# Calculate autocorrelation for multiple participants at once and including the (ac) values as variable in new dataframe

Hi all,

I'm analyzing time-series data, one of the variables I want to study is the autocorrelation. In the process of getting the data ready for analyses, I'm experiencing some difficulties.

My goal: one single continuous value per participant representing the autocorrelation of the participant at hand.

I have +-200 participants in my dataset, with 20 completed (repeated) measurements ('ratings') each. I know I can use the ACF-function to calculate autocorrelation, but I was wondering whether there is a way (or function) to manipulate the data in such way I can calculate the autocorrelation for each of the participants without needing to make a separate dataframe for each participant. I.e. without having to do the following 200 times

df = long dataframe with all measurements (ratings) of the participants

PIDENT 1

d<-subset(df, pid == "a")
d<-acf(d\$rating, plot = FALSE, lag.max=1)
d
Autocorrelations of series ‘d\$rating’, by lag
0 1
1.000 0.495

ac<-data.frame(pid="a", ac=d[["acf"]][2, ,1])
ac
pid ac
1 a 0.495

PIDENT 2

d<-subset(df, pid == "b")
d<-acf(d\$rating, plot = FALSE, lag.max=1)
d
Autocorrelations of series ‘d\$rating’, by lag
0 1
1.000 -0.250

ac2<-data.frame(pid="b", ac=d[["acf"]][2, ,1])
d2
pid ac
1 b -0.250

ac<-rbind(ac, ac2)

ac
pid ac
1 a 0.495
2 b -0.250

Hope you can help me!

Kind regards,
Rose

Indeed it can be simplified a lot!

set.seed(1)
df <- data.frame(pid = rep(letters[1:2], each=5),
rating = runif(10))
df
#    pid     rating
# 1    a 0.26550866
# 2    a 0.37212390
# 3    a 0.57285336
# 4    a 0.90820779
# 5    a 0.20168193
# 6    b 0.89838968
# 7    b 0.94467527
# 8    b 0.66079779
# 9    b 0.62911404
# 10   b 0.06178627

Now we can run your manual approach:

d<-subset(df, pid == "a")
d<-acf(d\$rating, plot = FALSE, lag.max=1)
ac<-data.frame(pid="a", ac=d[["acf"]][2, ,1])
d<-subset(df, pid == "b")
d<-acf(d\$rating, plot = FALSE, lag.max=1)
ac2<-data.frame(pid="b", ac=d[["acf"]][2, ,1])
ac<-rbind(ac, ac2)

ac
#   pid         ac
# 1   a -0.1840563
# 2   b  0.1849619

To simplify things, we can put the actual autocorrelation computation in a function, so we just need to call it with the data:

autocor <- function(x, ...){
acf(x, plot=FALSE, lag.max=1)[["acf"]][2, ,1]
}

autocor(df\$rating[1:5])
# [1] -0.1840563
autocor(df\$rating[6:10])
# [1] 0.1849619

So, the problem reduces to applying this function to every set of rating corresponding to a given pid. The package dplyr has functions for this purpose:

library(tidyverse)
df %>%
group_by(pid) %>%
summarize(ac = autocor(rating))
# A tibble: 2 x 2
#   pid       ac
#   <chr>  <dbl>
# 1 a     -0.184
# 2 b      0.185

That's it!

Many thanks Alexis, this is absolutely great!

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