[R] linear mixed model question

[Jason Morgan]

Hello Wen:

On 2009.09.06 10:49:03, Wen Huang wrote:
> Hello,
> 
> I wanted to fit a linear mixed model to a data that is similar in  
> terms of design to the 'Machines' data in 'nlme' package except that  
> each worker (with triplicates) only operates one machine. I created a  
> subset of observations from 'Machines' data such that it looks the  
> same as the data I wanted to fit the model with (see code below).
> 
> I fitted a model in which 'Machine' was a fixed effect and 'Worker'  
> was random (intercept), which ran perfectly. Then I decided to  
> complicate the model a little bit by fitting 'Worker' within  
> 'Machine', which was saying variation among workers was nested within  
> each machine. The model could be fitted by 'lme', but when I tried to  
> get
> confidence intervals by 'intervals(fm2)' it gave me an error:
> 
> Error in intervals.lme(fm2) :
>    Cannot get confidence intervals on var-cov components: Non-positive  
> definite approximate variance-covariance
> 
> I am wondering if this is because it is impossible to fit a model like  
> 'fm2' or there is some other reasons?

The problem doesn't seem to be the model specification but is most likely the
result of estimating a more complicated model with very little data. Using
the complete Machines dataset with the same model specification seems to work
fine:

# ----------------------------------------------------------------------------- #

> fm3 <- lme(score ~ Machine, random = ~ Machine - 1 | Worker, data = Machines)
> intervals(fm3)
Approximate 95% confidence intervals

 Fixed effects:
                lower      est.    upper
(Intercept) 48.972459 52.355556 55.73865
MachineB     3.093747  7.966667 12.83959
MachineC    10.816607 13.916667 17.01673
attr(,"label")
[1] "Fixed effects:"

 Random Effects:
  Level: Worker 
                            lower      est.      upper
sd(MachineA)            2.1702468 4.0792807  7.6675752
sd(MachineB)            4.6301082 8.6252908 16.0677975
sd(MachineC)            2.3387870 4.3894795  8.2382579
cor(MachineA,MachineB)  0.1992744 0.8027499  0.9647702
cor(MachineA,MachineC) -0.1702480 0.6225047  0.9260744
cor(MachineB,MachineC)  0.1235115 0.7708309  0.9579666

 Within-group standard error:
    lower      est.     upper 
0.7629124 0.9615766 1.2119736 

# ----------------------------------------------------------------------------- # 

With the restricted dataset, there are only 18 observations in 6 groups. This is
probably too little data for the (restricted) maximum likelihood technique used
by lme().

Hope that helps,

~Jason


-- 
Jason W. Morgan
Graduate Student
Department of Political Science
*The Ohio State University*
154 North Oval Mall
Columbus, Ohio 43210