statistics - how to evaluate ANOVA repeated measures in R?

Question

I need to do an ANOVA analysis between the proportions of natural area for some study areas that I am evaluating, however, I encountered a difficulty when evaluating my data.

My data set is extremely large but I will try to reproduce it with fictitious data here, so that you can better understand.

I have 80 study areas divided into two regions, totaling 40 areas for each region, within each region I have four categories totaling ten study areas for each category. For each study area I have 11 buffers from 0 to 10 km away.

My data set has four predictor variables which are:

• Region: with two levels (North, South)

• Category: with four levels, (Category: A, B, C and D) -areas: with 80 study areas

• Distances: with 11 levels (distances ranging from 0 to 10 kilometers)

And as a Response variables:

• Proportion: with the proportion of natural area for each distance

I know that it would be necessary for me to do ANOVA of repeated measures but I am not able to do it, precisely because I have measures that are repeated within my sample units

I tried to do this, but I know it is wrong, because my distances from 0 to 10 are pseudo-replicas:

Reproducible example:

    My_data<-data.frame(Area= rep(sprintf("area[%d]",seq(1,80, 1)),each=11),
             Region = factor(rep(c("North","South"), each=440)),
             Category= factor(rep(c("A","B", "C", "D"), each=11, times=20)),
             Distances=factor(rep(c(seq(0,10,1)), times=80)),
             Proportion=  c(sample.int(101,size=880,replace=TRUE)-1)/1000)
 

Data Structure:

str(My_data)
'data.frame':   880 obs. of  5 variables:
 $ Area      : Factor w/ 80 levels "area[1]","area[10]",..: 1 1 1 1 1 1 1 1 1 
 1 ...
 $ Region    : Factor w/ 2 levels "North","South": 1 1 1 1 1 1 1 1 1 1 ...
 $ Category  : Factor w/ 4 levels "A","B","C","D": 1 1 1 1 1 1 1 1 1 1 ...
 $ Distances : Factor w/ 11 levels "0","1","2","3",..: 1 2 3 4 5 6 7 8 9 10 
  ...
 $ Proportion: num  0.076 0.032 0.013 0.013 0.037 0.07 0.045 0.046 0.093 
 0.067 ...

     library(stats)
     modelo1<- aov ( Proportion ~ Category + Region * Distances, My_Data)
     
     Anova(modelo1, type=3, test="F")
     
     modelo2<- aov (Proportion ~ Category + Region + Distances, My_Data) 
       
     Anova(modelo2, type=3, test="F")
    

question from:https://stackoverflow.com/questions/65925088/how-to-evaluate-anova-repeated-measures-in-r

Answer 1

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