| Detailed description |
I (and I believe others) think it would be valuable for lmer() to be
able to handle models with *no* random effects in them. This would
allow testing for a single random effect by likelihood ratio test, by
fitting the full model incorporating the random effect, and then the
reduced/null model without that effect. Currently one *can't* fit the
null model in lmer(). One has to go over to plain lm(), and then one
can't do the likelihood ratio test because the two functions scale the
likelihood differently.
There is admittedly a problem with such a test in that the likelihood
ratio statistic won't have a chi-squared distribution. But then the
test could be conducted via Monte Carlo methods, is it not so?
It seems to me that it should not be very difficult to implement this
feature. Perhaps I'm being hopelessly naive, but ``no random
effects'' is kind of a boundary case of the mixed model, and it should
be possible to handle boundary cases, shouldn't it? I have no idea
how the innards of lmer() work, so perhaps ``shouldn't be difficult''
is a load of dingos' kidneys, but at first blush that's how it seems.
Couldn't there at least be a fork in the code whereby if there are no random
effects in the model, then lm() gets called (rather than an error being
thrown) --- and the lm() likelihood rescaled to be consistent with the lmer()
likelihood?
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