On 17/05/16 20:12, Gary Grossman wrote:
I'm having a bit of difficulty getting a clear understanding of what
should be considered a fixed vs. a random effect in a linear mixed model
analysis of field data. Even the statisticians seem to say "it depends
on who's defining it" or "sometimes the same treatment/variable can be
either". Some examples may help, let's say I collected samples annually
in three sites and wanted to test for the effect of daily rainfall,
daily temperature, and density, on recruitment of individuals in the
following year. Using the lmer function in R which of these would be
fixed effects and which would be random? A reference or two would help.
I really couldn't find much in a google search on field studies, but I
didn't go to anything like zoological abstracts. TIA, g2
That's easy! If you only have 3 sites, you don't have enough levels to
make it worth fitting a random effect.
I look at random effects hierarchically. Basically, the values of random
effects are assumed to be drawn from a normal distribution, whereas
fixed effects are assumed to be totally free. What this means is that if
you have an effect with an unobserved level of the factor, do you think
the observed levels would tell you something about what values are
likely for the unobserved level. If you think they do then a random
effect make make sense.
What you are doing when you have a random effect is estimating the
variance of the values of the level of the factors. In the example you
give, I think a random effect would probably make sense if you had (say)
20 sites, but with three sites you are trying to estimate the variance
from (in effect) 3 data points. the estimate won't be very good, so as a
practical matter it's not worth bothering with the extra hassle.
Of course, this is only my opinion: there are other ways of looking at
random effects, so pick the one which works for you. There will always
be cases where it's not clear if something should be considered fixed or
random.
Bob
--
Gary D. Grossman, PhD
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