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Estimation of variance components in random- and mixed-effects models

Ben Bolker 
A couple of *quick* responses.

   * I don't recommend dropping non-significant predictors, this is a 
good way to overfit models.
   * Are the temperatures for your three cohorts in a strictly linear 
sequence? i.e., temperature (cohort 1) = T1, temp (2) = T1 + delta, temp 
(3) = T1 + 2*delta ? In that case, the two effects are indeed 
identical/confounded.  In principle, your original model (using cohort 
as a random effect and temperature as fixed) is the right way to handle 
this, but for the size of data set you can't really identify 
among-cohort variation beyond the effect of temperature.

   A nice way to handle this is to treat cohort as an *ordered* 
categorical fixed effect (see ?ordered), and leave out temperature (this 
is assuming that the temperatures are as suggested above).  If you do 
this (i.e. convert cohort to 'ordered' type), R will fit two parameters, 
one labeled .L and the other labeled .Q, which together explain all of 
the among-cohort variation; if you like (although it is quite a big 
assumption, and you must be explicit about it), you can ascribe the 
linear (".L") variation to temperature and the other (".Q" or quadratic) 
to non-temperature effects.  However, given your experimental design, 
the following two explanations would be *equally well supported*:

  * none of the between-cohort variation is due to temperature;
  * temperature has a quadratic effect, so all of the between-cohort 
variation is due to temperature.

  cheers
    Ben Bolker
On 6/28/21 3:20 PM, Amy Huang wrote:

Thread (7 messages)

Amy Huang Estimation of variance components in random- and mixed-effects models Jun 28 Ben Bolker Estimation of variance components in random- and mixed-effects models Jun 28 Thierry Onkelinx Estimation of variance components in random- and mixed-effects models Jun 28 Ben Bolker Estimation of variance components in random- and mixed-effects models Jun 28 Amy Huang Estimation of variance components in random- and mixed-effects models Jun 28 Thierry Onkelinx Estimation of variance components in random- and mixed-effects models Jun 28 Ben Bolker Estimation of variance components in random- and mixed-effects models Jun 28