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I have a "3-level" 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 counter-intuitive that it would be, but I have at least one stat-book 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. |
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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 non-zero variances whereas without covariates they have zero variances. |
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Hi, There is discussion that the general way of specifying the effects of time-invariant covariates might be too restrictive i.e. this ”mediated model” specification assumes that all of the effects of the time-invariant 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 time-constant 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 chi-square 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 |
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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. |
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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; |
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I don't know about the Stoel article. For your first model, perhaps you want instead the 9 parameters y1 on a1-a3; y2 on a1-a3; y3 on a1-a3; Otherwise, the second model with its 6 ON parameters isn't nested within the first model. |
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Hi I have a follow up question the original question and answer on this post. I am running a conditional growth model with the quadratic growth variance constrained to zero: i s q | var1@0 var2@2 var3@3 var4@4 var5@5; q@0; q ON predictor1; output: stdyx; In the above example there are no stdyx results for the quadratic. However when I add a second predictor there are stdyx results for the quadratic. i s q | var1@0 var2@2 var3@3 var4@4 var5@5; q@0; q ON predictor1 predictor2; output: stdyx; Why are there stdyx results in the second model, but not the first? Thanks |
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We need to see the output of both runs - send to Support along with your license number. |
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