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Hello

I am new to MLwiN and have encountered this IGLS/RIGLS numeric warning. I see there have been posts on this before, and have tried the suggested solutions but am still having problems.
Attached is a screenshot

I did find that it worked if I selected RIGLS rather than IGLS and allowed negative variances at level 2 and level 1 - however I don't know if this is a valid thing to do. I also then found that when I ran it again, MLwin didn't like it and produced inconsistent results.

Please could you tell me when it is appropriate to use RIGLS or IGLS estimation, and under what circumstances it is appropriate to allow negative variances? And any suggestions about how best to solve my issue would be very much appreciated.

Thank you!

One method of estimation in MLWIN is a likelihood based one and there are 2 versions. Iterative Generalised Least Squares estimates the random part under the assumption that fixed part estimates are known. Restrictive IGLS estimates the random part variances as if the fixed part means have been estimated. This is like the formula for the ordinary descriptive variance: the IGLS equivalent divides by n; the RIGLS equivalent divides by n-1 as one degree of freedom has been consumed in estimating the mean. This does not usually make much difference except when there is not much information around to estimate the model eg you have a complex model involving lots of random terms but few level 2 observations. So RIGLS is to be preferred in this situation as it is more realistic and often helps with convergence to a stable estimate. So why bother with IGLS? It is slightly computationally quicker and this used to matter with slow machines and big models, And strictly you should use IGLS based estimates to test the change in the deviance if the models differ in the fixed part of the model (and RIGLS if they differ in the random part). But the best piece of advice is not to overcomplicated models.
Now to negative variances! The key to this is to understand that in the random part you are really modelling variance functions at level 2 and while the overall variance function should not go negative elements of them could go negative. Again this tends to be a problem when you fitting a more complex model than the data can support.

We have developed a lot of resources for understanding and using the software and this is the best place to start:
http://www.bristol.ac.uk/cmm/software/m ... urces.html

On testing and IGLS/ RIGLS see Chapter on significance testing in C&Hvol1: Jones, K and Subramanian, V S (2014) Developing multilevel models for analysing contextuality, heterogeneity and change using MLwiN, Volume 1 , University of Bristol.

On variance functions see Chapter 7 of the User manual. USER: Rasbash, J., Steele, F., Browne, W.J. and Goldstein, H. (2012) A User's Guide to MLwiN (PDF, 4,244kB), Centre for Multilevel Modelling, University of Bristol.

Finally (and this is more advanced) MCMC estimation is available in MLwiN and this is full uncertainty modeling so that both the random and fixed parameters are estimated on the basis that the other parameters have been estimated and are not known. This generally does not make much of a difference but can do for more complex models especially those with discrete outcomes, see
MCMC: Browne, W.J. (2012) MCMC Estimation in MLwiN, Centre for Multilevel Modelling, University of Bristol.