Two-way linear model with interaction but without one main effect
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 d?a 12/06/2012 a las 14:17, "ONKELINX, Thierry"
<Thierry.ONKELINX at inbo.be> escribi?:
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
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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 Mart?nez Researcher INSTITUTO DE BIOMEC?NICA DE VALENCIA Universidad Polit?cnica de Valencia ? Edificio 9C Camino de Vera
s/n ? 46022
VALENCIA (ESPA?A) Tel. +34 96 387 91 60 ? Fax +34 96 387 91 69
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