REML not calculating DF or p values

[#1]

Hi All,

I've got an experiment where I am comparing two species of fish and need to control for individual. In this case I actually am controlling for groups of individuals because I was not able to track specific individuals. Regardless, in essence I am trying to run a fancy t-test to check for differences between species where I can control for individual within species. I know that individual needs to be random and nested within species. I also have two treatments and am including that in the model. my model construction includes:

• Species,
• individual(species)&random,
• treatment,
• species*treatment,
• treatment*individual(species)*random

I'm running this base set of effects in the standard least squares personality with REML

I am testing this base model against a bunch of continuous variables, some are actual values like duration and body curvature, and there are a couple that are percentages, like percent body length. When I fit the model the models fitting against "real responses" all have no problem running all the statistics I would expect. The model is not calculating the degrees of freedom or the p values for the responses that are percent body length. The distributions of these % body length response variables are normal. I can't think of why I am unable to get the results. On the tests that don't calculate DF or p: there is a warning that says "convergence questionable: Check iterations". I check iterations and it runs through 101 iterations and says at the bottom Estimation Failed: Hessian Not Positive. I'm not sure what the Hessian is other than a revolutionary war era mercenary.

Is there something wrong with my data or my design that is causing this issue. When I run using EMS I get negative variance components in these "problem models" not sure what that means.

I've included some screen shots down below.

I appreciate all the help,

Stephen

[#2 · Accepted solution]

I think that the individual or group of individuals is your smallest experimental unit and should not be explicitly included as a term in the model. It will be used to estimate the errors as the model residuals. So the variance across individuals is accounted for as a random effect.

I do not recommend using the EMS method for estimating the variance components.

I do not think that there is any problem with your study (design) or data.

The covariance matrix is used to obtain the variances (covariances, actually). REML is an iterative method to the solution. If it does not converge then the variances and hence the standard errors are not available. The Kenward-Rogers method of estimating the degrees of freedom is part of the variance estimation, so it will also fail.

See if the removal of the individual from the linear combination helps. I think that you might have over-specified the model and caused problems with the convergence.