
 Dear Ross,

 In our upcoming book "Zero Inflated Models and Generalized Linear
Mixed Models with R" (sorry for the advertising here) we have a
section in which we simulate data and apply GLMMs with and without an
observation level random effect. Just a plain simple linear mixed
model with a random intercept, and some extra noise added for the
OLRE.

 Y_ij = alpha + beta * X_ij + a_i + eps_ij

 a_i      ~ N(0, sigma1^2)
 eps_ij ~ N(0, sigma2^2)

 In most scenarios (different values for sigma1 and sigma2) both
variances are estimated close to what they should be. Occasionally I
see (real) data sets in which the OLRE consumes all the variation, and
the variance of the random effect a_i is nearly 0. This is confusing
as the steps are often along the lines of:

 Y_ij = alpha + beta * X_ij + a_i
 a_i      ~ N(0, sigma1^2)

 Sigma1 bigger than 0....but..he.....there is overdispersion....add
the OLRE.....and then the sigma1 is close to 0. I guess that is a
scenario where the a_i are all close to 0 anyway.

 To fully understand the mechanism of the OLRE I suggest that you
simulate data according to the model above..use different valeus for
sigma1 and sigma2...and then estimate them. It helps understanding
what such models do!

 In my opinion it is perhaps better to ask yourself the question why
there is overdispersion (zero inflation, correlation, outliers,
missing covariates, large variation in the data, non-linear patterns
modeled as linear). Instead of fixing the problem with a big canon the
like observation level REs I prefer to dig deeper and fix the problem
in the appropriate way.

 Alain
www.highstat.com [1]

	Hello all, I am comparing two GLMMs (please see below), one that
includes the observer-level random effect (OLRE) and one that does
not. As I understand it, without the OLRE the variance is absorbed in
the FINAL_ID_FAC (variance = ca. 0.14). By comparing the two models
there is clearly a considerable difference in the variance of the
FINAL_ID_FAC, and more importantly the OLRE, which now explains
considerably more of the variance (ca. 0.4) as compared to the
FINAL_ID_FAC (ca. 0.12). Ultimately, I am interested in using the
random effect (FINAL_ID_FAC) to make inference on the importance of
considering individual in the model. My concern is that the OLRE is
accounting for the variation within and between individuals, which is
what I am trying to (somehow) quantify. Previous researchers have
published without using OLRE (as this field of ecology is constantly
evolving this very understandable!). However, my results lead me to
different conclusions (by using the BLUPs for each ID in a subsequent
analysis) depending on whether or not I include or exclude the OLRE. I
have posted about this before (many thanks to David Duffy for his
reply) and I have read numerous posts from other members that
constantly post on this forum, perhaps I have missed the point, but I
am still not entirely comfortable with exactly what variation the OLRE
is accounting for. Many thanks for your time, and any advice you are
willing to share! Ross
########################################################################################
Generalized linear mixed model fit by the Laplace approximation
Formula: cbind(PC_C_T, PC_C_F) ~ S_ACT_PUP_PROP + S_POOL_DIST + (1 |
FINAL_ID_FAC) Data: MODEL_DATA_ID_2009 AIC BIC logLik deviance 1149
1170 -570.4 1141 Random effects: Groups Name Variance Std.Dev.
FINAL_ID_FAC (Intercept) 0.14343 0.37872 Number of obs: 1525, groups:
FINAL_ID_FAC, 15 Fixed effects: Estimate Std. Error z value Pr(>|z|)
(Intercept) -3.95641 0.11727 -3374 < 2e-16 *** S_ACT_PUP_PROP 0.42450
0.05467 7.76 8.21e-15 *** S_POOL_DIST 0.15400 0.07245 2.13 0.0336 *
--- Signif. codes: 0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1
Correlation of Fixed Effects: (Intr) S_ACT_ S_ACT_PUP_P -0.170
S_POOL_DIST -0.079 -0.045
########################################################################################
Generalized linear mixed model fit by the Laplace approximation
Formula: cbind(PC_C_T, PC_C_F) ~ S_ACT_PUP_PROP + S_POOL_DIST + (1 |
FINAL_ID_FAC) + (1 | OBS_INDEX) Data: MODEL_DATA_ID_2009 AIC BIC
logLik deviance 1144 1171 -567.2 1134 Random effects: Groups Name
Variance StdDev. OBS_INDEX (Intercept) 0.40142 0.63358 FINAL_ID_FAC
(Intercept) 011623 0.34092 Number of obs: 1525, groups: OBS_INDEX,
1525; FINAL_ID_FAC, 15 Fixed effects: Estimate Std. Error z value
Pr(>|z|) (Intercept) -4.13969 0.11132 -37.19 < 2e-16 ***
S_ACT_PUP_PROP 0.43440 0.05960 729 3.12e-13 *** S_POOL_DIST 0.15137
0.07498 2.02 0.0435 * --- Signif. codes: 0 ?***? 0.001 ?**? 0.01 ?*?
0.05 ?.? 0.1 ? ? 1 Correlation of Fixed Effects: (Intr) S_ACT_
S_ACT_PUP_P -0.179 S_POOL_DIST -0.081 -0038
########################################################################################


Links:
------
[1] http://www.highstat.com/


	[[alternative HTML version deleted]]


