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Student 09 posted on Monday, January 16, 2012  10:33 am



Hi using the multiple group analysis in Mplus, I would like to test whether an indirect effect differs between two subsamples (group a & group b). For each group, I requested the indirect effect by using the model constraint command. MODEL: y2 ON y1 (p1a); y1 ON x (p2a); MODEL CONSTRAINT: NEW (ind_1); Ind_1 = p1a*p2a; MODEL group b: y2 ON y1 (p1b); y1 ON x (p2b); MODEL CONSTRAINT: NEW (ind_2); Ind_2 = p1b*p2b; This syntax yields the two indirect effects (ind_1 & ind_2). But now I wonder how to test their difference – how would I constrain these parameters to be equal, given that they come from two different groups? 


You should use a Model Constraint where you define their difference  this will give you the test as a z score: MODEL CONSTRAINT: NEW (ind_1 ind_2 diff); ind_1 = p1a*p2a; ind_2 = p1b*p2b; diff = ind_1ind_2; 


Hello, Can I run a moderated mediation analysis as a twogroup model, employing the MODEL INDIRECT command? In other words, can MODEL INDIRECT be used in conjunction with a grouping variable, allowing for tests of moderated mediation? Thanks! 


You can run moderated mediation using multiple group analysis but you can't use MODEL INDIRECT. You will need to use MODEL CONSTRAINT to compare indirect effects across groups. MODEL INDIRECT does not have this function. 


How do I test whether multiple indirect effects differ between 2 groups? The model includes paths from 2 Xs (ext2, stigma2) through a single mediator (ai_t) to 2 DV's (VDATE, PDATE). I used the model constraint language as per Bengt's response above to create the 4indirect diffs... MODEL CHILD: ai_t on ext_pt2 (a1a); ai_t on STIGMA2 (a2a); PDATE on ai_t (b1a); VDATE on ai_t (b2a); MODEL ADOLESCENT: ai_t on ext_pt2 (a1b); ai_t on STIGMA2 (a2b); PDATE on ai_t (b1b); VDATE on ai_t (b2b); MODEL CONSTRAINT: NEW (ind_1 ind_2 diff); ind_1 = a1a*b1a; ind_2 = a1b*b1b; diff = ind_1ind_2; NEW (ind_3 ind_4 diff); ind_3 = a2a*b1a; ind_4= a2b*b1b; diff = ind_3ind_4; NEW (ind_5 ind_6 diff); ind_5 = a1a*b2a; ind_6 = a1b*b2b; diff = ind_5ind_6; NEW (ind_7 ind_8 diff); ind_7 = a2a*b2a; ind_8 = a2b*b2b; diff = ind_7ind_8; Mplus will run a single constraint test but when I include more than one I get an error message saying that I've entered an already used parameter. Although true, each indirect is comprised of unique pairs of parameters. Is there a way to simultaneous test differences in the 4 indirect effects? 


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


Hello, In using the MODEL CONSTRAINT option to define new parameters for one's model, does this increase the number of parameters estimated and hence affect degrees of freedom? A fiveknownclass model in which I used MODEL CONSTRAINT to define an a*b indirect path (to test for mediation) had different degrees of freedom than I expected, and I wondered if this is because I added parameters to the model through using this command? Thanks! 


If you put a constraint on a parameter in MODEL CONSTRAINT, this can affect the degrees of freedom. If you define a new parameter, this should not. 


Thanks, Linda. Can I label parameters that are classspecific estimates in a knownclass model, then use those classspecific labels to constrain parameters within classes? For examplewould this work? !Whites %cg#1% [gender] (gen_m_w); gender (gen_v_w); !Chinese() !%cg#2% [gender] (gen_m_cn); gender (gen_v_cn); !MODEL CONSTRAINT: gen_v_w = gen_m_w*(1gen_m_w); gen_v_cn = gen_m_cn*(1gen_m_cn); 


Yes, you can label classspecific parameters. 


Hi Dr. Muthen, Similar to Student09 in Jan 2012 of this thread, I am interested in testing whether an indirect effect differs between two groups. On Jan 16 2012, you wrote: You should use a Model Constraint where you define their difference  this will give you the test as a z score: MODEL CONSTRAINT: NEW (ind_1 ind_2 diff); ind_1 = p1a*p2a; ind_2 = p1b*p2b; diff = ind_1ind_2; I ran my model with this syntax, but I want to be sure that I am looking in the right place in the output and interpreting correctly. My understanding is that I should be looking at the third and fourth columns of the model results section, under "New/additional parameters." This section of my output looks like this: New/Additional Parameters INDIRECT 0.003 0.024 0.144 0.885 INDIRECT 0.001 0.065 0.010 0.992 DIFF 0.003 0.069 0.039 0.969 My understanding is that for DIFF, Est./S.E = 0.039 and p = .969, meaning that the population means are equal across groups. This would mean that the indirect effect is not moderated by the variable I used to group (weight status). Am I interpreting this correctly? Thank you! 


That's correct. One cannot reject that the two indirect effects are equal. 


Thank you for your response. As a follow up question related to my model, I found partial measurement invariance across gender in my initial invariance testing (at the weak level). Once freeing one parcel loading on my independent latent variable, the chi sq diff tests held for weak and strong invariance. My understanding is that I would need to free this loading across gender groups in my structural model. However, I am already specifying two groups for my moderated mediation analyses. Can I also specify two separate groups by gender to account for that partial measurement invariance? If so, what would that syntax look like? And how would that change my interpretation of model fit and the diff score created to determine moderation? Thank you! 


Sounds like you would then have 4 groups (2 x 2). In which case you can e.g. specify genderinvariance of the slopes involved in the moderated mediation. Just label the parameters according to the equalities you want to specify. 


Is there a way to determine probability of finding group differences in a multiple group analysis, posthoc? I ran a moderated mediation model using a multiple group analysis and did not find significant moderation. This may be because one group only had 29 participants in it, compared to 95 in the other. I am wondering if I can determine the probability of detecting group differences, given the numbers that I had? Thank you! 


You can do a Monte Carlo simulation  see the UG chapter 12. This would give you an idea of the power to reject equality. 

Shiny posted on Tuesday, August 26, 2014  1:48 pm



I d like to follow up with this discussion. I understand that when difference test Shows insignificant p value, it means the indirect effects are equal. Is the difference test in mplus a heterogenity test in its nature? I checked some statistical mateirals. Some researchers used a relatively subjective approach, comparing the Mediation sizes (the coefficients) or simply look at whether the indirect effects are full v.s parital v.s non effects in different groups. They sometimes skipped the difference test. or they consider the Group difference existed (e.g., when full Mediation in one Group and partial in another), although in the difference test result p is not significant. I would love to get a comment from Dr. Muthen. 


Q1. I don't know what a heterogeneity test is in this context. I think it is good to carry out a test. 

ri ri posted on Saturday, September 06, 2014  6:24 am



To compare two indirect effects, I ran the difference test. In one Group I have a Mediation effect, in the other Group, there is no Mediation effect. However, difference test showed no difference, because p>.05. I wonder how could that be? New/Additional Parameters ind1 0.657 0.311 2.113 0.035 ind2 0.567 0.397 1.427 0.153 diff 0.090 0.505 0.179 0.858 I guess the difference of the Parameters is small (.090), thus it gives a big p value? Can I Report the indirect effects differ across groups? Does it only make sense, to conduct a difference test when indirect effects exist in both Groups? Maybe in my case, when in one Group there is no indrect effect, I do not Need a difference test? 


I think it is natural that if ind2 is not significantly different from zero, the ind2ind1 difference is not significantly different from zero  the latter distance is smaller. I would report all 3 findings. 

ri ri posted on Saturday, September 06, 2014  5:05 pm



Thank you for your answer! I will Report all the findings as you suggested. But can I still say, there is a moderated Mediation because the Mediation effects are not the same in two Groups. may I ask the statistical Background of the ind1  ind2? I think I read somewhere this is a z score test?I would like to also indicate in my paper what the difference test means in mplus. Thanks! 


If ind1 and ind2 are not significantly different you can't say that you have moderated mediation. The estimate/SE for "diff" is a Zscore. 

ri ri posted on Friday, September 19, 2014  4:10 pm



Thank you for the helpful Information. I am now summarizing the Analysis and Tools in my paper and want to add one sentence about difference test provided by mplus. can I say: we used a zscore difference test in Mplus to test whether indirect effects vary across Groups. Or is there a more precise term to describe this difference test? It is good to get your expert view! Thanks! 


It looks like you used MODEL CONSTRAINT to test the difference. The test of the difference is a zscore. There is nothing more to say. 

Meike Slagt posted on Thursday, May 07, 2015  12:30 pm



Dear dr. Muthén, I’m testing a moderated mediation model in which the association between an independent variable IV and a dependent variable DV is mediated by Med, and paths a and c are moderated by Mod. The moderation effect is represented by a product term (Int = IV*Mod). We used the following syntax: MODEL: DV on IV Mod Int; DV on Med (b1); Med on IV (a1); Med on Mod; Med on Int (a3); MODEL CONSTRAINT: new (indlow indmed indhigh indirect difind); !indirect effect at low, medium, and high value of moderator (moderator is centered) indlow=(a1+a3*0.5)*b1; indmed=(a1+a3*0)*b1; !also represents indirect effect regardless of moderation indhigh=(a1+a3*0.5)*b1; !total indirect effect indirect =(a1+a3)*b1; !difference between total indirect effect and indirect effect regardless of moderation difind = indirect  indmed; However, I get two error messages: *** ERROR (A1+A3*0.5) *B1 ^ERROR *** ERROR in MODEL CONSTRAINT command A parameter label has been redeclared in MODEL CONSTRAINT. Problem with: INDMED So there seems to be a problem with the way I define new variables in the MODEL CONSTRAINT command. What am I specifying wrongly here? Thank you for your help! 


Try changing indlow=(a1+a3*0.5)*b1; to indlow=(a1+a3*(0.5))*b1; 


Thank you, that get's rid of the first warning. The second warning still remains, however: *** ERROR in MODEL CONSTRAINT command. A parameter label has been redeclared in MODEL CONSTRAINT. Problem with: INDMED If I remove all the syntax pertaining to INDMED, the warning persists, but then starts blaming another new variable, INDIRECT. 


Then we need to see the output  send to support along with license number. 

ri ri posted on Monday, May 11, 2015  2:50 pm



I did a difftest using MODEL CONSTRAINT.Is there a Name for the estimate coefficient? Here is an example of my result: DIFF2 0.117 0.548 0.214 0.830 I want to Report what .0117 represents for. I understand the difftest is a zscore test, but is it possible to get a z value in difftest? Thanks! 


The DIFF2 parameter is what you specified in MODEL CONSTRAINT. The third column is the ztest. 

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