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Help desk => Questions and Answers => Topic started by: Scherge on March 04, 2021, 09:42:00 AM

Title: Two-Dimensional Analysis: covariance matrix not positive definite
Post by: Scherge on March 04, 2021, 09:42:00 AM
Hi Conquest Community,

I am currently performing a unidimensional vs. a two-dimensional assessment. However when I do a cross-check against the indended dimensionality I allways get the  "covariance matrix not positive definite" - error. Do you have any idea whether this can be solved getting deviances and fit results? It happens both using PCM and RSM. The indended two dimensional model converges without any issues which is good. Now I'd like to compare them. I am using conquest version 5.12.3.

Code: [Select]
Title Two Dimensional Model (PCM): Testheft A1;
data A1.dat;
format id 1-10 responses 12-15;
labels << A1.lab;
score (0,1,2,3,4,5,6,7,8) (0,1,2,3,4,5,6,7,8) () ! items (1,4);
score (0,1,2,3,4,5,6,7,8) () (0,1,2,3,4,5,6,7,8) ! items (2,3);
model item+item*step;
Estimate ! nodes=2000; method=montecarlo;
show !estimates=eap, tables=1:2:3:4:5 >> A1_2D_Probe.shw;
itanal >> A1_2D_Probe.itn;

Kind Regards

Scherge
Title: Re: Two-Dimensional Analysis: covariance matrix not positive definite
Post by: dan_c on March 04, 2021, 12:00:36 PM
Hi Scherge,

I think you are encountering issues because the latent correlation between your two dimensions is approaching 1. This is strong evidence of a unidimensional structure.

There are several ways you can get deviances and fit. The first is to not estimate standard errors - they are not required.

Code: [Select]
estimate ! stderr = none;
You can also try quick standard errors (assumes off diagonals of the variance-covariance matrix of the model parameters are 0). See the details in the manual: https://conquestmanual.acer.org/s4-00.html#est (https://conquestmanual.acer.org/s4-00.html#est)

Another way of considering dimensionality is user-defined residual fit statistics. You fit a 1D model and then test the hypothesis that the observed responses to items 1 and 4 (and alternatively 2 and 3) fit the expectation given the model (that is, this group of items, fit a 1D model). As with fit statistics for individual items, the expected value is 1. The fit command gives confidence intervals around the estimate. see https://conquestmanual.acer.org/s4-00.html#fit (https://conquestmanual.acer.org/s4-00.html#fit).

I have attached a show file and some fit analysis from a 1D run.
Title: Re: Two-Dimensional Analysis: covariance matrix not positive definite
Post by: Scherge on March 04, 2021, 01:51:02 PM
Hi dan,

true. I have expected these combinations of items to be strongly unidimensional and on a similar dimension like all 4 items together. So I really like your idea of residual fit statistics.

Thanks a lot for your quick and effective support.

Regards,

Scherge