This is a question about estimation and interpretation of random effects.
We would appreciate any comments or references.
We are monitoring several physical variables used to describe stream health
in over 200 streams in the NW. Monitoring will continue for several years,
and data are collected by crews, of which there are several in each year and
which change between years. Each stream will be measured once each season
by one crew. We would like to be able to put a number on the precision of
an observed stream value.
To assess variability due to different crews (the "repeat" study), we have
data from a study in which 7 crews sampled 6 streams for 30 or so variables;
each crew sampled each stream. We fit a random effects model with stream,
crew, and residual as random factors using PROC MIXED in SAS. We are
interpreting the variance component estimate for crew as estimating
variability due to crews; for stream as estimating variability among
streams; and for residual as capturing the unique inconsistencies of
different crews working in different streams. (But we are not positive that
our interpretations are correct.) We computed "estimates" (BLUPs) for each
stream and used the estimated "standard errors" to construct confidence
intervals. At the moment, we are evaluating precision based on 1) the width
of the confidence interval, 2) the width of the CI divided by the point
estimate, and 3) the proportion of total variability attributed to
crew+residual.
To assess variability due to measuring streams at different times of the
season (the "temporal" study), we have data from a study in which 3 crews
each measured 3 different streams (thus, 9 different streams), at 3 times
over the summer (each stream was measured by only one crew). We fit a
random effects model with crew, stream within crew, and residual (which we
considered as the date effect) as random factors, and acquired estimates
both for each stream and for each crew at each stream. We are interpreting
the variance component estimate for crew as estimating variability due to
crews; for stream within crew as estimating variability among streams; and
for residual as estimating variability due to dates. Because of the
(really) small number of crews in the temporal study, we think that the
estimate of crew variability in the repeat study likely is better than the
estimate of crew variability in the temporal study.
Our question is, how do we combine crew variability (from the repeat study)
with temporal variability (from the temporal study) to obtain a measure of
precision for any given stream measured by any given crew in any given year?
Can we calculate an interval estimate?
Thanks in advance for any help.
Nick Bouwes
[EMAIL PROTECTED]
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