[R-sig-ME] No data for 1 interaction combination: problem in R not in Genstat

[Ben Bolker]

Roger Humphry <roger.w.humphry at ...> writes:

> 
> I've found that when I do a linear mixed model either with lme or lmer 
> with interactions amongst some fixed effects that if there are any 
> interaction levels unoccupied with data that the model fails.
> "Error in MEEM(object, conLin, control$niterEM) :
>    Singularity in backsolve at level 0, block 1" for lme and
> 
> "Error in mer_finalize(ans) : Downdated X'X is not positive definite, 
> 6." in lmer.
> 
> Strangely in Genstat the model does produce output.
> My solutions will be either to use Genstat or to create a single new 
> factor variable which has the levels of the interaction that *are* 
> represented in the interaction.
> 
> I haven't found anything about this when searching. I guess that this 
> may be deliberate (e.g. Genstat uses a fudge considered inappropriate) 
> but please could anybody advise me?
> I can provide a simple fictitious example that I invented in which the 
> interaction would be of interest but can't be modelled. (I haven't 
> posted it here because I'm unsure about the etiquette of posting large 
> e-mails containing data onto the discussion list).

  I don't know that the fudge is inappropriate, it may just not
have been implemented.  For example, lm() in base R is sensible
about setting empty factor levels to NA (if Genstat gives you an
*estimate* for the interaction term with the missing levels,
that would be weird).

  One way of posting compact examples is to make them from
synthesized data, for example:

d <- expand.grid(f1=LETTERS[1:3],f2=letters[1:3],rep=1:5)
d2 <- subset(d, !(f1=="A" & f2=="a"))


with(d2,table(f1,f2))

   f2
f1  a b c
  A 0 5 5
  B 5 5 5
  C 5 5 5

d3 <- data.frame(d2,y=runif(nrow(d2)))

lm(y~f1*f2,data=d3)

Call:
lm(formula = y ~ f1 * f2, data = d3)

Coefficients:
(Intercept)          f1B          f1C          f2b          f2c      f1B:f2b  
    0.60964     -0.32352     -0.15239      0.13997     -0.11326      0.10615  
    f1C:f2b      f1B:f2c      f1C:f2c  
   -0.03831      0.47481           NA  

  showing in this case that lm() does a sensible thing, setting
one confounded parameter to NA.

  If you have long examples you can also try posting the data
somewhere and supplying a URL.

  Your solutions sound sensible.