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 Tracy Witte posted on Monday, April 06, 2009 - 5:02 pm
I have 2 latent variable predictors (X & Z) and 1 DV that is categorical (Y). Running the model separately for each IV, X predicts Y & Z predicts Y. However, when I have both X & Z predicting Y, neither is statistically significant. My DV is categorical, so Mplus doesn't give me the residual variance for it. However, in the Brown (2006) book, it says that the residual variance for categorical indicators is 1 minus the squared standardized solution. Thus, I assume that the square of the standardized solution for each predictor is the amount of variance accounted for in the categorical DV. When I have X & Z predicting Y, the sum of their squared standardized loadings is less than what I get for each of them individually. It seems to me like I'm not accounting for the shared effects of X & Z on Y. Is that correct? If so, how can I get this information?

I created factor scores for my latent variables (X & Z), and ran a logistic regression. In the logistic regression, when I have both X & Z predicting Y, neither is individually statistically significant, but that step is statistically significant. I'm just not sure how to show that in an SEM (i.e., that both things together are predicting). It seems to me that whatever is common between X & Z is driving the relationship that I find in the regression. Any information you have would be very helpful. Thanks!
 Bengt O. Muthen posted on Tuesday, April 07, 2009 - 12:07 am
This can happen when X and Z are fairly highly correlated (see books on linear regression with topics such as multicollinearity).

Mplus gives you the R-square for Y when you request a standardized solution. This takes into account that the IVs are correlated.

You can avoid problems due to high X, Z correlation by creating a factor measured by X and Z and letting the factor predict Y. If that makes substantive sense.
 Tracy Witte posted on Tuesday, April 07, 2009 - 12:30 am
Thanks! When I try to do that (i.e., creating a latent factor with X and Z as indicators), it says that my model is not identified. Any ideas why that would be?
 Jon Heron posted on Tuesday, April 07, 2009 - 3:06 pm
Hi Tracy,

if you've just fitted

factor by X* Z;
Y on factor;

then you are trying to estimate too many things.

As you have 3 continuous variables, you have a maximum of 6 parameters for your covariance model (from the 3 variances and 3 covariances).

One option would be to add a third indicator of your factor. Alternatively you can constrain the factor model in someway - e.g. constrain the residual variances or the loadings to be equal

option 1 (add an indicator):

factor by X* Z W;
Y on factor;

option 2 (constrained residual variances):

factor by X* Z;
X Z (1);
Y on factor;

option 3 (constrained factor loadings):

factor by X* Z (1);
Y on factor;

Cheers, Jon
 Jon Heron posted on Tuesday, April 07, 2009 - 3:07 pm
Sorry, took me so long to type that, that the question had already been answered - doh!
 Jon Heron posted on Tuesday, April 07, 2009 - 3:07 pm
No it hadn't! sigh
 Bengt O. Muthen posted on Tuesday, April 07, 2009 - 5:56 pm
Tracy & Jon,

The model is (just-) identified; see the Topic 1 slides 235-237.
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