Dear list,

 I have encountered many cases where lmer() with default starting values yield wrong estimates but it yields the good estimates when restarted with the wrong estimates as starting values for the new lmer() launching.

Thus I use a code such as:

fit <- lmer(y ~ (1|day), data=dd) 
vc <- VarCorr(fit)
names(vc) <- NULL
refit <-  lmer(y ~ (1|day), data=dd, start=list(ST=vc)) 

and the good estimates are given in the refit object.

With lme4 development version, I think the option  control=list(restart=TRUE)  directly performs such a restarting (please correct me if I'm wrong). But here I'm talking about the CRAN version.


My problem is that there are some cases for which the opposite happens ! Consider the following dataset :

day        y
A 2.666890
A 2.599832
B 2.605875
B 2.646852
C 2.668442
C 2.683047

Then lmer() returns the good estimates with the default starting values (this is a balanced case and the REML estimates should coincide with the traditional least-squares estimates - lme4 development as well as SAS returns the good estimates)). But when I relaunch lmer() with the good estimates as starting values it gives wrong results. How can one explain that ?

Below are the outputs. All the best,
Stéphane


> ( fit <- lmer(y ~ (1|day), data=dd) )
Linear mixed model fit by REML 
Formula: y ~ (1 | day) 
   Data: dd 
    AIC    BIC logLik deviance REMLdev
 -11.66 -12.28  8.828   -24.26  -17.66
Random effects:
 Groups   Name        Variance   Std.Dev.
 day      (Intercept) 0.00018152 0.013473
 Residual             0.00106489 0.032633
Number of obs: 6, groups: day, 3

Fixed effects:
            Estimate Std. Error t value
(Intercept)  2.64516    0.01543   171.5
> vc <- VarCorr(fit)
> names(vc) <- NULL
> ( refit <- lmer(y ~ (1|day), data=dd, start=list(ST=vc)) )
Linear mixed model fit by REML 
Formula: y ~ (1 | day) 
   Data: dd 
   AIC    BIC logLik deviance REMLdev
 -11.6 -12.23  8.802   -24.37   -17.6
Random effects:
 Groups   Name        Variance   Std.Dev.  
 day      (Intercept) 3.9871e-11 6.3144e-06
 Residual             1.2101e-03 3.4787e-02
Number of obs: 6, groups: day, 3

Fixed effects:
            Estimate Std. Error t value
(Intercept)   2.6452     0.0142   186.3
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