thr3ads.net - R help - [R] repeated measure with quantitative independent variable [Dec 2015]

If this information is useful, please help other people find it:
Share via:

Cristiano Alessandro

2015-Dec-14 13:43 UTC

[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

Fox, John

2015-Dec-14 16:25 UTC

head link

[R] repeated measure with quantitative independent variable

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.

Cristiano Alessandro

2015-Dec-14 19:10 UTC

head link

[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.

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

[R] repeated measure with quantitative independent variable

[R] repeated measure with quantitative independent variable

[R] repeated measure with quantitative independent variable