Hello!

I've been working through Dorothy Bishop's tutorial, linked from this website here:

https://openmx.ssri.psu.edu/wiki/ideas-simplified-manual-beginners-smb

or can be found in online form on her blog here:

http://dbtemp.blogspot.co.uk/2011/08/structural-equation-modeling-in-openmx.html

I found I was getting NaN std errors (see the comments at the bottom of the blog link above for the full discussion - I've paraphrased and extended the comments there in the question below).

Dorothy Bishop kindly replied with some suggestions, but thought that I should ask on this forum.

I think the model she's using is underdefined. I'll try to explain why below.

### First, The model

S<-b-V-a->W

B<-c-N-d->P

there are recurrent bidirectional connections on S,W,B and P (e,f,g,h).

(8 unknowns: a,b,c,d,e,f,g,h).

The covariance matrix would have numbers in the following places:

W S B P W x1 x2 0 0 S x2 x3 0 0 B 0 0 x4 x5 P 0 0 x5 x6

(10 observed values? x1,x2,x3,0,0,0,0,x4,x5,x6)

### The problem

The NaN Std Deviations are caused by the inverted Hessian matrix (which is the covariance matrix) having negative values on the diagonal. I think this is generally due to something being underdefined in the design?

In layman terms, I think it is a problem that the strength of the correlation between W and S can be modified by EITHER changing a or changing b? In some ways the model isn't defined well enough?

### Under or over defined?

In the tutorial it is shown that there are 10 observed values (in the covariance matrix) and 8 unknown parameters, suggesting 2 dof. I'm a bit worried that the 0s in the covariance matrix don't help much - if that makes sense?...

Thinking about this a bit more: Given that this model can be split into two smaller models, surely these should be possible to estimate too? But when I count up the DoF for just the V,W,S sub-graph...

(the model looks like: V-(a)->W, V-(b)->S, V-(1)->V, W-(e)->W, S-(f)->S)

This gives us 4 unknowns (a,b,e,f), and only three values in the covariance matrix (a^2+e, b^2+f and ab)...

...doesn't this mean the model is "secretly" underdefined?

### Summary

Because the model can be split into two submodels which are both underdefined, the combined model is also going to be underdefined.

What do people think?

Thanks! (just learning about SEM).

Mike Smith

University of Edinburgh