Helios de Rosario
2012-Jun-12 11:35 UTC
[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
www.ibv.org
Antes de imprimir este e-mail piense bien si es necesario hacerlo.
En cumplimiento de la Ley Org?nica 15/1999 reguladora de la Protecci?n
de Datos de Car?cter Personal, le informamos de que el presente mensaje
contiene informaci?n confidencial, siendo para uso exclusivo del
destinatario arriba indicado. En caso de no ser usted el destinatario
del mismo le informamos que su recepci?n no le autoriza a su divulgaci?n
o reproducci?n por cualquier medio, debiendo destruirlo de inmediato,
rog?ndole lo notifique al remitente.
ONKELINX, Thierry
2012-Jun-12 12:17 UTC
[R] Two-way linear model with interaction but without one main effect
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 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 www.ibv.org
Antes de imprimir este e-mail piense bien si es necesario hacerlo.
En cumplimiento de la Ley Org?nica 15/1999 reguladora de la Protecci?n de Datos
de Car?cter Personal, le informamos de que el presente mensaje contiene
informaci?n confidencial, siendo para uso exclusivo del destinatario arriba
indicado. En caso de no ser usted el destinatario del mismo le informamos que su
recepci?n no le autoriza a su divulgaci?n o reproducci?n por cualquier medio,
debiendo destruirlo de inmediato, rog?ndole lo notifique al remitente.
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