# Tutorial Model

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Joined: 09/10/2012 - 06:56
Tutorial Model

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?