# [R] repeated measure with quantitative independent variable

Cristiano Alessandro cri.alessandro at gmail.com
Mon Dec 14 20:10:44 CET 2015

```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
> 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
>>
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