[R-sig-ME] Random vs. fixed effects
Gabor Grothendieck
ggrothendieck at gmail.com
Fri Apr 23 18:41:05 CEST 2010
Here is a simulation of 10k cases using 4 and 50 level factors for the
random effect. With 4 levels there are numerical problems and the
accuracy of the random effect is terrible. With 50 levels there are
no numerical problems and the accuracy is much better.
> library(lme4)
> set.seed(1)
> n <- 10000
> k <- 4
> f <- function(n, k) {
+ set.seed(1)
+ x <- 1:n
+ fac <- gl(k, 1, n)
+ fac.eff <- rnorm(k, 0, 4)[fac]
+ e <- rnorm(n)
+ y <- 1 + 2 * x + fac.eff + e
+ lmer(y ~ x + (1|fac))
+ }
> # simulation with 4 level random effect
> f(n, 4)
Linear mixed model fit by REML
Formula: y ~ x + (1 | fac)
AIC BIC logLik deviance REMLdev
28733 28762 -14363 28702 28725
Random effects:
Groups Name Variance Std.Dev.
fac (Intercept) 1.1162 1.0565
Residual 1.0298 1.0148
Number of obs: 10000, groups: fac, 4
Fixed effects:
Estimate Std. Error t value
(Intercept) 1.313e+00 5.286e-01 2
x 2.000e+00 3.515e-06 568923
Correlation of Fixed Effects:
(Intr)
x -0.033
Warning message:
In mer_finalize(ans) : false convergence (8)
> # simulation with 50 level random effect
> f(n, 50)
Linear mixed model fit by REML
Formula: y ~ x + (1 | fac)
AIC BIC logLik deviance REMLdev
29040 29069 -14516 29009 29032
Random effects:
Groups Name Variance Std.Dev.
fac (Intercept) 11.2016 3.3469
Residual 1.0251 1.0125
Number of obs: 10000, groups: fac, 50
Fixed effects:
Estimate Std. Error t value
(Intercept) 1.396e+00 4.738e-01 3
x 2.000e+00 3.507e-06 570242
Correlation of Fixed Effects:
(Intr)
x -0.037
On Fri, Apr 23, 2010 at 9:38 AM, Schultz, Mark R. <Mark.Schultz2 at va.gov> wrote:
> I just read a post by Andrew Dolman suggesting that a factor with only 3
> levels should be treated as a fixed effect. This seems to be a perennial
> question with mixed models. I'd really like to hear opinions from
> several experts as to whether there is a consensus on the topic. It
> really makes me uncomfortable that such an important modeling decision
> is made with an "ad hoc" heuristic.
>
>
>
> Thanks,
>
> Mark Schultz, Ph.D.
>
> Bedford VA Hospital
>
> Bedford, Ma.
>
>
> [[alternative HTML version deleted]]
>
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