Hello, I have 2 questions regarding correlating variables in multilevel models.
1) In addition to having 2 latent variables at level 1, I have a measured predictor variable (no error). I was wondering why, at the second level, this measured variable (which becomes latent at level 2) is not correlated to the other latent exogenous variables by default? I tried correlating it through syntax, but it made the model fit considerably worse.
2) If I want to make a variable at level 1 only correlate with the error terms of the other variables at that level, how would that be stated in Mplus sytax? In the manual, I could only figure out how to correlate variables themselves, not a variable with error terms of other variables.
Please send your questions along with output that you can point to along with your license number to firstname.lastname@example.org. I am not sure exactly what you are asking. Please be specific in your questions referring the the parameters in question by name.
I am using a multilevel growth curve modeling to examine whether any of my covariates explain variance in the growth factors at the within and between level. Why would the model fit (chi-square value) change when I explicitly specify (WITH command) the correlations/covariances among the predictors?
Means, variances, and covariances of observed exogenous variables, covariates, are not part of a regression model. When you mention these variables using WITH statements, they are treated as dependent variables in the model. Distributional assumptions are made about them and their means, variances, and covariances are estimated.
Thank you for your answer. I am not sure whether I really understand though. Does it mean that if I don't use WITH statements, exogeneous variables are considered to be orthogonal to each other?
What also confuses me is that when I am running a simple path model (not a multilevel model) where I use WITH statements (to specify correlations among the exogeneous variables) vs. when I don't include WITH statements, the chi-square value stays the same.
No, it does not mean that the covariances are zero. You can think about it as though the covariances are fixed at the sample values.
When TYPE=GENERAL is used with continuous outcomes, it just so happens that whether observed exogenous variables are treated as independent variables in the model or dependent variables in the model, the results are the same. This is not the case in other situations like multilevel modeling.
So, I have not used WITH commands to specify covariances among exogeneous variables in my multilevel model. However, if I want to present covariances and correlations of these variables, will I use the estimates from the output (using sampstat command)? And, how do I get the significance values for those?
For correlations among exogenous factors you can look at the STD solutions. A general approach is to express correlations using the model parameters by giving the model parameters labels that are then referred to in Model Constraint. For guidance, see UG ex 5.20.
Anabel posted on Monday, February 07, 2011 - 9:48 am
thanks a lot for your response.
But I think I have to follow up on my question. I need the significances for the correlations among the endogonous and exogonous factors and the manifest variables respectively for my SEM models.
I don´t really understand how to calculate those through the model constraint. Could you please give an example?
With an SEM, why don't you focus on the structural parameter estimates (perhaps in standardized form) that the model specifies rather than the factor correlations? If you want the factor correlations, why not formulate a CFA model? Those estimates and their significance should be close to the SEM if the model fits well.
I would like to know why it is so that when I am estimating correlations between many variables simultaneously (x with y z b), I get different estimates compared to when I only estimate a correlation between two variables (x with y)? In both instances, I should be estimating bivariate correlations (and there are no missing data).
Please send your output to support so we know what your situation is.
Eric Deemer posted on Sunday, September 29, 2013 - 5:18 pm
I'm fitting a multilevel mediation model with just 3 variables--X, M, and Y. M has variation on both levels. I want to estimate the between-level correlations but I know that Mplus doesn't provide SEs with correlation output. I was thinking of separately regressing Y on M and M on X since these regression coefficients would be the same as correlation coefficients. Would this be true in the ML framework?
Eric Deemer posted on Sunday, September 29, 2013 - 6:35 pm
We are examining the validity of therapist scores from a new measure; many therapists rate more than one client. ICCs for the therapist scores range from .21 to .34, and are lower for other variables. We wish to model correlations at the client (within) level to examine construct validity.
We used (TID = therapist id): Cluster = tid; Analysis: Type = twolevel; Model: %within% X with Y; output: standardized;
We could also use type=complex to examine the same issue. I have run a few correlations with both approaches, and the results differ more than I thought they would (e.g., r=.25 vs. .32). Why would the correlations differ so much? With a very simple analysis such as this, what should we consider in choosing one approach over the other?