[R] Two-way linear model with interaction but without one main effect

[Helios de Rosario]

Thanks for the suggestion, Thierry.

Nevertheless, in this example I'm not considering "shoe" as a random,
nuisance factor with zero mean. I'm considering three specific shoe
models, and I'm interested in modelling how the output changes between
the different shoes for those grounds, given that the average output is
the same for all shoes. That's not the type of question addressed by a
mixed model, I'm afraid.

Helios

>>> El día 12/06/2012 a las 14:17, "ONKELINX, Thierry"
<Thierry.ONKELINX at inbo.be>
escribió:
> Dear Helios,
> 
> I think you rather want a mixed model with shoe as random effect.
> 
> library(lme4)
> lmer(Y ~ Ground + (1|Shoe)) #the effect of shoe is independent of the
ground 
> effect
> or
> lmer(Y ~ Ground + (0 + Ground|Shoe)) #the effect of shoe is different
per 
> ground.
> 
> Best regards,
> 
> Thierry
> 
> 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-help-bounces at r-project.org
[mailto:r-help-bounces at r-project.org] 
> Namens Helios de Rosario
> Verzonden: dinsdag 12 juni 2012 13:35
> Aan: r-help at r-project.org 
> Onderwerp: [R] Two-way linear model with interaction but without one
main 
> effect
> 
> Hi,
> 
> I know that the type of model described in the subject line violates
the 
> principle of marginality and it is rare in practice, but there may be
some 
> circumstances where it has sense. Let's take this imaginary example
(not 
> homework, just a silly made-up case for illustrating the rare
situation):
> 
> I'm measuring the energy absorption of sports footwear in jumping. I
have 
> three models (S1, S2, S3), that are known by their having the same
average 
> value of this variable for different types of ground, but I want to
model the 
> energy absorption for specific ground types (grass, sand, and
pavement).
> 
> To fit the model I take 90 independent measures (different shoes,
different 
> users for each observation), with 10 samples per footwear model and
ground 
> type.
> 
> # Example data:
> shoe <- gl(3,30,labels=c("S1","S2","S3")) ground <- 
> rep(gl(3,10,labels=c("grass","sand","pavement")),3)
> Y <- rnorm(90,120,20)
> 
> My model may include a main effect of the ground type, and the
interaction 
> shoe:ground, but I think that in this peculiar case I could neglect
the main 
> effect of shoe, since my initial hypothesis is that the average
energy 
> absorption is the same for the three models.
> 
> My first thought was fitting the following model (with effect coding,
so 
> that the interaction coeffs have zero mean.):
> 
> mod1 <- lm(Y ~ ground + ground:shoe,
>     contrasts=list(shoe="contr.sum",ground="contr.sum"))
> 
> But this model has the same number of coefficients as a full
factorial, and 
> actually represents the same model subspace, isn't it? In fact, the
marginal 
> means are not the same for the three types of shoes:
> 
> # Marginal means for my (random) example data
>> tapply(predict(mod1),shoe,FUN=mean)
>       S1       S2       S3
> 116.3581 121.0858 118.3800
> 
> If I'm not mistaken, to create the model that I want I can start with
the 
> full factorial model and remove the part associated to the main shoe
> effect:
> 
> # Full model and its model matrix
> mod1 <- lm(Y~shoe*ground,
>     contrasts=list(shoe="contr.sum",ground="contr.sum"))
> X <- model.matrix(mod1)
> # Split X columns by terms
> X1 <- X[,1]
> X.shoe <- X[,2:3]
> X.ground <- X[,4:5]
> X.interact <- X[,6:9]
> # New model without method main effect
> mod2 <- lm(Y~X.ground+X.interact)
> 
> For this model the marginal means do coincide:
>> tapply(predict(mod2),shoe,FUN=mean)
>      S1      S2      S3
> 118.608 118.608 118.608
> 
> My questions are:
> Is this correct? And is there an easier way of doing this?
> 
> Thanks
> Helios De Rosario
> 
> --
> Helios de Rosario Martínez
> 
>  Researcher
> 
> 
> INSTITUTO DE BIOMECÁNICA DE VALENCIA
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  Antes de imprimir este e-mail piense bien si es necesario hacerlo.
En cumplimiento de la Ley Orgánica 15/1999 reguladora de la Protección
de Datos de Carácter Personal, le informamos de que el presente mensaje
contiene información confidencial, siendo para uso exclusivo del
destinatario arriba indicado. En caso de no ser usted el destinatario
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