[R-sig-ME] To conjoin or not to conjoin factorial variables?

[Douglas Bates]

On Sat, Oct 17, 2009 at 10:33 AM, Antoine Tremblay <trea26 at gmail.com> wrote:
> Hello all,
>
> We are interested in an interaction between FACTOR A (levels "a" and
> "b"), FACTOR B (levels "c" and "d") and variable TIME (which we model
> with a 5 knot restricted cubic spline). That is:
>
>              m1=
> lmer(LogRT~A*B*rcs(TIME,5)+(1|Subject)+(1|Item)+(1|TIME)+(0+TIME|Subject),data=dat).
>              (1)

I'm not sure I understand the model specification.  Is TIME numeric or
a factor or ...?  It unusual to have a term (1|TIME), which would
indicate that TIME is a factor with a large number of levels, and
another term of the form (0+TIME|Subject), which would indicate that
TIME is a continuous covariate or a factor with a small number of
levels.

> Because (i) plotLMER.fnc cannot plot 3-way interactions,

Are you referring to a function in the languageR package?

> and (ii) we
> are unable to look at the contrasts of interest, which are ("ac" vs.
> "bc"), ("ad" vs. "bd"), ("bc" vs. "bd"), and ("ac" vs. "ad"), we
> decided to collapse factors A and B into a new variable ConjVar with 4
> levels "ac", "ad", "bc", and "bd". The model thus becomes:
>
>              m2=lmer(LogRT~ConjVar*rcs(TIME,5)+(1|Subject)+(1|Item)+(1|TIME)+(0+TIME|Subject),data=dat)
>          (2)
>
> We find significant differences in the first spline only between
> levels "ac" and "bc", between "ad" and "bd", between "bc" and "bd",
> but not between "ac" and "ad". Having the ConjVar also enables us to
> plot the ConjVar*rcs(TIME,5) interaction with plotLMER.fnc():
>
>              plotLMER.fnc(m2,pred="TIME",intr=list("ConjVar",levels(dat$ConjVar),"mid",list(1:4,rep(1,4))),lwd=2)
>       (3)
>
> Now, here comes the part we don't understand.
>
> If we do "anova(m1)", the interaction A*B*rcs(TIME,5) is not
> significant, but if we look at the table returned by "anova(m2)", then
> the ConjVar*rcs(TIME,5) interaction is highly significant. The
> questions we have are the following:
>
>   (i)  Is it correct to conjoin factors A and B into ConjVar and run
> our analyses using this variable?
>
>   (ii) Why is the interaction A*B*rcs(TIME,5) not significant in (1)
> but highly significant in (2)?
>
>   (iii) Would the proper steps here rather be:
>                        (I) run the model with A*B*rcs(TIME,5) and see
> if this interaction is significant
>                            (as shown in the "anova(m1)" table);
>                        (II) and, if it is significant, then refit a
> model with the conjoined variable ConjVar and
>                             determine where the actual differences
> are and plot them?
>
> Thank you very much for your time,
>
> --
> Antoine Tremblay
> Department of Neuroscience
> Georgetown University
> Washington DC
>
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