# [R-sig-ME] Interpreting 2-way aov interaction

Brandstätter Christian bran.chri at gmail.com
Fri Feb 13 15:28:24 CET 2015

```Thank you for the answer, also for the very useful link.
However, we are thinking to stick with aov(), for its easier
interpretation.
There is a strong interaction between the variables, but even for each
group seperately the difference between the treatments remains significant.
And the interaction is in so far of importance, as that we want to know if
the treatment would differ even without the influence from other factors.
With best regards
Brandstätter Christian

2015-02-13 10:19 GMT+01:00 ONKELINX, Thierry <Thierry.ONKELINX at inbo.be>:

> Dear Christian,
>
> If the interaction is important, you can model it by a random slope. See
> the example below. Caveat: a random effect with only 4 levels is not a good
> idea. See http://glmm.wikidot.com/faq for more details.
>
> f2 <- factor(c(rep(seq(1,4),each=20)))
> meas <- factor(c(rep(1,18),c(rep(2,44),c(rep(1,18)))))
> df <- data.frame(f2,meas)
> df\$interaction <- interaction(df\$meas, df\$f2)
>
> rf <- rnorm(length(levels(df\$interaction)))
> main <- c(10, 20)
> noise <- rnorm(nrow(df), sd = 0.1)
> df\$res <- main[df\$meas] + rf[df\$interaction] + noise
>
>
> library(lme4)
> model.interaction <- lmer(res ~ meas + (0 + meas|f2), data = df)
> model.no.interaction <- lmer(res ~ meas + (1|f2), data = df)
> anova(model.interaction, model.no.interaction)
>
> Best regards,
>
> ir. Thierry Onkelinx
> Instituut voor natuur- en bosonderzoek / Research Institute for Nature and
> Forest
> team Biometrie & Kwaliteitszorg / team Biometrics & Quality Assurance
> Kliniekstraat 25
> 1070 Anderlecht
> Belgium
> + 32 2 525 02 51
> + 32 54 43 61 85
> Thierry.Onkelinx at inbo.be
> www.inbo.be
>
> To call in the statistician after the experiment is done may be no more
> than asking him to perform a post-mortem examination: he may be able to say
> what the experiment died of.
> ~ Sir Ronald Aylmer Fisher
>
> The plural of anecdote is not data.
> ~ Roger Brinner
>
> The combination of some data and an aching desire for an answer does not
> ensure that a reasonable answer can be extracted from a given body of data.
> ~ John Tukey
>
> -----Oorspronkelijk bericht-----
> Van: R-sig-mixed-models [mailto:r-sig-mixed-models-bounces at r-project.org]
> Namens Brandstätter Christian
> Verzonden: vrijdag 13 februari 2015 9:58
> Aan: r-sig-mixed-models at r-project.org
> Onderwerp: [R-sig-ME] Interpreting 2-way aov interaction
>
> Dear community,
>
> I encountered a problem with an experimental setup; we had one treatment
> step and a few mixing steps in a laboratory experiment.
> The data was stored in a usual dataframe (df as below, long format) with
> the categorial variables as factors left.
> We could clearly observe an interaction between mixing (f2) and treatment
> (meas) by applying aov as in the (extreme) example below.
>
> f2 <- factor(c(rep(seq(1,4),each=20)))
> meas <- factor(c(rep(1,18),c(rep(2,44),c(rep(1,18)))))
> res <- 15*as.numeric(f2)*as.numeric(meas)
> df <- data.frame(f2,meas,res)
> summary(aov(data=df,res~f2*meas))
>
> My question is, would there be a way to somehow "exclude" the variation
> from the mixing step?
> Would it be correct to include an error term as follows:
> summary(aov(data=df,res~meas+Error(f2)))
>
> And would that mean, what I am thinking it does: the treatment is still
> significant, even if the variation through mixing (f2) is considered?
> One obvious alternative I could think of would be to separate the mixing
> steps, but of course in the experiment there were a few of them.
>
> Another option would be a lmer-model I found, but the interpretation of
> the output is harder to interpret:
> library(lme4)
> mix.model = lmer(res ~ meas + (1|f2),data=df)
> summary(mix.model)
>
> I am unfortunately not very familiar with mixed anova-setups and available
> sources usually mention rather catchy examples from psychology which I find
> hard to translate for this case.
>
> Best regards
> Brandstätter Christian
>
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>
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