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 Adam Blake posted on Tuesday, March 09, 2010 - 10:08 pm
I was wondering if Mplus can output residuals for the endogenous variables in the model (similar to those generated by regression). I am hoping to exam these for autocorrelation and normality.

I'm guessing if I am unable to generate them in mplus, it should be fairly simple to generate them using the estimated parameters using a spreadsheet program.


Adam Blake
 Linda K. Muthen posted on Wednesday, March 10, 2010 - 9:54 am
The current version of Mplus does not provide these residuals. You can use the DEFINE command to create them.
 Adam Blake posted on Tuesday, March 30, 2010 - 10:31 am
I had a followup question involving calculating predicted values for latent variables, so as to calculate the predicted values and residuals of one my endogenous variables. You can see a simplified copy of my model below.

MODEL: pvig by sd ph;
cswf on n p k s
cswm on pvig cswf

I have been able to calculate predicted values for endogenous variables (such as cswf) with only non-latent variable predictors from the unstandardized coefficients and the intercepts provided by the m-plus output. Am am unsure how to calculate the predicted values for an endogenous variable (such as cswm) that is dependent upon latent variables (such as pvig). To calculate these predicted values I would first need to calculate the predicted values of the latent variables, but I am unsure how to derive these values from coefficients and intercepts used to calculate the predicted values for indicators (such as sd or ph). Any help or advice would be appreciated.


Adam Blake
 Linda K. Muthen posted on Wednesday, March 31, 2010 - 10:35 am
You can get the mean and variance of the pvig factor from TECH4. You can use the mean, the mean plus one standard deviation, and the mean minus one standard deviation to get predicted values.
 Adam Blake posted on Wednesday, March 31, 2010 - 11:18 am
I not sure I follow you here. I am unsure how I would calculate predicted values from simply the mean and the variance. Perhaps I was unclear in my question. I was interested in calculating predicted and residual values for individual observations not for the variables themselves.


Adam Blake
 Linda K. Muthen posted on Wednesday, March 31, 2010 - 11:37 am
If you want individual values, you would need to use the factor scores as the covariate. With only two indicators, I doubt that the factor scores would have acceptable factor score determinacy because that part of the model is not identified.
 Adam Blake posted on Thursday, April 01, 2010 - 10:02 am
So my best bet if I want individual predicted/residual values would be to eliminate the latent variables from the model allowing me to calculate these values based on the unstandardized coefficients and intercept values given in the output? This should not impact my model to a great degree as I only have one latent variable and my indicators had fairly high reliability.


Adam Blake
 Linda K. Muthen posted on Thursday, April 01, 2010 - 10:18 am
That sounds correct if you don't want to use factor scores.
 Adam Blake posted on Thursday, April 01, 2010 - 1:52 pm
I had another look through the manual after I knew that I was looking to output factor scores. I was then able to output both the factor scores and the factor score determinacy. The determinacy for the latent variable pvig (from the above model) was 0.942, which based on my limited understanding of factor score determinacy seems acceptable. Given its acceptability, I should then be able to use these factor scores to generate individual values for cswm without a problem?
 Bengt O. Muthen posted on Thursday, April 01, 2010 - 4:49 pm
It is surprising that would have such a high factor score determinacy with only 2 indicators, but it is probably because the factor score estimation also draws on information from the other observed variables in the model, including covariates and the DV. The fact that the DV contributes to the factor score may make the prediction questionable. It would perhaps be better to use the factor score based on the 2 factor indicators and covariates. Unfortunately you cannot base the factor score on the factor indicators alone since that part of the model is not identified (you need at least 3 indicators). You could for instance fix the parameters at the values of the full model (including the DV) and estimate the factor scores pretending that the DV has missing values for everyone.
 Adam Blake posted on Friday, April 02, 2010 - 10:42 pm
I was constraining the standardized parameters of the two indicators to be equal to ensure convergence so the measurement model is identified with the model constraints below. The factor score determinacy for the measurement model was 0.948, similar to that for the full model. Given this situation the factor scores from the limited model should then be acceptable?

pvig by sd
ph (b1); sd (ve1); ph (ve2); pvig (v1);

cswf on n p k s;
cswm on cswf pvig;

NEW(stansd stanph);
stansd = sqrt(v1)/sqrt(v1 + ve1);
stanph = b1*sqrt(v1)/sqrt(b1**2*v1 + ve2);
stansd = stanph;
 Antti Kärnä posted on Wednesday, March 14, 2012 - 2:21 am
It is stated in the Mplus manual (p. 644) that "Residuals are computed as the difference between the value of the observed sample statistic and its model estimated value."

In Kline's book (2010) an example of CFA is given:

HANDMOV 11.560
NUMBREC 3.182 5.760
Model Estimated Covariances
HANDMOV 11.503
NUMBREC 3.255 5.731
Residuals for Covariances
HANDMOV -0.001
NUMBREC -0.089 0.000

Why is it not the case here that Observed covariances - Model estimated covariances = Residuals ?
Thanks in advance!
 Linda K. Muthen posted on Wednesday, March 14, 2012 - 11:16 am
I would think this is a mistake in the book. The definition of a residual is pretty clear.
 chris pp posted on Sunday, April 08, 2012 - 4:51 pm

A question about standardized residuals for SEM: Some of the standardized residual mplus outputs are reported as 999.00, and looks like it is for an exogenous variable with one or two outcome variables (that are also set as predictors in the model). I imagine the 999 indicates that the residual was not calculated. Is this correct and if so why is it not relevant to calculate in this instance?


USEVARIABLES ARE edu cfit social selfr pa pop age sex;


MODEL: sr BY selfr@0.78;
soc BY social@.72;
sr ON edu cfit;
soc ON sr pop cfit age;
pa ON pop soc age sex;
cfit ON edu age;
pop ON edu sex;


Normalized residuals were provided for all pairs of variables.

Standardized residuals for edu and pop,
and sex and pop, were 999.00.

Look forward to your reply.
 Linda K. Muthen posted on Monday, April 09, 2012 - 9:08 am
The 999 means the residual could not be computed most likely due to a zero denominator. See the Technical Appendix on the website called

Standardized and Normalized Residuals
 chris pp posted on Monday, April 09, 2012 - 10:49 pm
Hi Linda,

Thank you for speedy reply!

Following up - given a range of model fit indices suggest the model is correctly specified (e.g. RMSEA, CFI), am I correct that:

- the 999 does not signal a 'major issue' with the model, rather is due to negative variance estimates that can arise when applying Hausman's calculation?

- can still diagnose local model fit with
the normalized residuals and
modification indices?
 Linda K. Muthen posted on Tuesday, April 10, 2012 - 1:47 pm
No, thee 999 does not signal a major issue. Yes, you can use normalized residuals and modification indices.
 Chelsea Wiener posted on Sunday, June 05, 2016 - 1:47 pm

Per the technical appendix "Standardized and Normalized Residuals", normalized residuals can often be used instead of standardized residuals when Mplus prints 999 for standardized residual estimates.

It is stated that "normalized residuals should have distribution smaller than the standard normal distribution and any deviation from that would indicate model misfit."

How does one determine if the normalized residual is smaller than the standard normal distribution in these circumstances?

Thank you!
 Tihomir Asparouhov posted on Monday, June 06, 2016 - 10:01 am
You can use the normalized residuals the same way you use the standardized residual.

Keep in mind that significant residual (any value above 1.96 by absolute value) is even more meaningful with the normalized residual than the standardized.

For example if the standardized residual is exactly 1.96 you should interpret that as having p-value of 0.05 in the standardized case and <0.05 in the normalized case.
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