WOMBAT – A program for Mixed Model Analyses by Restricted Maximum Likelihood

## Standard errors

I am getting a value of -1.0 as standard error for some of my estimates of genetic parameters, together with a note that Negative values for s.e. indicate failed approximation!. What does is mean and what can I do about it? ?

As it says in plain English: the approximation of standard errors failed.

Standard errors in WOMBAT are derived

1. assuming large samples, and
2. a series of approximations - see the Technical Details section of the manual.

In some cases, this approximation simply fails. Typically, this is the case when the average information matrix (from which sampling covariances are derived) is not safely' positive definite. Reasons for this may be, for instance, that your sample is very small, or that you are dealing with a model which is over-parameterised. Please consult the statistical literature on maximum likelihood estimation for background information.

The latter includes multivariate analyses where some covariance matrices have eigenvalues which are effectively zero. In that scenario, it may help to fit a reduced rank model. Otherwise, you should attempt to use a better' data set (i.e. one which supports the question you are asking) - if that is not feasible you may simply have to accept that the approximation of standard errors does not always work.

Alternatively, you could try the sampling based approximation of standard errors - note though that this may alos be problematic if your model is overparameterised.

My REML analysis has converged but the results file does not report standard errors for (co)variance components or genetic parameters. How do I make the show up?

WOMBAT provides several algorithms to locate the maximum of the likelihood function. Only the `average information' algorithm provides an estimate of sampling covariances from the inverse of the information matrix (and s.e. derived from them). If your analysis terminated having used one of the other algorithms no estimates are thus reported - without further comments.

This means that you could try a continuation run with the average information algorithm - a single iterate should suffice to give you estimates of standard errors. Make sure though to inspect the likelihood - it should not change compared to the previous run: if it increases, your analysis did not reach convergence previously and you need to keep going, if it decreases something has gone wrong and results are not valid!

I have run a standard variance component analysis and found the solutions for effects fitted in the model. However, corresponding standard errors are missing - how do I get them?

In a mixed model analysis, approximate lower bound standard errors are obtained from the diagonal elements of the inverse of the coefficient matrix. The default method for variance component estimation is the “average information” algorithm. The implementation of this algorithm in WOMBAT does not involve inversion of the coefficient matrix – hence standard errors are not simply a by-product.
You can enforce calculation of standard errors by simply adding the option FORCE-SE in a SPECIAL block at the end of the parameter file. Note though that this forces inversion of the coefficient matrix and, for large models, may thus increase computing time markedly.

SPECIAL
FORCE-SE
END