Hi mixed-modellers

I am fitting a simple linear mixed model to some abundance data which are mean densities on the log10 scale for a set of spatial cells with sample sizes used as prior weights. I define a random cell intercept model and fit a linear year trend. I get very similar estimates of the intercept and slope when using each of lmer(.) and asreml(.) but get much smaller estimates of the SEs of these parameters for lmer(.). This is due to a much smaller estimate of the residual standard error with estimate of 0.534 for lmer and 3.016 for asreml with corresponding estimates of the cell-level standard deviation of 0.0014 for lmer and  0.2151 (=0.04626^0.5) for asreml. Comparing these to a simple lm(.) fit gives a similar but slightly higher estimate of the residual standard error compared to the asreml estimate with the a value of 3.116. The lmer estimate appears to be orders of magnitude out. Am I interpreting these results correctly? Has it something to do with how the weighting is done? Reading the lm( ), lmer( ), and asreml( ) documentation I cannot see a difference in how these prior weights are handled. Any clarification would be appreciated.


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> library(lattice)
> library(asreml, verbose=T)
> library(lme4, verbose=T)
Loading required package: Matrix

Attaching package: 'lme4'

># use lmer and include random cell intercepts
>
> lme.02 <- lmer(log10Abund ~ YEAR.vcentred + (1|cell.f), weights=data.tab.sci$vT_noshots, data=data.tab.sci)
> summary(lme.02)
Linear mixed model fit by REML
Formula: log10Abund ~ YEAR.vcentred + (1 | cell.f)
   Data: data.tab.sci
   AIC   BIC logLik deviance REMLdev
558.1 568.8 -275.1    539.5   550.1
Random effects:
Groups   Name        Variance  Std.Dev.
cell.f   (Intercept) 0.0014489 0.038065
Residual             0.2849452 0.533803
Number of obs: 106, groups: cell.f, 10

Fixed effects:
               Estimate Std. Error t value
(Intercept)    1.006344   0.019176   52.48
YEAR.vcentred -0.005477   0.001286   -4.26

Correlation of Fixed Effects:
            (Intr)
YEAR.vcntrd 0.191
> anova(lme.02)
Analysis of Variance Table
              Df Sum Sq Mean Sq F value
YEAR.vcentred  1 5.1711  5.1711  18.148

># use asreml and include random cell intercepts

> asreml.02 <-asreml(fixed = log10Abund ~  YEAR.vcentred,
+        random=~ cell.f, weights=vT_noshots,
+        data=data.tab.sci, na.method.Y = "exclude",
+        na.method.X = "exclude", maxiter=50)

asreml(): 3.0.1 Library: 3.01gl IA32  Run: Mon Feb 18 12:53:25 2013

     LogLik         S2      DF
    -46.5028      8.4276   104  12:53:25  (1 component(s) restrained)
    -41.2529      9.0284   104  12:53:25
    -41.2395      9.0656   104  12:53:25
    -41.2362      9.0952   104  12:53:25
    -41.2362      9.0966   104  12:53:25
    -41.2362      9.0967   104  12:53:25

Finished on: Mon Feb 18 12:53:25 2013
LogLikelihood Converged
>
> summary(asreml.02)
$call
asreml(fixed = log10Abund ~ YEAR.vcentred, random = ~cell.f,
    data = data.tab.sci, weights = vT_noshots, na.method.Y = "exclude",
    na.method.X = "exclude", maxiter = 50)

$loglik
[1] -41.23618

$nedf
[1] 104

$sigma
[1] 3.016078

$varcomp
                     gamma  component std.error  z.ratio constraint
cell.f!cell.f.var 0.005085 0.04625686 0.0534366 0.865640   Positive
R!variance        1.000000 9.09672869 1.3140724 6.922548   Positive

attr(,"class")
[1] "summary.asreml"

> anova(asreml.02)
Wald tests for fixed effects

Response: log10Abund

Terms added sequentially; adjusted for those above

              Df Sum of Sq Wald statistic Pr(Chisq)
(Intercept)    1    839.78         92.317    <2e-16 ***
YEAR.vcentred  1      5.17          0.568    0.4509
residual (MS)         9.10
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> asreml.02$coefficients$fixed
YEAR.vcentred   (Intercept)
 -0.005476788   1.006336847
> ((asreml.02$vcoeff$fixed)^0.5)
[1] 0.002408342 0.035927218
> summary(asreml.02)$sigma
[1] 3.016078

># use lm and ignore random cell intercepts

> lm.02 <- lm(log10Abund ~ YEAR.vcentred, weights=data.tab.sci$vT_noshots, data=data.tab.sci)
>
> summary(lm.02)

Call:
lm(formula = log10Abund ~ YEAR.vcentred, data = data.tab.sci,
    weights = data.tab.sci$vT_noshots)

Weighted Residuals:
     Min       1Q   Median       3Q      Max
-11.0579  -1.9706  -0.6171   1.6421   6.9404

Coefficients:
               Estimate Std. Error t value Pr(>|t|)
(Intercept)    1.083599   0.053572   20.23   <2e-16 ***
YEAR.vcentred -0.002986   0.007107   -0.42    0.675
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 3.116 on 104 degrees of freedom
Multiple R-squared: 0.001695,   Adjusted R-squared: -0.007904
F-statistic: 0.1766 on 1 and 104 DF,  p-value: 0.6752

Information on package 'lme4'

Description:

Package:            lme4
Version:            0.999375-42
Date:               2011-10-02

Dr Steven G. Candy
Senior Applied Statistician
Wildlife Conservation and Fisheries
Australian Antarctic Division
203 Channel Hwy, Kingston, Tasmania, 7050, Australia
ph: (+61) 3 62 323135


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