbook seems to suggest that currently MPlus cannot handle crosslevel interactions. However, I would like to take advantage of MPlus's groupmean centering options to decide whether I am dealing with a crosslevel interaction or a betweengroup interaction. 


I think you will get the results you want by the following partial setup: WTIHIN = x; BETWEEN = w; MODEL: %WITHIN% s  y ON x; %BETWEEN% s ON w; 


I would like to estimate a path model with manifest variables in which a variable that varies within as well as between clusters (i.e., intelligence) is regressed on intelligence measured at an earlier time point and several other variables that vary ONLY between clusters (school classes) but are constant within clusters (i.e., variables such as class climate etc.). Furthermore, several of these clusterlevel variables are supposed to be connected to other cluster level variables via regression or covariance paths. I am not sure if and how such a model can be specified in Mplus? It would be great if you could provide an appropriate example input code. Thank you very much. 


Here is an example. Note that on the between level, y1 and y2 are the between parts of intelligence. Between = w1 w2 w3; Model: %within% y2 on y1; %between% y2 on y1 w1w3; w3 on w2; w2 on w1; 


I have a multilevel analysis in which I have betweenlevel dependent variable that needs to be regressed on a few withinlevel predictor variables, as well as a few betweenlevel predictor variables (all variables are manifest variables). I'm not sure if the MPlus code that I am currently using is correct, so could you possibly give me an example of the setup file that could handle this analysis? 


I think you mean that you want to regress a betweenlevel variable on the between part of a withinlevel variable. This can be done by not putting the variable on the WITHIN list. See Chapter 9 for multilevel examples. 

jan posted on Thursday, March 08, 2007  10:57 am



I'm new to multilevel modeling and maybe my question is simple, but I didn't find the answer, yet. I need to predict an individuallevel variable (selfconcept) by another individuallevel variable (achievement) as well as by the aggregated level of the latter one (class achievement). Doing the following is wrong, of course, because then I'll have a between level selfconcept. %within% self ON achiev; %between% self ON achiev; What I need is something like: self ON indiv_achiev class_achiev So, I'm wondering how to perform this in Mplus. Thank you very much. 


The standard multilevel approach is to say that the influence of classlevel achievement on selfconcept is through the classlevel part of selfconcept (the classlevel part of selfconcept is of course a part of the student's selfconcept score). The classlevel part of selfconcept is the random intercept of students' selfconcept regressed on achievement. In other words, your Mplus setup is correct. 

jan posted on Thursday, March 08, 2007  12:44 pm



Dear Mr. Muthen, thanks for your quick answer. I understand your point, but I don't think that it solves my problem. I want to research the bigfishlittlepondeffect, which supposes that students' individual selfconcept correlates positiv with their individual achievement and negativ with classaverage achievement. Several studies found this effect using HLMModels with classaverage achievement as a level2 predictor and individual achievement as a level1 predictor for students' selfconcept both times on level1, I think (e.g. Lüdtke et al. 2005 in Contemporary Educational Psy; Marsh et al. 2000 in JPSP). I am not dealing with HLM but with Mplus, so I hope to find this effect using Mplus. Maybe I made a big error in reasoning, but I'm still looking for the solution. A misunderstanding in my first message might have been that I talked about aggregated class achievement and not classaverage achievement. I would be very grateful for another idea. 


Let's see if we can understand each other more fully. In the HLM model references you refer to, I would guess that they do what corresponds to the random intercept model in Mplus: %within% self ON achiev; %between% self ON achiev;  except that their betweenlevel covariate is aggregated class achievement rather than the latent variable score that Mplus produces (the difference is probably not large)  and you can do that in Mplus. You can have a positive beta on within and a negative beta on between. But are you saying that you don't find this HLMtype approach sufficient? 

jan posted on Friday, March 09, 2007  3:41 am



I find this HLM approach sufficient. I just wanted to say, that I've no access to the HLMsoftware, but I'd like to find the bflpe (see my prior message) in my data using Mplus. So, what Marsh et al. did is the following: self = b0 + b1*achiev_ind + r (level 1) b0 = g00 + g01*achiev_class + u0 (level 2) b1 = g10 + g11*achiev_class + u1 (level 2) I think this in your short course (day 5) on slide 24 ff. So I tried the following in Mplus: %within% s  self ON achiev; %between% self s ON ach_class; self with s; Doing this, I get following error message: ...PROBLEM INVOLVING VARIABLE SELF. THE RESIDUAL CORRELATION BETWEEN S AND SELF IS 1.001 Am I  aside from the error message  on the right track, now? Should I fix the variance of s with self to 0 (I'm not familiar with fixing variances)? Doing this, I get another error: ... THE VARIANCE OF S APPROACHES 0. FIX THIS VARIANCE AND THE CORRESPONDING COVARIANCES TO 0, DECREASE THE MINIMUM VARIANCE, OR SPECIFY THE VARIABLE AS A WITHIN VARIABLE. 


self with S mean the corelation of intercept of self with slop, do you wanna know this correaltion? for higher corelation between slop and slop, we always center X before run the model, try center X to see what will happen well, since veriance of S approach 0(not statistically significant?), it means the slop is not random among level 2 units, if yes, you should run a random intercept only model if the intercept is random, if level 2 variance of self is also not statistically significant, then, just run an OLS regression. 


I would try a random intercept only model first, so get rid of the random slope. This means using the input %within% self ON achiev; %between% self ON ach_class; 

jan posted on Monday, March 12, 2007  3:13 am



Thanks again, this worked  even though I didn't get different directions for the two beta. 


I'm posting my question here since it's closely related with questions posted on this thread. I have a set of HLM equations that I want to run with Mplus. It's a 3level growth model(time points ?individual ?classroom) Level 1: Yijt = P0ij + P1ij*Time + eijt Level 2: P0ij = B00j + B01j*HRisk + r0ij P1ij = B10j + B11j*HRisk + r 1ij Level 3: B00j = G000 + G001*ECredit + u00j B01j = G010 + G011*ECredit + u01j B10j = G100 + G101*ECredit + u01j B11j = G111 + G111*ECredit + u11j continued on the next post... 


My model statement is as follow: model: %within% iw sw selfc@0 selfc2@1 selfc3@2 selfc4@3; selfc selfc2 selfc3 selfc4 (1); b01 iw on HRisk; b11 sw on HRisk; %between% ib sb selfc@0 selfc2@1 selfc3@2 selfc4@3; ib sb on ECredit; b01 on ECredit; b11 on ECredit; selfc@0 selfc2@0 selfc3@0 selfc4@0; I put the  statements to estimate the crosslevel interactions. I wonder if it's correct code. I looked at the examples in the manual, but it was not clear that I need  statements. Thank you for any help. 


This looks correct. Please keep posts within the size limitation. 

Dan Feaster posted on Wednesday, May 14, 2008  10:18 am



I am trying to estimate a crosslevel interaction with a latent variable score for the X variable at level 2(i.e. my X variable is defined at both within and between): %within% rshas pstmd_1 ON has_1; %between% pstmd_1 rhas ON has_1; rhas=0; Whether I free the random coefficient's variance or not I get errors like: "THE MODEL ESTIMATION DID NOT TERMINATE NORMALLY DUE TO A NONZERO DERIVATIVE OF THE OBSERVEDDATA LOGLIKELIHOOD." OR "THE LOGLIKELIHOOD DECREASED IN THE LAST EM ITERATION." Is this just 1)numerical problem with my data or 2) is this not possible in Mplus, at this time or 3) theoretically not possible (and I need to dig into the algorithm more)? I have no problem if I make this the calculated betweenlevel variable at level 2. 


Given the information that you provide, it sounds like it is something specific to your data and the model. Please send your input, data, output, and license number to support@statmodel.com so we can see the full picture. 

chris lo posted on Tuesday, July 08, 2008  9:23 am



I have repeated measurements over time (e.g., depression scores and pain scores) for a group of individuals. I also have some variables which were measured only once at study entry (e.g., personality trait scores and gender). I am running a multilevel model in which I am predicting the depression scores based on time and pain (level 1 variables). I have also entered the personality trait and gender variables as predictors (level 2 variables). My question concerns the specification of crosslevel interactions. Does a level 1 (repeated) variable have to be set as a random effect before I can enter in an interaction involving it and a level 2 variable? Thank you for any help with this. 


Yes, this is how it is done. See Example 9.2. 

M Hamd posted on Thursday, April 01, 2010  5:06 pm



I am trying to explore crosslevel effects. Here is the case: x leads to y (at level 1) x leads to M which leads to y (at level 2) M also moderates the relation between "x and y" at level 1. Is the following code correct? BETWEEN = M; MODEL: %WITHIN% s  y ON x; %BETWEEN% M on x; s Y ON M; 


Crosslevel interactions are obtained using a random slope model like the one you have specified. See Example 9.2 for further information and Slide 45 of the Topic 7 course handout. 


Hallo, I've question about between level interaction. Suppose I'v got simple multilevel path model with random intercept: WITHIN ARE w x*z; %WITHIN% y on x z x*z; x z on w; where x*z is interaction term. I want to replicate this structure on between level. To have: %BETWEEN% y on x z x*z; the problem is that I could not use XWITH option to specify interaction x*z on between level because x and z are not seeing as latent variables. Should I prepare aggregate variable with is interaction between clusters means of x and z or is it possible to do it in Mplus directly in the model? Best regards Artur 


Do you want a crosslevel interaction of a within variable x with a between variable z or do you want to create an interaction term to use on the between level. 


The second option. I want to create an interaction term to use on the between level. 


Are you going to use observed variables on within and between or are you going to use a latent variable decomposition of the variable. See Example 9.1 for an explanation of these two approaches. 


I try to have latent decomposition of two variables x and z and interactions between those latent parts on between level. 


Do not put x and z on the WITHIN list and use the following for the between part of the MODEL command: $BETWEEN% fx BY x; x@0; fz BY z; z@0; xz  fx XWITH fz; y ON fx fz xz; 


Hello, I am trying to analyze a model with a crosslevel interaction, with a onebetween (BEAT), onewithin (AGG) design. I tried the following code: WITHIN = beat ; BETWEEN = agg; CLUSTER = subj; DEFINE: beat_agg = beat * agg; ANALYSIS: TYPE = TWOLEVEL RANDOM; ALGORITHM = INTEGRATION; MODEL: %WITHIN% s  trusty ON beat ; %BETWEEN% trusty ON agg; s on agg; This gave an error mesage: THE MODEL ESTIMATION DID NOT TERMINATE NORMALLY DUE TO A NONZERO DERIVATIVE OF THE OBSERVEDDATA LOGLIKELIHOOD. I think the solution would be to fix the slope, using s@0. However, this gives the message: SERIOUS PROBLEM IN THE OPTIMIZATION WHEN COMPUTING THE POSTERIOR DISTRIBUTION. CHANGE YOUR MODEL AND/OR STARTING VALUES. Can you give any advice on how to get this model to run? 


Please send the files and your license number to support@statmodel.com. 


Hi, I would like to know how to set up the data for multilevel analysis. I have a unit level construct (team environment) with its measure is referring to the team environment but these survey items are reported by indivduals within the team. So, it is the unit level construct. In my case, I have 200 teams with 45 team members each. I wonder if I should aggregate the data from individual level to the unit level and treat this construct as the variable in the 'between' group command. Please advise. Thanks. 


See the following paper which is available on the website: Lüdtke, O., Marsh, H.W., Robitzsch, A., Trautwein, U., Asparouhov, T., & Muthén, B. (2008). The multilevel latent covariate model: A new, more reliable approach to grouplevel effects in contextual studies. Psychological Methods, 13, 203229. 

Katy Roche posted on Thursday, May 26, 2011  9:25 am



I am trying to test interactions while accounting for clustering (these are NOT crosslevel interactions)...the clustering is only being accounted for in order to obtain correct standard errors. With clustered data and tests of interactions, it is correct to specify: TYPE=COMPLEX and ALBORITHM=INTEGRATION? I am wanting to compare my results from the models accounting for clustering to those that did not  in those models I specified TYPE=RANDOM. 


You need to specify TYPE= COMPLEX RANDOM. This can be used with ALGORITHM=INTEGRATION. 

Katy Roche posted on Thursday, May 26, 2011  11:05 am



Thank you  that did it. One more related question. When I run this same model without the interactions I get the error message that others have posted before (see below) and am curious to know why this would NOT be a problem in the model testing interaction effects. Do you suggest I need to run a Montecarlo for the main effects structural model or am OK to rely on results despite this message? Nothing in results looks very different from teh model that does not account for clustering. THE MODEL ESTIMATION TERMINATED NORMALLY THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES MAY NOT BE TRUSTWORTHY FOR SOME PARAMETERS DUE TO A NONPOSITIVE DEFINITE FIRSTORDER DERIVATIVE PRODUCT MATRIX. THIS MAY BE DUE TO THE STARTINGVALUES BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION. THE CONDITION NUMBER IS 0.234DPROBLEM INVOLVING PARAMETER 33. THIS IS MOST LIKELY DUE TO HAVING MORE PARAMETERS THAN THE NUMBER OF CLUSTERS MINUS THE NUMBER OF STRATA WITH MORE THAN ONE CLUSTER. 

Katy Roche posted on Friday, May 27, 2011  8:42 am



In thinking about the problem I am running into with this error message for the main effects model (not interaction effects model)accouning for clustering, I redid analyses and specificed TYPE = COMPLEX RANDOM; in the main effects model. In that case, I do not get the error message. Of course, I also do not get standardized estimates that I want. So, I guess I am still wondering if I am OK to report coefficients from the main effects model accounting for clustering (TYPE=COMPLEX) despite the error message. 


I think you are, but only a Monte Carlo study could show it clearly. 

kirsten way posted on Friday, October 21, 2011  10:46 pm



Hi, I'm trying to plot my significant cross level interaction using preacher's calculator. I've requested TECH3 in the output to get the coefficient covariances, but wanted to ask  how do I ascertain what variables the parameter numbers in the printout refer to? Thankyou! 


They refer to the parameter numbers in TECH1. 

MT posted on Monday, February 27, 2012  6:18 am



Dear Linda, I am trying to model the following paths: At the withinlevel, I have one predictor (strucjr) and a dependent variable (bevl). This relationship is maybe moderated by a level2 variable (Tafh). At the betweenlevel, I have one predictor (Tstrucjr) and a dependent variable (Tbevl). This relationship may be moderated by a second level2 variable (Tauto). I have the following syntax but am not sure how to model the betweenlevel moderation. Could you please help me with this? CLUSTER IS Team; BETWEEN IS Tafh Taut Tbevl Tstrucjr; WITHIN IS StrucJR; Centering = Grandmean (Tafh Taut); Centering = Groupmean (StrucJR); USEVARIABLES ARE StrucJR Bevl Tafh Taut Tstrucjr Tbevl; ANALYSIS: TYPE = TWOLEVEL RANDOM; ESTIMATOR = ML; ALGORITHM = INTEGRATION; MODEL: %WITHIN% s  Bevl ON StrucJR; %BETWEEN% s Bevl ON Tafh; !crosslevel interaction Tbevl ON Tstrucjr; ! betweenlevel interaction? Thank you so much in advance! 


You can use the DEFINE command to create the betweenlevel interaction terms. 


Hello, I am estimating a multilevel path model and estimate a crosslevel interaction effect. When doing that, I cannot specify the direct effect of the level1 predictor on the dependent any more. In nonSEM Multilevel models that usually is still possible  I would be grateful if you could let me know how I might be able to specify the direct effect of the level1 predictor despite also estimating the crosslevel interaction. The relevant part of the model (there are some paths and covariates at the individual level) reads %Between% I ON A_SocCap; LifeSat ON A_SocCap; %Within% I  LifeSat on DV_U; So essentially my question is whether I can estimate the direct effect of DV_U on LifeSat at level1 still or whether that is not possible in a ML SEM. Thank you very much for your help!! 


Do you mean the direct effect LifeSat on DV_U? You specify this on within as a random effect. The mean and variance of this random effect are found on between. 


Dear Linda, thank you very much  I forget that I get the mean estimated and that it would be that of course. Thanks for your quick help! Best wishes 


Dear Linda, I have specified a crosslevel effect model investigating employee perceptions at the individual level and their impact on the group level performance. The model is: %within% B on A; %between% C on B; D on C; The results are fine but the journal reviewers would like to know if we can identify the impact of A on C and D. Thanks. Pat 


To estimate crosslevel interactions between A with C and C, you need a random slope model. See Example 9.2 in the user's guide. 


Dear Linda, Thanks for the advise on using a random slope to explain the corsslevel interactions. I have questions about the model specification provided in Example 9.1. I would like to know how the grandmean (x) contributes to the analysis. There are both x and xm which already represent x variable in the within and between levels. The other question is I wonder if we can assume that the system refer to random intercept y to represent y in the between part of the model if we use latent variable y in the within level. Thanks. Pat 


Centering x is not necessary. It sometimes helps in interpretation to have a variable with mean zero. y is not on the WITHIN list so y is a random intercept on the between level. 


Dear Linda, I am testing the moderating effects of coping (AVO) between stressor (AS) and outcome (PD). I ran it with following codes. USEVARIABLES ARE SV_ID AS_1 PD_1 AVO_1 AS_AVO; WITHIN are AS_AVO; CLUSTER = SV_ID; ANALYSIS: TYPE = TWOLEVEL random; ALGORITHM=INTEGRATION; ! AVOIDANCE coping MODEL: %WITHIN% PD_1 on AS_1; ! pd=psychologcial distress PD_1 on AVO_1; PD_1 on AS_AVO; %BETWEEN% fx by AS_1; AS_1@0; fz by AVO_1; AVO_1@0 xz  fx XWITH fz; PD_1 on fx fz xz; I received... *** WARNING in MODEL command In the MODEL command, the following variable is a yvariable on the BETWEEN level and an xvariable on the WITHIN level. This variable will be treated as a yvariable on both levels: AS_1 ... as a yvariable on both levels: AVO_1 2 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS THE ESTIMATED BETWEEN COVARIANCE MATRIX COULD NOT BE INVERTED. COMPUTATION COULD NOT BE COMPLETED IN ITERATION 106. CHANGE YOUR MODEL AND/OR STARTING VALUES. THE MODEL ESTIMATION DID NOT TERMINATE NORMALLY DUE TO AN ERROR IN THE COMPUTATION. CHANGE YOUR MODEL AND/OR STARTING VALUES. Could you me any suggestions? 


Please send the output and your license number to support@statmodel.com. 


Dear Linda, I am working on a model with 3 crosslevel interactions predicting 3 withinlevel outcomes, resulting in 6 tested random slopes. I am following example 9.2 of the guide. This example has two alternative options. In the first alternative you specify: y s ON w xm (between level) And in the second alternative you specify: y s ON w x (between level) In my example I am interested to see if the moderator (w) explains the relationship from x to y (specified at the within level). So I can't see why I would include x or xm in this two statements above. Can I skip that completely and simply say the following: y s ON w (between level) ? When I do this, though, I cannot interpret my results. At the within level I can only see residual variances and corelations. If I know the estimate from w to s, don't I also need to know the estimate from x to y at the within level in order to interpret the pattern of my interaction? 


You don't need to include x or xm, but often these "contextual" variables have a significant influence on between. When you have a random slope s and regress it on w (crosslevel interaction) you estimate this regression's intercept, slope, and residual variance. The slope gives the interaction effect. You can think of the intercept as the influence of x on y at w=0. 


Thank you for your reply, Bengt. So if I understand correct the intercept of the slope shows the main effect of x to y (irrespective of w). How can I interpret the pattern of my interaction, though? Do I need to make a plot or can I interpret it directly from my findings? I assume that in order to have a significant interaction the path from w to s needs to be significant. In my example, the intercept of the slope is nonsignificant. If the path from w to s is positive significant, does it mean that x to y becomes positive for high levels of w? Best, Paris 


If you center w, the intercept is the effect of x to y at the w mean. Your sample statistics tell you what the SD of w is, so that you can evaluate the effect of x on y at say 1 SD and +1 SD away from the w mean. Yes, a significant interaction happens when the influence of w on s is significant. The sign and value of the influence of x on y for different values of w is obtained as in my first paragraph. You may also want to study this topiic in multilevel books such as RaudenbushBryk. 


We are trying to examine cross level interactions (i.e., s1 s2 on M032MNRT;) in this multilevel model. We received a ‘fatal error’ that we had a memory shortage due to 5 dimensions of integration needed. We are using an 8 processor. Is there something incorrect with our input statement? Model: %WITHIN% Conct by CO1R CO4R CO6R CO7R CO8R CO12R CO13R CO20R SE1R SE2R; Schl by SE4R SE7R AE1R AE2R AE3R MR1R SV23R; culture by FC1R FC3R FC4R FC8R; S1  Conct on culture; S2  Schl on culture; Conct on Male White; Schl on Male White; CO12R WITH CO7R; SE2R WITH SE1R; SE7R WITH SE4R; CO4R WITH CO1R; AE3R WITH AE1R; MR1R WITH CO4R; CO13R WITH CO6R; AE1R WITH SE7R; CO20R WITH CO4R; %BETWEEN% Conctb by CO1R CO4R CO6R CO7R CO8R CO12R CO13R CO20R SE1R SE2R; Schlb by SE4R SE7R AE1R AE2R AE3R MR1R SV23R; CO1RSE2R@0; SE4RSV23R@0; Conctb on M032Tnrl M032MNRT M032SUSP; Schlb on M032Tnrl M032MNRT M032SUSP; s1 s2 on M032MNRT; 


I assume you have a 64bit computer. With 5 dimensions you have 15^5 = a very high number of integration points. Taken together with a large sample, this causes memory problems. Try integration = montecarlo(5000); 

Ewan Carr posted on Wednesday, June 27, 2012  10:11 am



I have several questions relating to crosslevel interactions in Mplus. I'm using Bayesian estimation. The model is: %WITHIN% s  y ON x; %BETWEEN% x ON w; s ON w; y on x w; (this model also includes a mediating pathway, from x > w > y) [1] How can I interpret the crosslevel interaction effect (i.e. the regression of s on w, where s is the slope and w is the contextual effect)? Bengt's comment on May 16th makes sense, but when I ask for sample statistics I get: > SWMATRIX is available only for TYPE=TWOLEVEL with estimators ULSMV, WLS, WLSM or WLSMV. Request for SWMATRIX will be ignored. [2] Related to [1] is there any way of getting predicted values from Mplus? [3] How can I test the significance of the interaction? (beyond just looking at the pvalue or credible intervals). I'm guessing DIC isn't available with type=twolevel yet? In other words: is there any way of comparing nested models, when "type=twolevel random" and "estimator=bayes"? [4] I've run similar models in R/MLwiN  testing the crosslevel interaction effect the MLM way (i.e. with an interaction term). I get substantially different results, which is slightly worrying. Obviously, these are completely different approaches, but is there any reason to expect such variation? Many thanks, Ewan  


1. Do a Type = twolevel basic run to the sample statistics. Bayes does not use sampstat in its analysis and that's why you don't get that in your run. 2. Not directly. 3. The CI for s on w would seem to be the best way. 4. If the same estimator (ML/Bayes) is used, you should get the same results. If not, send the 2 outputs to Support. 

Ewan Carr posted on Thursday, June 28, 2012  3:00 am



Thank you Bengt, once again, for such a speedy response. It's much appreciated. 

Ewan Carr posted on Thursday, June 28, 2012  6:10 am



A quick followup question: I've rerun the model using "type=twolevel basic", and the following estimation options: type = twolevel basic; estimator = WLS; algorithm = integration; integration = 7; (Bayesian estimation isn't possible). [Question 1]: I've removed the "MODEL:" statement — that is, I'm just estimating an empty model. This is because "type=random" isn't possible with WLS. Is this correct? [Question 2]: I get a file "swmatrix.dat" out. How is this file organised? It just appears as a single column of numbers, with no labels (see here. I've searched the user guide and website for help with this, but can't find anything. I need the SD of the betweenlevel variable (w). Many thanks, Ewan  


Q1. Yes. Q2. SW saving is described on page 668. It is not meant for inspection but rather to be available in a second run so these quantities don't have to be computed again. If you are interested in the within and between sample statistics, you look at the output from a Type=Twolevel Basic run, where you put w on the Between list. 

Ewan Carr posted on Friday, June 29, 2012  4:39 am



Thanks Bengt. I think I've got this sorted. In case this is of use to others, I'll put my working here. The model is: %WITHIN% s  satlife ON empsec; %BETWEEN% s ON rrlongsing; satlife ON rrlongsing; The sample statistics for the contextual variable (rrlongsing) are: The coefficient for the regression of "S ON RRLONGSING" is 0.007, and the intercept for S is 0.195. I then calculate values for the regression at 1 SD above and below the mean of RRLONGSING:
19.68 * 0.007 = 0.138 This gives me the following values:
 rrlongsing  S ON empsec  Mean  1 SD  19.44  0.333  Mean  0.24  0.195  Mean + 1 SD  19.92  0.057  These can be plotted (see here), which seems to make sense. Thanks! 


If you express your computations in Model Constraint using model parameter labels you will both get better precision (more decimals) and SEs for the points in your graph. 


I have come across a reference that suggests that random slopes are not necessarily required to test for (and subsequently find) a significant crosslevel interaction. However, Hox makes no mention of thisnor have I seen any reference to this in searching the mplus forum. In a 2level model, I have systematically tested for variation in level 1 slopes, and nothing is significant. However, when I 'cheated' and tested for crosslevel interactions, several are significant. Is it reasonable to do this based on theory? Thanks. 


What's the reference? 


Multilevel Analysis: An Introduction to Basic and Advanced Multilevel Modeling. T. A. B. Snijders, Roel J. Bosker. (1999) p 96. This comes up in a google search: "multilevel cross level interaction non significant random slopes." AlsoLesa Hoffman's talk: Society of Multivariate Experimental Psychology Annual Meeting October 2011 Systematically Varying Effects in Multilevel Models: Permissible or Problematic? available at: http://psych.unl.edu/hoffman/Sheets/Talks.htm Thanks. 


I see. Yes, this is a phenomenon that also happens in growth modeling where a slope growth factor may not have significant variance when excluding timeinvariant predictors, but including them the effect of them on the slope is significant so the slope does vary. As the book page you mention says, it is a matter of having more power when you include the level 2 covariate and its interaction with the level 1 covariate. So, yes, it is reasonable to do this. 


Thank you Bengt. I also noticed that in Mplus Short Course Lesson 5A (slide 29) the random slopes are correlated with the dv, in what looks like a crosslevel interaction (pasted below). Is this correct? I have seen elsewhere just the crosslevel interaction, without "M92 with s1 s2". Thanks. %WITHIN% s1  m92 ON female; s2  m92 ON stud_ses; %BETWEEN% m92 s1 s2 ON per_adva private catholic mean_ses; m92 WITH s1 s2; 


Yes, this is a crosslevel interaction model because s1, s2 are regressed on betweenlevel covariates. The between level has 3 dependent variables and whenever there are several DVs I would covary their residuals. So, I would even add s1 with s2. But that covariation is a separate issue from crosslevel interaction. 


That makes sense, thanks. Finally, when I run my MLM models (MLF estimator) with cross level interactions, they have significant pvalues. However, testing nesting models using 2LL none of interaction models are significantly better. My understanding is that the 2LL is the better test, but this seems unusual. Can you indeed test nested models with MLF? Also, I'm assuming this is a 2tailed test? Thanks very much. 


Please send the two outputs and your license number to support@statmodel.com. 


Thanks, I realized I needed to zero out the crosslevel effects in the null model. I was incorrectly comparing a general twolevel model to a twolevel random model. 

Ewan Carr posted on Sunday, July 29, 2012  2:53 am



Dear Bengt/Linda, I'm trying to interpret a coefficient in a twolevel path analysis model. The model is:
%WITHIN% s  satlife ON empsec; %BETWEEN% satlife ON uempav grow; empsec ON cons; empsec ON uempav grow; satlife ON empsec; The betweenlevel output is below; the coefficient of interest is highlighted:
SATLIFE ON UEMPAV 0.000 GROW 0.037 EMPSEC 0.810 EMPSEC ON CONS 0.927 UEMPAV 0.000 GROW 0.038 Means S 0.230 My question, then, is what exactly does this coefficient represent? The mean S shows the individuallevel effect of EMPSEC on SATLIFE, but I'm not sure how the betweenlevel effect should be interpreted? Many thanks, Ewan  


Please send the output and your license number to support@statmodel.com. Empsec should not be used on between. It should be on the WITHIN list. I need to see the full situation. 

Ewan Carr posted on Sunday, July 29, 2012  11:55 am



Thanks, I will do. I was following the example of:
Preacher, K. J., Zhang, Z., & Zyphur, M. J. (2011). Alternative methods for assessing mediation in multilevel data: The advantages of multilevel SEM. Structural Equation Modeling, 18, 161 182. The syntax was adapted from: http://www.quantpsy.org/pubs/syntax_appendix_081311.pdf 

Tom Carwell posted on Wednesday, February 06, 2013  11:19 am



Hi, first of all the forum is a great learning platform, thank you for managing it. After reading the relevant posts, I wanted to ask your input on Mplus codes I set up for testing two crosslevel interactions. Model A in which a dichotomous level2 variable (high1, low0) moderates the relationship between two level1 continuous variables: USEVARIABLES ARE x y w; WITHIN = x y; BETWEEN = w; Cluster = id; ANALYSIS: TYPE IS COMPLEX TWOLEVEL random; MODEL: %WITHIN%; beta1  y ON x; %BETWEEN%; beta1 ON w; Model B in which a continuous level2 variable moderates the relationship between a level2 continuous variable and level1 continuous variable USEVARIABLES ARE x y w inter; WITHIN = y; BETWEEN = x w; Cluster = id; DEFINE: inter=x*w ANALYSIS: TYPE IS TWOLEVEL random; MODEL: %WITHIN%; %BETWEEN%; y ON x w inter; 


These look correction. In Model B, be certain the variance of y is estimated as the default. Otherwise add it on within. y; 

Tom Carwell posted on Saturday, February 09, 2013  1:06 am



Hi Linda, thanks for time and suggestion. 

Kätlin Peets posted on Thursday, February 14, 2013  10:25 am



Hi, I am conducting a simple slope analysis (following up a crosslevel interaction). I am interested in associations between my individuallevel predictor and dependent at high and low values of the classroomlevel covariate (when pbur_1 is one standard deviation below and above the mean; or at .032 and at .032). Is this syntax (Model constraint part) correct? %within% s1pder_1 on affemp; %between% s1 ON pbur_1(gam1); [s1] (gam0); s1 with pder_1; MODEL CONSTRAINT: New (ylow yhigh); ylow = (gam0+gam1*(.032)); yhigh = (gam0+gam1*.032); 


I think this is correct as long as pbur_1 is centered with mean zero. 


Hello, I am trying to estimate a multilevel CACE model. We have students nested within schools. The schools were randomly assigned to receive an intervention and some students complied (i.e., attended) the intervention. My CACE model was working fine, but now I am trying to add a crosslevel interaction between the intervention (at level two) and a student characteristic (i.e., Spanish at level one). When I do that using the syntax below, I get the message "Fatal error: Internal code GH1002." Do you have any suggestions? Cluster = sid; Classes = c(2); Training = c1c2; Within = Spanish FRL Latino Other logabs pretest p6 recip shexp1 shexp2 shexp3; Between = FAST D1 D2 D3 B1 S1 S2 Cohort1; Analysis: Type = twolevel random mixture; miterations = 200; Model: %within% %overall% pscale on Spanish FRL Latino Other logabs pretest; c#1 on Spanish FRL Latino Other logabs pretest p6 recip shexp1 shexp2 shexp3; s  pscale on Spanish; %between% %overall% pscale on FAST D1 D2 D3 B1 S1 S2 Cohort1; s on FAST; %c#1% pscale on FAST; %c#2% pscale on FAST@0; 


Please send your output and license number to support@statmodel.com. 


Dear Muthen, We are trying to estimate a model with a level 2 outcome variable (pub) and two crosslevel interactions (gender x motiv & goalcom x restime) We have used the syntax below. DEFINE: CENTER gender goalcom pub (GRANDMEAN); ANALYSIS: TYPE = TWOLEVEL RANDOM; ESTIMATOR = ML; ALGORITHM = INTEGRATION; MODEL: %WITHIN% s1  restime ON motiv; %BETWEEN% s1 ON gender; s2  pub ON restime; s2 ON goalcom; This resulted in the following warning: *** WARNING in MODEL command In the MODEL command, the following variable is an xvariable on the BETWEEN level and a yvariable on the WITHIN level. This variable will be treated as a yvariable on both levels: RESTIME *** ERROR in MODEL command Observed variable on the righthand side of a betweenlevel ON statement for a random slope must be a BETWEEN variable. Problem with: RESTIME Is there a way to model this model? Thank you 


The two random regressions should be on the within level not the between level. Why do you have s2  pub ON restime; on between? 


Dear Linda, Thank you for your response. pub is a between level outcome, that's why we defined it on the between level. Gender and goalcom are also on the between level. 


T think what you want is: WITHIN = RESTIME; BETWEEN = gender clusrest goalcom inter; MODEL: %WITHIN% s1  restime ON motiv; %BETWEEN% s1 ON gender; pub ON clusrest goalcom inter; where clusrest is a cluster level observed variable that you create in DEFINE along with the interaction between that variable and goalcom (inter). 


Thank you for your response. I've made the adjustments, but I still get an error. My input looks like this: WITHIN = motiv restime; BETWEEN = gender clusrest goalcom pub inter; CLUSTER = employee; MISSING ARE ALL (999); DEFINE: CENTER gender goalcom pub (GRANDMEAN); ANALYSIS: TYPE = TWOLEVEL RANDOM; ESTIMATOR = ML; ALGORITHM = INTEGRATION; MODEL: %WITHIN% s1  restime ON motiv; %BETWEEN% s1 ON gender; pub ON clusrest inter; And this is the error I get: *** WARNING in MODEL command Variable on the lefthand side of an ON statement in a  statement is a WITHIN variable. The intercept for this variable is not random. Variable: RESTIME *** ERROR One or more betweenlevel variables have variation within a cluster for one or more clusters. Check your data and format statement. Between Cluster ID with variation in this variable Variable (only one cluster ID will be listed) INTER 1 


I think it should be WITHIN = motiv; not restme The inter variable should be the same for each cluster member. All variables on the between list need to be the same for each cluster member. Check you data. 


Thank you for your response. I've checked my data and tried different things. Now I get this error: One or more variables in the data set have no nonmissing values. Check your data and format statement. Continuous Number of Variable Observations Variance PUB 200 19.296 DAY 200 2.010 RESTIME 200 6.476 MOTIV 200 1.241 GENDER 200 0.241 GOALCOM 200 0.498 CLUSREST 200 3.764 **INTER 0 This is what my define statement looks like: DEFINE: clusrest = CLUSTER_MEAN (restime); CENTER gender clusrest goalcom pub inter (GRANDMEAN); inter = goalcom * clusrest; Thank you in advance. 


Please send your input, data, output, and license number to support@statmodel.com. 


Hello, I would like to estimate a twolevel CACE model with a crosslevel interaction between the treatment and a covariate. Since the treatment effect is fixed at zero for noncompliers, I think the crosslevel interaction should also be fixed at zero for noncompliers. I thought the code would be something like this: Model: %within% %overall% pscale on EngLat Other FRL; c#1 on EngLat SpanLat Other FRL pretest p6 recip shexp1 shexp2 shexp3; s  pscale on SpanLat; %between% %overall% pscale on FAST D1 D2 D3 B1 S1 S2 Cohort1; s on FAST; %c#1% pscale on FAST; s on FAST; %c#2% pscale on FAST@0; s on FAST@0; However, I am getting this error command: "*** ERROR in MODEL command Parameters involving betweenlevel variables are not allowed to vary across classes." The model runs fine when I do not include the "s on FAST" commands separately for each compliance class, but then the results show a significant interaction between the treatment and the covariate for noncompliers. Thanks in advance. 


Please send the full output and your license number to support@statmodel.com. 

Dave posted on Thursday, May 16, 2013  9:45 am



I have encountered a situation similar to the one described by Kathryn Modecki posted on Monday, July 23, 2012  12:32 am. I am comparing the following models: %WITHIN% s1  DV on IV; %BETWEEN% DV ON Con1 Con2; S1 ON Mod1 Mod2 Int@0 Con1 Con2; DV with s1; MODEL FIT INFORMATION Free Parameters: 12 Loglikelihood H0 Value  0.154 H0 Scaling Correction Factor  1.5249 And %WITHIN% s1  DV on IV; %BETWEEN% DV ON Con1 Con2; S1 ON Mod1 Mod2 Int Con1 Con2; DV with s1; MODEL FIT INFORMATION Free Parameters: 13 Loglikelihood H0 Value  1.446 H0 Scaling Correction Factor  1.4745 Int is an interaction term created by multiplying Mod1 and Mod2 to create a three way cross level interaction. I believe these models are nested. Int has a significant p value (p = 0.033). When testing these two nested models using 2LL the model with the interaction is not significantly better (chi_sq = 3.66 vs 3.84; p = 0.055). I am wondering if you can provide me with guidance regarding how to interpret this finding. Thanks in advance for your attention. 


It sounds like you are comparing an approximate ztest (which when squared is approx. chi2 with 1 df) pvalue of 0.033 with an approximate chi2 test with 1 df with a pvalue of 0.055. Such a small pvalue difference can be expected, particularly in samples that are not large, in this case the number of clusters. You have two methods giving asymptotic approximations to chi2 and for any given sample size they can differ. 


Hi Linda: I ran a multilevel model to test some crosslevel interactions. Now, I am interested in plotting those effects using Preacher's website. I was not very sure if I was inputting the right numbers in the table. I would greatly appreciate if you could confirm where I should look for the numbers Regression Coefficients (gamma for Intercept, gamma for IV, Gamma for Moderator and gamma for Interaction effect)? Coefficient Variances? Coefficient Covariances? Conditional Values for w and x (if I want to model +1SD, mean,1SD values of the moderator)? df (int)? df (slope)? Here is the link to Preacher’s website and I am referring to case 3: http://www.quantpsy.org/interact/hlm2.htm Your help in this matter would be greatly appreciated! Thanks! 


The values you need are found in TECH3. Contact Kris Preacher is you have question about his link. You can also see Example 3.18 in the user's guide which uses the LOOP option. This can be applied to crosslevel interactions. 


Hi Linda: Thanks a ton for your response. I am sorry for the tardy reply. I was under the impression that I will get an email notification once you respond to my query, which obviously I did not get. Anyway, I greatly appreciate the help. Thanks again, Praneet 


Responses are given on Mplus Discussion not via email. 

Sara Guediri posted on Monday, September 09, 2013  10:35 am



Hi, I'm testing a crosslevel interaction and depending on whether I grand mean centre the Level 2 moderator or not, I get different results for the intercept of the random slope. This affects the direction of the crosslevel interaction. Should I go with the results when the level 2 moderator is grandmean centred or leave the level 2 variable at its raw score? Many thanks 


You should grand mean center. See the Raudenbush and Bryk book for further information. 


As a follow up to the previously posted question and answer: " kirsten way posted on Friday, October 21, 2011  10:46 pm Hi, I'm trying to plot my significant cross level interaction using preacher's calculator. I've requested TECH3 in the output to get the coefficient covariances, but wanted to ask  how do I ascertain what variables the parameter numbers in the printout refer to? Thankyou! Linda K. Muthen posted on Saturday, October 22, 2011  6:29 am They refer to the parameter numbers in TECH1." Since I have 10 parameters and TECH3 reports 11 in the covariance matrix, should I be looking at the number labels assigned under Beta in TECH1? I thought it odd that the numbering goes 0,2,3,4... and just want to be sure I am looking at the correct number labels. THANK YOU! Johnna 


Please send your output to Support so we can see what you are referring to. Note also that you no longer need to use the Preacher calculator to plot crosslevel interactions because Mplus offers the LOOP and PLOT options of MODEL CONSTRAINT. See slides 2124 of the Utrecht training August 2012: http://mplus.fss.uu.nl/files/2012/09 V7Part1.pdf 


Bengt  Thank you. I just sent my output. I could not find the slides or presentation you suggested. It says file not found. Would you mind checking the link and resending? I'd appreciate it. Regards, Johnna 


Perhaps you didn't get both lines of the link? http://mplus.fss.uu.nl/files/2012/09 V7Part1.pdf 


Dear Bengt & Linda, Below is a crosslevel interaction I am testing in a multilevel latent SEM model: Within = x1 x2 x3; Between = m1 m2 m3 w1 w2 w3; ANALYSIS: Type is random twolevel; ESTIMATOR = ML; ALGORITHM=INTEGRATION; MODEL: %WITHIN% F1 by y1 y2 y3; F2 by x1 x2 x3; s  F1 ON F2; %BETWEEN% F3 by m1 m2 m3; F4 by w1 w2 w3; s ON F3; F1 ON F4; The above model works but only without the very last statement "F1 ON F4" because F1 has been defined as withinlevel. I need this statement to control for the effect of a betweenlevel variable to a withinlevel variable. In path analysis I am able to work around this problem but not in a latent model. What could I do? Thanks! Paris 


You must create a factor on between that uses the between part of y1, y2, and y3. MODEL: %WITHIN% wF1 by y1 y2 y3; F2 by x1 x2 x3; s  F1 ON F2; %BETWEEN% bF1 by y1 y2 y3; F3 by m1 m2 m3; F4 by w1 w2 w3; s ON F3; bF1 ON F4; 


Dear Linda, Thank you! I am wondering if the statement "s  F1 ON F2" is a full test of moderation. Normally in moderation you also need the main effect of the moderator on the outcome, e.g., "bF1 ON F3". Should I include this statement or is it accounted for by the statement "s  F1 ON F2"? Also, how do I plot this interaction? 


s  F1 ON F2 defines a random slope. I'm not sure how you see this as moderation. 

Ewan Carr posted on Monday, March 03, 2014  1:44 pm



Dear Bengt/Linda, I'm following up on a question from two years ago. I have a multilevel path model, with a crosslevel interaction (implemented as a random slope). Mplus doesn't currently offer overall model fit statistics for multilevel SEM models (e.g. DIC). To test the significance of the crosslevel interaction, I asked:
quote:How can I test the significance of the interaction? (beyond just looking at the pvalue or credible intervals)
The response I got was:
quote:3. The CI for s on w would seem to be the best way. (Bengt, 20120627 2054)
Is there any reference/citation you could suggest that would either support this decision, or where a similar approach is taken? (A reviewer is asking for a measure of overall model fit; I'm trying to argue that this approach  of looking at the credible intervals  is adequate). Many thanks, Ewan  


In this situation, no absolute fit statistics are available. There is not a single covariance matrix because the variance of y varies as a function of x. This is not something specific to Mplus. The confidence interval gives the same result as a one degree of freedom chisquare difference test between a model without the interaction term and a model with the interaction term. 

Ewan Carr posted on Saturday, March 08, 2014  10:46 am



Many thanks, that is most useful. Ewan 


Dear Bengt & Linda, I am attempting to write syntax for a multilevel structural equation model with several crosslevel interactions. The relationship of interest is between 7 indicators for race/gender (e.g., White Female, Black Male, Black Female, etc) and a continuous latent variable. This relationship is defined by partially mediated moderation by grouplevel variables where B1 moderates these relationships and B2 partially mediates this moderation. Given that I would need 7 random slopes to specify the crosslevel interactions as typically defined in Mplus (and that from my understanding, modeling several random slopes can get quite hairy), I would like to estimate this model with a random intercept only (and no random slopes). Can I create cross products between my 7 indicators and B1 for use in such a model instead of utilizing random slopes? Thank you for any help! Briana 


Yes. 

C G posted on Tuesday, September 16, 2014  1:20 pm



Dear Dr. Muthen I am using Mplus to do multilevel path analyses. I want to test the interaction results from a cross level prediction of a level 1 random effect by a level 2 covariate. When I interpret and plot the results, I am not sure which mean score to use as there are two sorts of mean scores, one at the within level and another at the between level. Any help will be highly appreciated. Thank you very much. 


Have a look at the crosslevel interaction plot information at http://www.statmodel.com/Mediation.shtml 

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