Theta Matrix--Non positive Definite
Message/Author
 Anonymous posted on Friday, September 30, 2005 - 1:28 pm
I'm running a growth curve model. My fit statistics are fine and my intercept and slope make sense given the data. However, I keep getting an error message that the theta matrix is non-positive definite.

I've checked to see if the observed variables are collinear (I ran a regression with them in SPSS and examined the collinearity diagnostics). They do not seem to be collinear.

The program is telling me that it is with my second measure. The correlation matrix is as follows:

1.000
0.342 1.000
0.505 0.430 1.000
0.355 0.368 0.281 1.000

with a sample size of 257. Should I be concerned with the .505 correlation? Why else would I be getting a negative in my residual covariance matrix?

Thank you in advance for any assistance.
 Linda K. Muthen posted on Friday, September 30, 2005 - 3:18 pm
That message points to a negative residual variance, correlation of one, or some linear dependence with two or more variables. Look at your output to see if you have a negative residual variance. You can look at RESIDUAL from the output command to see where there may be correlation of one in the model estimated values. If you can't see what the problem is, send your input, data, output, and license number to support@statmodel.com.
 William Johnston posted on Thursday, September 06, 2012 - 6:43 am
I have the same error in my 2-level growth model that includes random slopes for different cohorts. From what I can see there are no negative residual variances or correlations of one. Here is my syntax:

USEVARIABLES ARE wiscraw wiscraw2 wiscraw3 nhood sex_r affluence cohort3 cohort6
cohort9 cohort12;
WITHIN = sex_r cohort3 cohort6 cohort9 cohort12;
BETWEEN = affluence;
CLUSTER = nhood;

ANALYSIS: TYPE = TWOLEVEL RANDOM;

MITERATIONS = 50000;

MODEL:

%WITHIN%
iw sw | wiscraw@0 wiscraw2@1 wiscraw3@2;
s3 | iw on cohort3;
s6 | iw on cohort6;
s9 | iw on cohort9;
s12 | iw on cohort12;

%between%

ib sb | wiscraw@0 wiscraw2@1 wiscraw3@2;
s3@0; s6@0; s9@0; s12@0;
wiscraw@0; wiscraw2@0; wiscraw3@0;
s3 s6 s9 s12 ON affluence;
ib sb on affluence;

OUTPUT: SAMPSTAT TECH1 TECH8;
 Bengt O. Muthen posted on Thursday, September 06, 2012 - 7:51 am