Jan Brenner posted on Tuesday, October 11, 2005 - 1:51 am
I have estimated a rather large MIMIC model and now want to check whether two parameter estimates are significantly different from each other. Hence, I need the covariance estimate of the two variables. From TECH1 I got the numbers of my parameters and using TECH3 I saved the variance-covariance matrix of all parameters. When I look at it though I have five columns of values but can't really find the value I am looking for. Could you please tell me in which order the variance-covariance matrix is saved.
They are saved in the order the parameters are numbered in TECH1. So it is a covariance matrix of parameters 1-10 by 1-10 for example. It may be easier to ask for TECH3 in the OUTPUT command. Then it is printed in the output and labelled.
thanks for your advice. I am back on this issue now and I am concerned that the covariances in the TECH3 output are not precise enough since they round rather early. So basically I am back at my original question. Maybe I give an illustration of how I thought it is done but what does not seem to work out. The TECH3 output looks e.g. as follows:
x1 x2 x3 x4 x5 x6 x7 x8 x9 x10
The saved file (which contains much more precise values) then consists of two rows with five columns. Are they ordered like this?
x1 x2 x3 x4 x5 x6 x7 x8 x9 x10
My problem really is that the parameters I am interested in are numbers 38 to 56 of a couple of hundreds and it does not seem to work out the way I have described above. Any assistance would be great! Thanks in advance!
For Q2, instead of having a number for each parameter, I would have a single number that seemed to indicate the covariance/correlation between two parameters, for instance, I would have number 79 that corresponded to the covariance/correlation for the slope and the interaction term. I am not sure how I should find number 79 in TECH3.
Tech1 gives the number for each parameter. Tech3 gives the variance of each parameter on its diagonal and gives the covariance between two parameters in its off-diagonal entries. The rows and columns of Tech3 are numbered according to the numbers in Tech1.
So when you talk about covariance between two parameters you find that among the off-diagonal entries of Tech3. You won't find that in Tech1. But if you talk about a parameter that is a covariance, you find its number in Tech 1 and then its variance and covariance with other parameters in Tech3. Hope that helps.
I'm doing a path analysis (no latent variables included) and I'm having problems interpreting the outputs of TECH1 and TECH3. I would be interested to compare observed correlations of variables included in the model (OUTPUT SAMPSTAT) with the model-implied correlations (TECH3), but I'm not sure what parameters (ALPHA, BETA?) I should be looking at in TECH1 to find the model-implied correlations? Moreover, is it possible to calculate confidence intervals for these correlations in Mplus?
Thanks a lot! I'm however unsure whether this option gives estimated covariances or correlations (because it is labelled "Model Estimated Covariances/Correlations/Residual Correlations")? Although I'm not sure which one I should be using, because prior to analysis I have already mean-standaridized my independent variables. Any comment on that?
One more question: is it possible to calculate confidence intervals for noncausal effects as it for total effects?
What is given depends on the scale of the dependent variables. With continuous variables, covariances are given because these are the sample statistics used in model estimation. With categorical variables and models with no covariates, correlations are given for the same reason. With categorical variables and models with covariates, residual correlations are given for the same reason.
A confidence interval can be computed for any parameter. I'm not sure what you mean.
I was referring to decomposing the model-implied covariances/correlations. MPlus output gives me confidence interval for total effects, but I would like to also know confidence intervals for noncausal (spurious) effects and model-implied covariance/correlations. How these can be calculated in MPlus?
Sorry about my delayed reply. As noncausal effects (unanalysed associations), I'm talking about any backward connections between the variables due to shared causes and/or correlated effects. These are not printed in Mplus, but could be calculated by subtracting total effects from model-implied covariances/correlations. I'm wondering is there any way to calculate confidence intervls etc. for these noncausal effects e.g. by using MODEL CONSTRAINT-command?
You need to label the parameters in the MODEL command and then specify the effects you are interested in using MODEL CONSTRAINT. The user's guide has examples of how this works. As far as which parameters to label and how to use them to create the noncausal effects, that you would need to figure out.
Regarding the variance-covariance matrix obtained through TECH 3 I have the following question. In my two-level model with a cross-level interaction I noticed that both for my random slope (i.e., g11) and the level-2 predictor (i.e., g01) there are two entries in TECH 1: An entry in the Alpha matrix and another one in the psi matrix. My question is which one should I consult to run a test of simple slopes as described in the webpage of Preacher, Curran, and Bauer (http://www.quantpsy.org/interact/hlm2.htm) ?
You don't need to go that route of getting TECH3 information. Instead, just specify the simple slope in Model Constraint and it is all done for you. This is also described in our book Regression and Mediation Analysis using Mplus.
I am trying to probe an multilevel modeling interaction. Does the book describe how to examine simple slopes for multilevel or single level interactions? Can you provide the syntax? I don't see it in the user's guide.
That page illustrates a simple slopes analysis for single level interactions and cross-level interactions.
I am using multilevel modeling to test an interaction between two Level 1 predictors on a Level 1 outcome, a 1 x 1 --> 1 model, using "unconflated multilevel modeling" (or cluster means for Level 2 variables and group-mean centered indicators at Level 1). I'm not sure how this might change the testing of simple slopes. Here's the model...
I assume that x, m, and x1m1 are declared Within vbles. And that xmean, mmean, and x2m2 are Between. Then the formula for simple slope is analogous on the two levels. In my notation and thinking of x as the moderator:
y = b1*x + b2*m + b3*x*m + e
= b1*x + (b2 + b3*x)*m + e
So the simple slope is
(b2 + b3*x)
which can use Model Constraint to either compute the simple slope at different x values or plot it as a function of x using LOOP and PLOT which you have examples of on our website.