[R] repeated measure with quantitative independent variable

[Fox, John]

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
> 
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