Warning Message re linear dependency
Message/Author
 Susan Scott posted on Wednesday, October 18, 2006 - 11:44 am
I would like to understand the following warning message:

THE MODEL ESTIMATION TERMINATED NORMALLY

WARNING: THE LATENT VARIABLE COVARIANCE MATRIX (PSI) IS NOT POSITIVE
DEFINITE. THIS COULD INDICATE A NEGATIVE VARIANCE/RESIDUAL VARIANCE FOR A
LATENT VARIABLE, A CORRELATION GREATER OR EQUAL TO ONE BETWEEN TWO LATENT
VARIABLES, OR A LINEAR DEPENDENCY AMONG MORE THAN TWO LATENT VARIABLES.
PROBLEM INVOLVING VARIABLE PCS_OB.

I have looked at Tech4, and there are no correlations>1 nor variances or residual variances <0. I assume this means there is a "linear dependency among more than two latent variables". What does this mean and how do I detect this (I am assuming that 1 of the latent variables involved must be the one with PCS_OB as an indicator.). If I leave this variable out (leaving that particular LV with 3 other indicators), the model converges fine without any warning messages. However, for theoretical reasons, I would like to keep this particular variable.
 Linda K. Muthen posted on Wednesday, October 18, 2006 - 1:47 pm
If the variable does not have a negative residual variance and does not correlate 1 or greater with another variable, then there must be a linear dependency. You would not be able to keep this variable in the model unless you remove the linear dependency.
 Susan Scott posted on Friday, October 20, 2006 - 1:52 pm
I am thinking I will rerun the model removing 1 var at a time to find the problem (beginning with variables with which it is most highly correlated). Is this a good approach?
 Linda K. Muthen posted on Saturday, October 21, 2006 - 6:41 am
A linear dependency is among more than two items. There is no easy strategy to find where the linear dependency arises. It would result in a correlation of one if there were only two variables involved. Thinking about why your variables might have this linear dependency is probably the best bet.
 Siran Zhan posted on Thursday, October 13, 2011 - 2:05 am
Dr. Muthen, I got the error message below:

WARNING: THE LATENT VARIABLE COVARIANCE MATRIX (PSI) IS NOT POSITIVE DEFINITE. THIS COULD INDICATE A NEGATIVE VARIANCE/RESIDUAL VARIANCE FOR A LATENT VARIABLE, A CORRELATION GREATER OR EQUAL TO ONE BETWEEN TWO LATENT VARIABLES, OR A LINEAR DEPENDENCY AMONG MORE THAN TWO LATENT VARIABLES. CHECK THE TECH4 OUTPUT FOR MORE INFORMATION. PROBLEM INVOLVING VARIABLE SW_RT.

In TECH4 output I did find a >1 correlation between SW_RT and another latent variable. I tried to either fix their correlation at 0.98 or 0, the same error message still appeared afterward, indicating problem involving another variable.

Can you advise me what this suggests and what I can do to redress the problem?
 Linda K. Muthen posted on Thursday, October 13, 2011 - 9:38 am
 Hallie Bregman posted on Wednesday, April 25, 2012 - 9:25 am
Hi,

I am trying to test a CFA to determine whether parent) and youth) factors are better specified together (3 factors) or separately (6 factors). However, when I run my model where I allow all 6 factors to freely correlate, I receive the following error message:
WARNING: THE LATENT VARIABLE COVARIANCE MATRIX (PSI) IS NOT POSITIVE DEFINITE. THIS COULD INDICATE A NEGATIVE VARIANCE/RESIDUAL VARIANCE FOR A
LATENT VARIABLE, A CORRELATION GREATER OR EQUAL TO ONE BETWEEN TWO LATENT
VARIABLES, OR A LINEAR DEPENDENCY AMONG MORE THAN TWO LATENT VARIABLES. CHECK THE TECH4 OUTPUT FOR MORE INFORMATION.
PROBLEM INVOLVING VARIABLE YCONTROL.

I have no negative residual variances, and no correlations > 1 in TECH4. Thus, I am assuming I have a linear dependency (probably between YCONTROL and PCONTROL?). I have also specified a model where the correlation between PCONTROL and YCONTROL is set at 1, although my model fit statistics are significantly worse. Do you have any recommendations about how to proceed? Thanks very much!
 Linda K. Muthen posted on Thursday, April 26, 2012 - 1:50 pm
You probably need to correlate the residuals across parent and youth.
 Florian Zach posted on Wednesday, August 29, 2012 - 2:37 am
Hi,

I run into two (for me so far) unsolvable problems with a higher-order CFA:

Data: Normal distributed, continuous

Model:

ACQ BY C2B_01 C2B_02 C2B_03;
ASS BY C2B_12 C2B_13;
TRAN BY C2B_07 C2B_08 C2B_09
C2B_10 C2B_11;
EXP BY C2B_04 C2B_05 C2B_06;

! second order
PAC BY ACQ@1 ASS;
RAC BY TRAN@1 EXP;

! third order
CC by RAC PAC;

Problem 1:

... MODEL NONIDENTIFICATION. THE CONDITION NUMBER IS -0.223D-16. PROBLEM INVOLVING PARAMETER 45.

>> In TECH4 Parameter 45 is CC. I assume this issue will be solved simultaneously with problem 2.

Problem 2:
WARNING: THE LATENT VARIABLE COVARIANCE MATRIX (PSI) IS NOT POSITIVE DEFINITE... PROBLEM INVOLVING VARIABLE RAC.

>> RAC does have a correlation >1 with PAC. Again, I think that is also causing problem 1.

My issue that I don't know how to fix problem 2. I fixed RAC to 0 (CC by RAC@0 PAC), but that did not work out (no estimates provided anymore). Fixing RAC at 1 (obviously) had no effect either).

I checked the correlations of observed variables and they are fine. There is a negative residual variance for RAC tough.

Any help is appreciated. Thanks!
 Linda K. Muthen posted on Wednesday, August 29, 2012 - 9:39 am
Second- and third-order factors are not identified unless they have at least three factor indicators. A negative residual variance indicates that the model needs to be changed.
 fzach posted on Wednesday, August 29, 2012 - 11:02 pm
Good to know. Thanks you so much your response.
 Lisanne Stone posted on Friday, September 06, 2013 - 4:10 am
Hello Dr. Muthen,

I am running a cross-lagged path model with latent indicators. However, the model is not identified. The reason for non-identification is unclear to me. The statement in the output is that there is no convergence.

model:
f1 by meania meanib;
f2 by meanea meaneb;
f3 by meania2 meanib2;
f4 by meanea2 meaneb2;

!cross-lagged paths
f4 on f1;
f3 on f2;

!AU autoregression
f3 ON f1;
f4 ON f2;

!latent correlation within time
f1 WITH f2;
f3 WITH f4;

!control whole model for sex and age
sex age on f1 f2 f3 f4;

Would it be possible for me to send you the .dat file and input file? (of course I can provide a license number)

Best,
Lisanne Stone.
 Linda K. Muthen posted on Friday, September 06, 2013 - 9:47 am
I think you mean

f1 f2 f3 f4 ON sex age;

sex age on f1 f2 f3 f4;

The covariates go on the right-hand side of the ON statement.

If you still get the message, send the output and your license number to support@statmodel.com.
 Minnik Findik posted on Wednesday, June 24, 2015 - 8:54 am
I am running a multilevel growth model.But I get the following warning:

"THE MODEL ESTIMATION TERMINATED NORMALLY
WARNING: THE LATENT VARIABLE COVARIANCE MATRIX (PSI) IS NOT POSITIVE DEFINITE. THIS COULD INDICATE A NEGATIVE VARIANCE/RESIDUAL VARIANCE FOR A LATENT VARIABLE, A CORRELATION GREATER OR EQUAL TO ONE BETWEEN TWO LATENT VARIABLES, OR A LINEAR DEPENDENCY AMONG MORE THAN TWO LATENT VARIABLES."

If I include "Algorithm = Integration;" I don't get such notification. Can you explain why this is happening please?
 Linda K. Muthen posted on Wednesday, June 24, 2015 - 11:24 am
 Jana Mullerova posted on Monday, August 01, 2016 - 4:50 am
Dear Dr. Muthen,

I am running a CFA model with 7 factors and I received the following warning:

THE LATENT VARIABLE COVARIANCE MATRIX (PSI) IS NOT POSITIVE DEFINITE. THIS COULD INDICATE A NEGATIVE VARIANCE/RESIDUAL VARIANCE FOR A LATENT VARIABLE, A CORRELATION GREATER OR EQUAL TO ONE BETWEEN TWO LATENT VARIABLES, OR A LINEAR DEPENDENCY AMONG MORE THAN TWO LATENT VARIABLES. CHECK THE TECH4 OUTPUT FOR MORE INFORMATION. PROBLEM INVOLVING VARIABLE EB.

I checked Tech4 and the EB variable does have a correlation of 1 with another latent variable.
What would be the best way of dealing with this?

Many thanks
 Linda K. Muthen posted on Monday, August 01, 2016 - 6:59 am
You would need to change your model. Two variables that correlate 1 are not statistically distinguishable. You might want to try an EFA as a first step.
 Jana Mullerova posted on Monday, August 01, 2016 - 7:57 am