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 Anthony S. Boyce posted on Thursday, April 05, 2007 - 3:22 pm
I am fitting a cross-lagged autoregressive model with two constructs measured over four waves. I had been unable to get an acceptable SRMR (i.e., ~.11) although the other fit indices (i.e., CFI, TLI, and RMSEA) indicated acceptable fit. I came across an article (Anderson & Williams, 1992) that suggested it may be important to include autocorrelated disturbances within a construct over time (i.e., disturbance of construct 1 at T2 correlated with disturbance of construct 1 at T3, etc.). When I included these autocorrelated disturbances, the SRMR was reduced substantially, but now I have a negative R-squared value for construct 1 only at T4. I'm confused as to why this occurred and wondering whether there are any additional models I could try that may reveal adequate fit without the within-construct correlated disturbances. Thanks very much in advance.
 Linda K. Muthen posted on Thursday, April 05, 2007 - 5:28 pm
Why don't you go back to the model without autocorrelated disturbances and see what modification indices may suggest. Maybe you added too many.
 Annie Desrosiers posted on Wednesday, July 06, 2011 - 12:16 pm
Hello Dr. Muthen,

I have a date-set with five time-points and I used cross-lagged autoregressive analysis to capture direction of effects. For my cross-lagged autoregressive model, I used SEM analysis with Mplus. And I used MODINDICES in the syntax. I found that variable X at times 1 and 2 did predict variable Y at times 2 and 3 respectively. The sign (positive) of the causal link and the direction are in line with theory. However, when we add “with” to improve the model, the direction did not change but the sign is reversed (negative). Also, some of the “with” values are negative and some are positive. Please note that without the “with” the fit indices are poor.
1) How much we interpret these findings
2) And is it possible to have negative “with” values
Thank you

USEVAR =
XT1 XT2 XT3 XT4 XT5
YT1 YT2 YT3 YT4 YT5 ;

ANALYSIS: ESTIMATOR = ML;

MODEL:
YT2 on YT1;
YT3 on YT2;
YT4 on YT3;
YT5 on YT4;

XT2 on XT1;
XT3 on XT2;
XT4 on XT3;
XT5 on XT4;

XT2 on YT1;
XT3 on YT2;
XT4 on YT3;
XT5 on YT4;

YT2 on XT1 ;
YT3 on XT2 ;
YT4 on XT3 ;
YT5 on XT4 ;

YT2 WITH XT2;
YT3 WITH XT3 ;
YT4 WITH YT3;
 Bengt O. Muthen posted on Wednesday, July 06, 2011 - 1:11 pm
Try it out with only 2 time points and see if the same sign change happens and for which sets of time points it happens.

Perhaps you have other important predictors that should be in the model. Then the regression assumption of residual uncorrelated with predictors is not fulfilled.

Yes, negative WITH values are valid. That means that the predictors you left out for each process (X or Y) are negatively correlated.
 Annie Desrosiers posted on Wednesday, July 06, 2011 - 3:21 pm
Dr. Muthen

Thank you very much for your response,
as suggested, I tried running the model with only 2 time points (T1 and T2), everything was fine. Then, I tried T2 and T3 and that resulted in a negative sign value but it was not significant (XT3 on YT2). Then I tried T1 T2 T3 without any “with”, and I also got the negative sign value but again it was not significant (XT3 on YT2). The modification indices suggest adding “XT3 WITH XT2”, “XT2 with YT2” and “YT2 with YT3”: when I run this a significant negative sign appears on the value “XT3 on YT2”. I notice that adding “XT3 WITH XT2”, significantly increases the fit of the model and causes the significant negative sign on the value “XT3 on YT2”. What do you think is happening?

Thanks again
 Bengt O. Muthen posted on Wednesday, July 06, 2011 - 6:44 pm
I think you may want to take this question to SEMNET since it is a general model fitting question.
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