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I've tried about a dozen tests and everything seems in working order now.

Thank you for all your efforts!

Hmmm... Well with this version, the model that was producing the error before (form.raceInteract3 in the original post) now runs.
Unfortunately, the two models that worked before (form.raceInteract1 and form.raceInteract2) no longer work. They now produce

Error in '[.data.frame'(indata, ,outvars ...

I tried to bypass the problem entirely by using a character string instead of a formula object, which the manual says can be done. I can't find examples of this approach, so I'm confused why I'm getting the following error. I think I'm following the syntax rules on page 22 of the manual correctly ...

Apologies for the delayed response. I tried that solution. Unless I misunderstood the suggestion, the same error comes up,
>
> form.raceInteract3B <- formula(z_pcm3partr ~ 1 + d0locIndeg + d0extIndeg + zN0mapDDpopBXisol + zN0mapDDextpopBXisol + d1BlackNonHisp_scs + d0locIndeg:d1BlackNonHisp_scs ...

Thanks for the prompt reply.

The form.raceInteract1 for the third model was just a typo copying to the post. The fitted model was correct.
It's the same data set for all models and the formula works fine with lmer.

runMLwiN is inconsistent accepting interactions in my formulas and I don't see a pattern. For example, interactions that work when in separate models create an error when included in the same formula. Here's an example. (Unfortunately, I haven't been able to recreate the problem with MLwiN's example ...