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Cristiano Alessandro

2015-Dec-14 19:10 UTC

[R] repeated measure with quantitative independent variable

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-bounces at r-project.org] On Behalf Of
>> Cristiano Alessandro
>> Sent: Monday, December 14, 2015 8:43 AM
>> To: r-help at 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
>>
>> ______________________________________________
>> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide http://www.R-project.org/posting-
>> guide.html
>> and provide commented, minimal, self-contained, reproducible code.

Fox, John

2015-Dec-14 19:37 UTC

head link

[R] repeated measure with quantitative independent variable

Dear Cristiano,
> -----Original Message-----
> From: Cristiano Alessandro [mailto:cri.alessandro at gmail.com]
> Sent: Monday, December 14, 2015 2:11 PM
> To: Fox, John
> Cc: r-help at r-project.org
> Subject: Re: [R] repeated measure with quantitative independent variable
> 
> 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?
I defined only one (linear) contrast for the factor -- but I made a mistake in
how I did it, see below.
> 
> 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?
There are two differences: (1) The repeated-measures analysis reported by
default by Anova() is a MANOVA; if you want the univariate analysis comparable
to aov(), you have to ask for it. (2) As I mentioned, I made a mistake in
defining the contrasts for the factor; what I did implicitly included the
quadratic component, which wasn't my intention.

Here's the correct version, which, as you can see, produces the same result
as aov():
> contrasts(myfactor_nc, 1) <- matrix(-1:1, ncol=1)
> contrasts(myfactor_nc)  [,1]
1   -1
2    0
3    1
> idata <- data.frame(myfactor_nc)
> summary(Anova(mlm1, idata=idata, idesign=~myfactor_nc), multivariate=FALSE)Note: model has only an intercept; equivalent type-III tests substituted.

Univariate Type III Repeated-Measures ANOVA Assuming Sphericity

                SS num Df Error SS den Df      F   Pr(>F)   
(Intercept) 187.27      1     12.4      4 60.409 0.001477 **
myfactor_nc  14.40      1      3.6      4 16.000 0.016130 * 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05
'.' 0.1 ' ' 1
> summary(am1_nc) # your result using aov()
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     

My apologies for the confusion about the contrasts.

John
          > 
> 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-bounces at r-project.org] On Behalf Of
> >> Cristiano Alessandro
> >> Sent: Monday, December 14, 2015 8:43 AM
> >> To: r-help at 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
> >>
> >> ______________________________________________
> >> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more,
see
> >> https://stat.ethz.ch/mailman/listinfo/r-help
> >> PLEASE do read the posting guide http://www.R-project.org/posting-
> >> guide.html
> >> and provide commented, minimal, self-contained, reproducible code.

R help - Dec 2015 - repeated measure with quantitative independent variable

[R] repeated measure with quantitative independent variable

[R] repeated measure with quantitative independent variable