If some individuals have only one measurement, that could be the cause of the Hessian problems. There’s no residual variation around the mean for that subject b/c the one data point is the mean. It’s really hard to diagnose that kind of thing without digging into the data, though.

To run a population averaged model, you would have to define individual as the subject and specify the covariance structure for each subject’s multiple measurements. Be careful here, as it can make a big difference.

And the significance tests for the random effects are generally considered pretty inaccurate tests. I don’t even look at them. You’re better off computing the intraclass correlation.

And fyi, West, Welch, and Galecki’s Linear Mixed Models book has a nice explanation about the Hessian matrix warning, if you’d like more info.

Best,
Karen

I’m not exactly sure what you mean by quantifying the context, but I would think the answer is ‘no.’ It’s really about stopping and thinking about what information you really have.

Karen

Thanks for this information, I had a lot of difficulty finding anything about this Hessian matrix warning. I get this problem coming up a lot in my analyses and I’m paritcularly surprised as it comes up when I use identidy as a random factor, as some of my data set includes measurements from more than one individual (and its not appropriate to average them). If I don’t include it, I worry I will be criticised for pseudoreplication. If I try a population model, do I use identity as the repeated statement even though not all individuals are used more than once?

Also, when you do have a random effect but it is not significant, should you then remove and re-run the anlaysis or still leave it in?

Any help would be great.
Thanks,
Leanne

Proc Mixed might be fine–you haven’t given me enough information. Is there a reason for mixed, like repeated measures on each cow or randomized blocks?

Karen

Karen

I have a data set with one control and two treatments. Basically, three groups of cows were fed a control diet, a contaminated diet, and a contaminated diet with additive. I have the following samples sized: control = 2 cows, trt1 = 5 cows, and trt2= 5 cows. These are pretty small numbers to begin with, but we were limited by money (yay research!). I’m using Proc Mixed in SAS for the ANOVA, but after reading some of the comments above, I’m not sure I’ve done this correctly. Can you offer some advice on the proper way to analyze this data?

Thanks
Stephanie

Can you give me more information. That sounds possible in a dummy coding situation, but I’d need to hear more specifics. It’s always about the details.

Yes, I see your point. I agree, it’s always ideal to have more of the variation explained. And for an outcome that is generally well understood for the population being studied, there is a higher expectation of being able to explain most of the variation. You’re absolutely correct that it would be better to model this hypothesis as an additional variation explained, and that not including the controls means you could be misattributing relationships.

However, there are some outcome variables (many in sociology, for example) for wide populations that just won’t ever be explained that much. So it’s not a matter of another variable that’s being left out of a model, but either so many competing variables each with a tiny effect that you can’t include them all or just randomness. (And I realize these are often the same thing).

Now it’s arguable that physical health isn’t one of those, and I concede that’s possible. But it’s possible that it is in certain populations. For example, you may be able to control for 70% of the variation in physical health in a clinical population, but not in a national population.

This is also true in more exploratory situations. If an outcome is a new construct that isn’t well known, it’s likely that data won’t have been collected on every possible control. In this case, it’s very possible that an effect of something like religiosity will later be explained away in another study. But that’s interesting–this effect we thought we had? Turns out it’s explained by X. If we never report the first small effect because we’re waiting for a model that explains everything, we may never know what needs to be built into the model.

Again, it’s the context.

A model that only *improves* by small amounts can still be useful (say going from .7 to .74), but a model that, in it’s entirety, only produces an R-sq of .04? I’d be worried that I haven’t even begun to properly model the relationship.

I agree (strongly) with the point about interpreting the result within the context in which the research is being conducted, though.