Randomly assign teachers to classrooms imposing restrictions - r

Question

This question is very similar to a question I asked before. The added complication is that I have N schools with G grades and C classrooms. Additionally, I want to assign each of T teachers to 2 classrooms within a single school and grade.
I can generate some fake data with the following code:
library(randomNames)
set.seed(6232015)
n.schools <-20
gen.names <- function(n, which.names = "both", name.order = "last.first"){
names <- unique(randomNames(n=n, which.names = which.names, name.order = name.order))
need <- n - length(names)
while(need>0){
names <- unique(c(randomNames(n=need, which.names = which.names, name.order = name.order), names))
need <- n - length(names)
}
return(names)
}
#Generates the classrooms data frame
grade <- c(3,4,5)
classroom <- c(LETTERS[1:4])
classroom <- expand.grid(grade=c(3,4,5),
classroom=c(LETTERS[1:4]),
School.ID=paste0(gen.names(n = n.schools, which.names = "last"), ' School'))
#Generates teachers data frame
n.teachers=nrow(classroom)/2
gen.teachers <- function(n.teachers){
Teacher.ID <- gen.names(n = n.teachers, name.order = "last.first")
Teacher.exp <- runif(n = n.teachers, min = 1, max = 30)
Teacher.Other <- sample(c(0,1), replace = T, prob = c(0.5, 0.5), size = n.teachers)
Teacher.RE <- rnorm(n = n.teachers, mean = 0, sd = 1)
Teachers <- data.frame(Teacher.ID, Teacher.exp, Teacher.Other, Teacher.RE)
return(Teachers)
}
Teachers <- gen.teachers(n.teachers = n.teachers)
The data frame that I want to create would have 240 rows with 7 variables. Using sample like in the answer to my previous question will not work (I think) because of the restrictions I want to impose. I thought about using group_by() but I don't think that would do the trick...
Thanks!

Answer 1

This works, but I'm hopping to learn a more elegant solution
library(randomNames)
library(dplyr)
set.seed(6232015)
n.schools <-20
n.grades <- 3
n.classrooms <- 4
total.classrooms <- n.classrooms*n.grades*n.schools
gen.names <- function(n, which.names = "both", name.order = "last.first"){
names <- unique(randomNames(n=n, which.names = which.names, name.order = name.order))
need <- n - length(names)
while(need>0){
names <- unique(c(randomNames(n=need, which.names = which.names, name.order = name.order), names))
need <- n - length(names)
}
return(names)
}
#Generates teachers data frame
n.teachers=total.classrooms/2
gen.teachers <- function(n.teachers){
Teacher.ID <- gen.names(n = n.teachers, name.order = "last.first")
Teacher.exp <- runif(n = n.teachers, min = 1, max = 30)
Teacher.Other <- sample(c(0,1), replace = T, prob = c(0.5, 0.5), size = n.teachers)
Teacher.RE <- rnorm(n = n.teachers, mean = 0, sd = 1)
Teachers <- data.frame(Teacher.ID, Teacher.exp, Teacher.Other, Teacher.RE) %>% mutate(Teacher.ID=as.character(Teacher.ID))
return(Teachers)
}
Teachers <- gen.teachers(n.teachers = n.teachers)
str(Teachers$Teacher.ID)
#Make a ‘schoolGrade’ object and then reshape
schoolGrade <- expand.grid(grade = c(3,4,5),
School.ID = paste0(gen.names(n = n.schools, which.names = "last"),
' School'))
# assign each of T teachers to 2 classrooms within a single school and grade
cuttoff1<-n.teachers/2
schoolGrade$A <- Teachers$Teacher.ID[1:cuttoff1]
schoolGrade$B <- Teachers$Teacher.ID[1:cuttoff1]
schoolGrade$C <- Teachers$Teacher.ID[(cuttoff1+1):n.teachers]
schoolGrade$D <- Teachers$Teacher.ID[(cuttoff1+1):n.teachers]
library(tidyr)
schoolGrade <- gather(schoolGrade, Classroom, Teacher.ID, A:D) %>% full_join(Teachers, by="Teacher.ID")
The main problem is if i want to increase n.classrooms from 4 to 20. In that case instead of having 4 lines going from A to D I would have 20, plus the additional cutoffs. Which is very complicated...

Answer 2

This answer allows me to easily set n.classrooms to whatever value, for example 20.
The problem is that this code is painfully slow. Suggestion to improve it are very welcome!
library(dplyr)
library(randomNames)
library(geosphere)
set.seed(7142015)
# Define Parameters
n.Schools <- 20
first.grade<-3
last.grade<-5
n.Grades <-last.grade-first.grade+1
n.Classrooms <- 20 # THIS IS WHAT I WANTED TO BE ABLE TO CHANGE
n.Teachers <- (n.Schools*n.Grades*n.Classrooms)/2 #Two classrooms per teacher
# Define Random names function:
gen.names <- function(n, which.names = "both", name.order = "last.first"){
names <- unique(randomNames(n=n, which.names = which.names, name.order = name.order))
need <- n - length(names)
while(need>0){
names <- unique(c(randomNames(n=need, which.names = which.names, name.order = name.order), names))
need <- n - length(names)
}
return(names)
}
# Generate n.Schools names
gen.schools <- function(n.schools) {
School.ID <-
paste0(gen.names(n = n.schools, which.names = "last"), ' School')
School.long <- rnorm(n = n.schools, mean = 21.7672, sd = 0.025)
School.lat <- rnorm(n = n.schools, mean = 58.8471, sd = 0.025)
School.RE <- rnorm(n = n.schools, mean = 0, sd = 1)
Schools <-
data.frame(School.ID, School.lat, School.long, School.RE) %>%
mutate(School.ID = as.character(School.ID)) %>%
rowwise() %>% mutate (School.distance = distHaversine(
p1 = c(School.long, School.lat),
p2 = c(21.7672, 58.8471), r = 3961
))
return(Schools)
}
Schools <- gen.schools(n.schools = n.Schools)
# Generate Grades
Grades <- c(first.grade:last.grade)
# Generate n.Classrooms
Classrooms <- LETTERS[1:n.Classrooms]
# Group schools and grades
SchGr <- outer(paste0(Schools$School.ID, '-'), paste0(Grades, '-'), FUN="paste")
#head(SchGr)
# Group SchGr and Classrooms
SchGrClss <- outer(SchGr, paste0(Classrooms, '-'), FUN="paste")
#head(SchGrClss)
# These are the combination of School-Grades-Classroom
SchGrClssTmp <- as.matrix(SchGrClss, ncol=1, nrow=length(SchGrClss) )
SchGrClssEnd <- as.data.frame(SchGrClssTmp)
# Assign n.Teachers (2 classroom in a given school-grade)
Allpairs <- as.data.frame(t(combn(SchGrClssTmp, 2)))
AllpairsTmp <- paste(Allpairs$V1, Allpairs$V2, sep=" ")
library(stringr)
xm <- do.call(rbind, str_split(string = AllpairsTmp, pattern = "-"))
separoPairs <- as.data.frame((xm), stringsAsFactors = FALSE)
separoPairs <- separoPairs %>% select(-V7) %>% #Drops empty column
mutate(V1=as.character(V1), V4=as.character(V4), V2=as.numeric(V2), V5=as.numeric(V5)) %>% mutate(V4 = trimws(V4, which = "both"))
#Only the rows with V1=V4 and V2=V5 are valid
validPairs <- separoPairs %>% filter(V1==V4 & V2==V5) %>% select(V1, V2, V3, V6)
# Generate n.Teachers
gen.teachers <- function(n.teachers){
Teacher.ID <- gen.names(n = n.teachers, name.order = "last.first")
Teacher.exp <- runif(n = n.teachers, min = 1, max = 30)
Teacher.Other <- sample(c(0,1), replace = T, prob = c(0.5, 0.5), size = n.teachers)
Teacher.RE <- rnorm(n = n.teachers, mean = 0, sd = 1)
Teachers <- data.frame(Teacher.ID, Teacher.exp, Teacher.Other, Teacher.RE)
return(Teachers)
}
Teachers <- gen.teachers(n.teachers = n.Teachers) %>%
mutate(Teacher.ID = as.character(Teacher.ID))
# Randomly assign n.Teachers teachers to the "ValidPairs"
TmpAssignments <- validPairs[sample(1:nrow(validPairs), n.Teachers), ]
Assignments <- cbind.data.frame(Teachers$Teacher.ID, TmpAssignments)
names(Assignments) <- c("Teacher.ID", "School.ID", "Grade", "Class_1", "Class_2")
# Tidy Data
library(tidyr)
TeacherClassroom <- Assignments %>%
gather(x, Classroom, Class_1,Class_2) %>%
select(-x) %>%
mutate(Teacher.ID = as.character(Teacher.ID))
# Merge
DF_Classrooms <- TeacherClassroom %>% full_join(Teachers, by="Teacher.ID") %>% full_join(Schools, by="School.ID")
rm(list=setdiff(ls(), "DF_Classrooms")) # Clean the work space!
Thanks!