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I have a "3level" Growth Model (2 level in MPLUS I believe) with time points nested in individuals and individuals nested in organizations. The DVs are manifest, and I am running separate models for each DV. To achieve convergence and a positive definite solution, I have to constrain the random variances associated with intercept and slope (on the individual and/or organization level) to zero in different case. I also have time varying covariates and have to sometimes set their random effects to zero in different cases on different levels to converge and/or get a positve definite solution. In a perfect situation, of course, I would like to estimate the random effect for everything (intercept, slope, and time varying covariates) in every case on every level. My question  is it permissible to "explain variance" using a covariate on a random effect that has been constrained to zero? It seems counterintuitive that it would be, but I have at least one statbook type reference where it seems that this is done, and I have until recently assumed it was appropriate. For example if my random slope variance has been constrained to zero, can I still do a Slope x Covariate interaction to test for slope differences? Any help would be appreciated. Thanks. 


In a conditional model, it is the residual variance of a random slope or growth factor that is fixed to zero not the variance. It is fine to regress such a random effect on a covariate. Also, when covariates are added to the model, it can make random effects have nonzero variances whereas without covariates they have zero variances. 


Hi, There is discussion that the general way of specifying the effects of timeinvariant covariates might be too restrictive i.e. this ”mediated model” specification assumes that all of the effects of the timeinvariant variables are captured by their impact on the growth parameters. Whereas it might be the case that these covariates directly affect the outcome variables. Moreover, the literature states that a model that includes both the direct and mediated effects of a timeconstant variable is not identified. But Stoel et al. 2004 (SEM) have shown that the mediated model is nested within the direct model such that a LR chisquare test can be used to determine whether the direct model is warranted. This said, I am a bit uncertain as to the syntax for this “direct effect” model i.e. which restrictions to apply. Would it be like this? I S  Y1@0 Y2@1 Y3@2; I on A1 A2 A3 @0; S on A1 A2 A3 @0; Y1 on A1; Y2 on A2; Y3 on A3; And, then the nested “mediated” (or standard spec’ed) model like this: I S  Y1@0 Y2@1 Y3@2; I on A1 A2 A3; S on A1 A2 A3; Y1 on A1@0; Y2 on A2@0; Y3 on A3@0; Kind thanks in advance 


A model with both the indirect and all direct effects is not identified. One approach is to include the direct effects for one outcome at a time (regressed on all covariates) and see which are significant. 


Tx Bengt  yes I understand that a model where both the indirect and direct paths are unconstrained won't identify however when I constrain either the direct or indirect paths and run these models separately (as per the annotation below) identification is respectively possible for each of these models. I just want to double check I have the syntax/specification right such that I can go with the nested LL_diff test as per Stoel et al 2004 (SEM). Any further thoughts on this would be greatly appreciated? I S  Y1@0 Y2@1 Y3@2; I on A1 A2 A3 @0;! time constant mediated effects constrained to zero S on A1 A2 A3 @0; Y1 on A1; Y2 on A2; Y3 on A3; And, then the nested “mediated” (or standard spec’ed) model like this: I S  Y1@0 Y2@1 Y3@2; I on A1 A2 A3; S on A1 A2 A3; Y1 on A1@0; ! direct effects constrained to zeros for time constant effects Y2 on A2@0; Y3 on A3@0; 


I don't know about the Stoel article. For your first model, perhaps you want instead the 9 parameters y1 on a1a3; y2 on a1a3; y3 on a1a3; Otherwise, the second model with its 6 ON parameters isn't nested within the first model. 

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