Dear John,
thanks for your reply! The reason why I did not want to factorize the
within-subjects variable was to avoid increasing the Df of the model
from 1 (continuous variable) to k-1 (where k is the number of levels of
the factors). I am now confused, because you have factorized the
variable (indeed using "factor"), but the Df of myfactor_nc seems to be
1. Could you explain that?
Comparing the results obtained with the two methods I seem to get
completely different results:
* aov()*
dv <- c(1,3,4,2,2,3,2,5,6,3,4,4,3,5,6);
subject <-
factor(c("s1","s1","s1","s2","s2","s2","s3","s3","s3","s4","s4","s4","s5","s5","s5"));
myfactor_nc <- c(1,2,3,1,2,3,1,2,3,1,2,3,1,2,3)
mydata_nc <- data.frame(dv, subject, myfactor_nc)
am1_nc <- aov(dv ~ myfactor_nc + Error(subject/myfactor_nc), data=mydata_nc)
summary(am1_nc)
Error: subject
Df Sum Sq Mean Sq F value Pr(>F)
Residuals 4 12.4 3.1
Error: subject:myfactor_nc
Df Sum Sq Mean Sq F value Pr(>F)
myfactor_nc 1 14.4 14.4 16 0.0161 *
Residuals 4 3.6 0.9
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Error: Within
Df Sum Sq Mean Sq F value Pr(>F)
Residuals 5 1.333 0.2667
*Anova()*
dvm <- with(mydata_nc, cbind(dv[myfactor_nc==1],dv[myfactor_nc==2],
dv[myfactor_nc==3]))
mlm1 <- lm(dvm ~ 1)
myfactor_nc <- factor(1:3)
contrasts(myfactor_nc) <- matrix(-1:1, ncol=1)
idata <- data.frame(myfactor_nc)
Anova(mlm1, idata=idata, idesign=~myfactor_nc)
Note: model has only an intercept; equivalent type-III tests substituted.
Type III Repeated Measures MANOVA Tests: Pillai test statistic
Df test stat approx F num Df den Df Pr(>F)
(Intercept) 1 0.93790 60.409 1 4 0.001477 **
myfactor_nc 1 0.83478 7.579 2 3 0.067156 .
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Why is that?
Thanks a lot
Cristiano
On 12/14/2015 05:25 PM, Fox, John wrote:
Dear Cristiano,
If I understand correctly what you want to do, you should be able to use
Anova() in the car package (your second question) by treating your numeric
repeated-measures predictor as a factor and defining a single linear contrast
for it.
Continuing with your toy example:
myfactor_nc <- factor(1:3)
contrasts(myfactor_nc) <- matrix(-1:1, ncol=1)
idata <- data.frame(myfactor_nc)
Anova(mlm1, idata=idata, idesign=~myfactor_nc)
Note: model has only an intercept; equivalent type-III tests substituted.
Type III Repeated Measures MANOVA Tests: Pillai test statistic
Df test stat approx F num Df den Df Pr(>F)
(Intercept) 1 0.93790 60.409 1 4 0.001477 **
myfactor_nc 1 0.83478 7.579 2 3 0.067156 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
With just 3 distinct levels, however, you could just make myfactor_nc an
ordered factor, not defining the contrasts explicitly, and then you'd get both
linear and quadratic contrasts.
I hope this helps,
John
-----------------------------------------------
John Fox, Professor
McMaster University
Hamilton, Ontario, Canada
http://socserv.socsci.mcmaster.ca/jfox/
-----Original Message-----
From: R-help [mailto:r-help-boun...@r-project.org] On Behalf Of
Cristiano Alessandro
Sent: Monday, December 14, 2015 8:43 AM
To: r-help@r-project.org
Subject: [R] repeated measure with quantitative independent variable
Hi all,
I am new to R, and I am trying to set up a repeated measure analysis
with a quantitative (as opposed to factorized/categorical)
within-subjects variable. For a variety of reasons I am not using
linear-mixed models, rather I am trying to fit a General Linear Model (I
am aware of assumptions and limitations) to assess whether the value of
the within-subjects variable affects statistically significantly the
response variable. I have two questions. To make myself clear I propose
the following exemplary dataset (where myfactor_nc is the quantitative
within-subjects variable; i.e. each subject performs the experiment
three times -- nc_factor=1,2,3 -- and produces the response in variable
dv).
dv <- c(1,3,4,2,2,3,2,5,6,3,4,4,3,5,6);
subject <-
factor(c("s1","s1","s1","s2","s2","s2","s3","s3","s3","s4","s4","s4","s5
","s5","s5"));
myfactor_nc <- c(1,2,3,1,2,3,1,2,3,1,2,3,1,2,3)
mydata_nc <- data.frame(dv, subject, myfactor_nc)
*Question 1 (using function aov)*
Easily done...
am1_nc <- aov(dv ~ myfactor_nc + Error(subject/myfactor_nc),
data=mydata_nc)
summary(am1_nc)
Unlike the case when myfactor_nc is categorical, this produces three
error strata: Error: subject, Error: subject:myfactor_nc, Error: Within.
I cannot understand the meaning of the latter. How is that computed?
*Question 2 (using function lm)*
Now I would like to do the same with the functions lm() and Anova()
(from the car package). What I have done so far (please correct me if I
am mistaking) is the following:
# Unstack the dataset
dvm <- with(mydata_nc, cbind(dv[myfactor_nc==1],dv[myfactor_nc==2],
dv[myfactor_nc==3]))
#Fit the linear model
mlm1 <- lm(dvm ~ 1)
(is that model above correct for my design?)
Now I should use the Anova function, but it seems that it only accepts
factors, and not quantitative within-subject variable.
Any help is highly appreciated!
Thanks
Cristiano
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