Counting Frequencies of Sequences - r

Question

Suppose there are two students - each student takes an exam multiple times (e.g.result_id = 1 is the first exam, result_id = 2 is the second exam, etc.). The student can either "pass" (1) or "fail" (0).
The data looks something like this:
library(data.table)
my_data = data.frame(id = c(1,1,1,1,1,1,2,2,2,2,2,2,2,2,2), results = c(0,1,0,1,0,0,1,1,1,0,1,1,0,1,0), result_id = c(1,2,3,4,5,6,1,2,3,4,5,6,7,8,9))
my_data = setDT(my_data)
id results result_id
1: 1 0 1
2: 1 1 2
3: 1 0 3
4: 1 1 4
5: 1 0 5
6: 1 0 6
7: 2 1 1
8: 2 1 2
9: 2 1 3
10: 2 0 4
11: 2 1 5
12: 2 1 6
13: 2 0 7
14: 2 1 8
15: 2 0 9
I am interested in counting the number of times that a student passes an exam, given that the student passed the previous two exams.
I tried to do this with the following code:
my_data$current_exam = shift(my_data$results, 0)
my_data$prev_exam = shift(my_data$results, 1)
my_data$prev_2_exam = shift(my_data$results, 2)
# Count the number of exam results for each record
out <- my_data[!is.na(prev_exam), .(tally = .N), by = .(id, current_exam, prev_exam, prev_2_exam)]
out = na.omit(out)
My code produces the following results:
> out
id current_exam prev_exam prev_2_exam tally
1: 1 0 1 0 2
2: 1 1 0 1 1
3: 1 0 0 1 1
4: 2 1 0 0 1
5: 2 1 1 0 2
6: 2 1 1 1 1
7: 2 0 1 1 2
8: 2 1 0 1 2
9: 2 0 1 0 1
However, I do not think that my code is correct.
For example, with Student_ID = 2 :
My code says that "Current_Exam = 1, Prev_Exam = 1, Prev_2_Exam = 0" happens 1 time, but looking at the actual data - this does not happen at all
Can someone please show me what I am doing wrong and how I can correct this?
Note: I think that this should be the expected output:
> expected_output
id current_exam prev_exam prev_2_exam tally
1: 1 0 1 0 2
2: 1 1 0 1 1
3: 1 0 0 1 1
4: 2 1 0 0 1
5: 2 1 1 0 1
6: 2 1 1 1 1
7: 2 0 1 1 2
8: 2 1 0 1 2
9: 2 0 1 0 0

Answer 1

You did not consider that you can not shift the results over id without placing NA.
. <- my_data[order(my_data$id, my_data$result_id),] #sort if needed
.$p1 <- ave(.$results, .$id, FUN = \(x) c(NA, x[-length(x)]))
.$p2 <- ave(.$p1, .$id, FUN = \(x) c(NA, x[-length(x)]))
aggregate(list(tally=.$p1), .[c("id","results", "p1", "p2")], length)
# id results p1 p2 tally
#1 1 0 1 0 2
#2 2 0 1 0 1
#3 2 1 1 0 1
#4 1 0 0 1 1
#5 1 1 0 1 1
#6 2 1 0 1 2
#7 2 0 1 1 2
#8 2 1 1 1 1
.
# id results result_id p1 p2
#1 1 0 1 NA NA
#2 1 1 2 0 NA
#3 1 0 3 1 0
#4 1 1 4 0 1
#5 1 0 5 1 0
#6 1 0 6 0 1
#7 2 1 1 NA NA
#8 2 1 2 1 NA
#9 2 1 3 1 1
#10 2 0 4 1 1
#11 2 1 5 0 1
#12 2 1 6 1 0
#13 2 0 7 1 1
#14 2 1 8 0 1
#15 2 0 9 1 0
An option would be to use filter to indicate those which had passed 3 times in a row.
cbind(., n=ave(.$results, .$id, FUN = \(x) filter(x, c(1,1,1), sides=1)))
# id results result_id n
#1 1 0 1 NA
#2 1 1 2 NA
#3 1 0 3 1
#4 1 1 4 2
#5 1 0 5 1
#6 1 0 6 1
#7 2 1 1 NA
#8 2 1 2 NA
#9 2 1 3 3
#10 2 0 4 2
#11 2 1 5 2
#12 2 1 6 2
#13 2 0 7 2
#14 2 1 8 2
#15 2 0 9 1
If olny the number of times that a student passes an exam, given that the student passed the previous two exams:
sum(ave(.$results, .$id, FUN = \(x) filter(x, c(1,1,1))==3), na.rm=TRUE)
#[1] 1
sum(ave(.$results, .$id, FUN = \(x)
x==1 & c(x[-1], 0) == 1 & c(x[-1:-2], 0, 0) == 1))
#[1] 1

Answer 2

When trying to count events that happen in series, cumsum() comes in quite handy. As opposed to creating multiple lagged variables, this scales well to counts across a larger number of events:
library(tidyverse)
d <- my_data |>
group_by(id) |> # group to cumulate within student only
mutate(
csum = cumsum(results), # cumulative sum of results
i = csum - lag(csum, 3, 0) # substract the cumulative sum from 3 observation before. This gives the number of exams passed in the current and previous 2 observations.
)
# Ungroup to get global count
d |>
ungroup() |>
count(i == 3) # Count the number of cases where the number of exams passes within 3 observations equals 3
#> # A tibble: 2 × 2
#> `i == 3` n
#> <lgl> <int>
#> 1 FALSE 14
#> 2 TRUE 1
# Retaining the group gives counts by student
d |>
count(i == 3) # Count the number of cases where the number of exams passes within 3 observations equals 3
#> # A tibble: 3 × 3
#> # Groups: id [2]
#> id `i == 3` n
#> <dbl> <lgl> <int>
#> 1 1 FALSE 6
#> 2 2 FALSE 8
#> 3 2 TRUE 1
Since you provided the data as data.table, here is how to do the same in that ecosystem:
my_data[ , csum := cumsum(results), .(id)]
my_data[ , i := csum - lag(csum, 3, 0), .(id)]
my_data[ , .(n_cases = sum(i ==3)), id]
#> id n_cases
#> 1: 1 0
#> 2: 2 1

Answer 3

Here's an approach using dplyr. It uses the lag function to look back 1 and 2 results. If the sum together with the current result is 3, then the condition is met. In the example you provided, the condition is only met once
my_data %>%
group_by(id) %>%
mutate(threex = ifelse(results + lag(results,1) + lag(results, 2) == 3, 1, 0)) %>%
filter(!is.na(threex))
id results result_id threex
<dbl> <dbl> <dbl> <dbl>
1 1 0 3 0
2 1 1 4 0
3 1 0 5 0
4 1 0 6 0
5 2 1 3 1
6 2 0 4 0
7 2 1 5 0
8 2 1 6 0
9 2 0 7 0
10 2 1 8 0
11 2 0 9 0
If you then just want to capture the cases when the condition is met, add a filter.
my_data %>%
group_by(id) %>%
mutate(threex = ifelse(results + lag(results,1) + lag(results, 2) == 3, 1, 0)) %>%
filter(threex == 1)
id results result_id threex
<dbl> <dbl> <dbl> <dbl>
1 2 1 3 1
If you are looking to understand how many times the condition is met per id, you can do this.
my_data %>%
group_by(id) %>%
mutate(threex = ifelse(results + lag(results,1) + lag(results, 2) == 3, 1, 0)) %>%
filter(threex == 1) %>%
select(id) %>%
summarize(count = n())
id count
<dbl> <int>
1 2 1