I'm have been fitting cross-lagged models in OpenMx, but I have some questions on the standard errors.

The same models can be fitted with other software, for example SAS and I do get, for exactly the same model the same estimates but different standard errors. To test this, I removed all missing values (as SAS and OpenMx handle them differently) and built 3 different models. As an illustration, I'll give the simplest model here.

* There are 124 subjects, each measured at 7 days.

* For each subject at each day, there are two variables measure, let's call them X and Y here.

* This gives a total of 1736 observations (as OpenMx correctly shows in the output)

* In SAS, the variables are recoded to get predictors and responses so that there are 1488 observed responses (days 2-7) and twice 1488 predictors (days 1-6 autoregressive & days 1-6 lagged)

The model in both cases is:

* Y_{i} = Y_{i-1} + X_{i-1}

* X_{i} = X_{i-1} + Y_{i-1}

for i = 2,...,7

and with residual covariance for each variable and between X_{i} and Y_{i}.

The summarized results for Open Mx and SAS are the following (error between brackets)

# Open Mx

* Effects

AR X 0.622942286 (0.02300498)

AR Y 0.787465914 (0.01841442)

X lag Y -0.105527933 (0.02479874)

Y lag X -0.029917726 (0.01773734)

* Covariance structure

Res X 0.556322176 (0.02229294)

Res Y 0.348904648 (0.01369003)

Res XY -0.152949023 (0.01257696)

# SAS

* Effects

AR X 0.6232 (0.03167)

AR Y 0.7874 (0.02552)

X lag Y -0.1054 (0.03223)

Y lag X -0.03000 (0.02508)

* Covariance structure

Res X 0.5579 (0.02896)

Res Y 0.3499 (0.01816)

Res XY -0.1534 (0.01717)

As one can see, the estimates are very similar, but the errors do differ.

A linear regression on these errors and the errors of a few similar models showed that on average the errors of Open Mx are linearly related to those of SAS, more exactly they are about 0.837 times the errors of SAS (with a small intercept) or 0.788 (without intercept).

Consequently, I have two questions:

* How are standard errors calculated in OpenMx?

* Can anyone explain the difference in this case? Does it have to do with the degrees of freedom only or may there be other reasons? If it were only the degrees of freedom, the difference should be smaller, I assume.