All computations done in R 
 
 
# This script aims to illustrate how to identify IRPs and NIRPS in survey data by 
# reconstructing the steps taken by Sausen and Blasius for the PISA 2009 
# Principal Survey Data. 
 
# Step 1: Download the Data and Syntax File from: https://www.oecd.org/pisa/pisaproducts/pisa2009database-downloadabledata.htm - "School Questionare Data" and the corresponding SPSS Syntax file; alternately you can use the txt.file)  
# Step 2: Execute Syntax File on Raw Data in SPSS. Save Results in "*.sav" file  
# Step 3: specify the path to the file in this script via variable "sav_file" 
# Step 4: specify the country-subset you want to get the distance matrix for via variable "i"  
# Step 5: Install required libraries (if not already installed) # install.packages("<package-name>") 
# Step 5: Execute Script 
 
 
# load dataset ------------------------------------------------------------ 
 
library("foreign") 
library("stringdist") 
 
 
# Subset to country (names must match on of the Levels for Variable "CNT") 
 
i = "Slovenia" 
sav_file = "C:/Users/*****/Hamming/INT_SCQ09_DEC11.sav" 
   
dataset <- read.spss(sav_file, use.value.labels = TRUE, to.data.frame = TRUE) 
 
# Cleaning the Data -------------------------------------------------------- 
 
# remove nonrespondents (all cases with more than 20 % NAs) 
 
dataset <- dataset[which(rowMeans(!is.na(dataset)) > 0.2), ] 
 
 
# Select columns for transformation and control variables ----------------- 
 
# Select the questions you like to analyze into "ranges", all questions  
# are subsetted for the further concatenation into a single string. 
# 
# If you want to select the ranges by colum names instead of column numbers you 
# may use the following function on a equivalent list of start-stop vectors of 
# column names: 
# 
# ranges <- lapply(ranges_by_colname, function(x) match(x, colnames(dataset))) 
 
ranges = list( 
  c(6, 20),   # every question from "SC01Q01" to "SC02Q01" (15 variables in total) 
  c(25, 26),  # questions "SC04Q01" and "SC05Q01" 
  c(41, 225)  # every question from "SC11Q01" to "SC27Q01" (185 variables in total) 
) 
 
# in addition to the variables for the following concatenation we also need 
# information that allows to identify the cases in relation to the original 
# dataset. For PISA these variables are the country and school-id. To ease the 
# transformation of the analyzed variables this information is stored seperately 
# and merged afterwards 
 
control_vars <- dataset[c("CNT","SCHOOLID")] 
 
# subset the ranges into a dataframe 
 
dataset <- as.data.frame(lapply(ranges, function(x) dataset[x[1]:x[2]])) 
 
 
# create the string ------------------------------------------------------- 
 
# Create a single column containing a string variable. This string consists of the 
# concatenated list of items you selected in the previous step. 
 
# An easy way to get rid of factor levels and other forms of encoding is to 
# convert the dataframe to a matrix of integers. This way, the labels are 
# replaced by their actual raw value. 
# 
# E.g. the levels of SC04Q01 are reduced from 
# ["Village","Small Town","Town","City","Large City"]  
# to  
# [1,2,3,4,5] 
 
dataset <- data.matrix(dataset) 
 
# Set "NA" to "X" (since we need ONE character per item / column, "NA"s would 
# cause a lot of problems in further analysis 
dataset[is.na(dataset)] <- "X" 
 
# the actual concatenation. Per row, every value is merged into one large 
# string. The "as.vector" is a wrapper for removing attributes, which can be 
# outsourced into a separe step as well by the following: 
# attributes(dataset) <- NULL 
 
concat_string <- as.vector(apply(dataset, 1, paste0, collapse = "")) 
 
# rejoin the string with the control variables 
 
dataset <- cbind(control_vars, concat_string) 
 
 
# compute the distance matrix --------------------------------------------- 
 
# subset dataset to country "i". This is just optional. However, 
# computing a distance matrix for a large sample might take a significant amount 
# of time since the number of computations is n(n-1)/2 
 
dataset_nat <- dataset[dataset$CNT == i,] 
 
# subset the column of strings (again) into a new vector and associate each 
# concatenated string with the respective school-id. After computing the 
# distance matrix, this step allows us to easily identify the combination of 
# involved schools if a distance value is suspiciously small 
 
concat_string_nat <- dataset_nat$concat_string 
names(concat_string_nat) <- dataset_nat$SCHOOLID 
 
# compute distance matrix with the hamming method. This matrix is the basis 
# of all further analyses. By doing a "table(dist)"  you can already 
# take a quick look on the frequency patterns 
 
dist <- stringdistmatrix(concat_string_nat, method = "hamming", useNames = "names") 
 
 
# generate the plots ------------------------------------------------------ 
 
# plotting the frequencies of the distance values for the subset (intentionally 
# not as histogram since outliers are better to identify if bin width = 1) 
 
plot(table(dist), main = paste("Absolute Freq of HDs for", i)) 
 
# generating the qq plot for the subset 
 
qqnorm(dist, main = paste("Normal Dist. Q-Q Plot for", i)) 
 
# adding a reference line based on the mean and std-dev. of the distance matrix 
 
abline(mean(dist), sd(dist), col="Red") 
 
# Identify minimal distance pairs  
# generate the plots ------------------------------------------------------ 
 
# plotting the frequencies of the distance values for the subset (intentionally 
# not as histogram since outliers are better to identify if bin width = 1) 
 
plot(table(dist), main = paste("Absolute Freq of HDs for", i)) 
 
# generating the qq plot for the subset 
 
qqnorm(dist, main = paste("Normal Dist. Q-Q Plot for", i)) 
 
# adding a reference line based on the mean and std-dev. of the distance matrix 
 
abline(mean(dist), sd(dist), col="Red") 
 
# Identify minimal distance pairs ----------------------------------------- 
 
# In this step it is demonstrated how to identify the most similar match for each 
# case. To do so, isolate the lowest value per column and look up the 
# resepective row-name which contains the school-id (see line 106). In a second 
# step, write these case-combinations and the corresponding HD value into a 
# new dataframe 
 
# transform the numeric vector of the "distance matrix" into an actual matrix 
# (This is necessary since R stores symmetric distance matrix as a special 
# vector with the class "dist". For more information see the documentation on 
# dist() ) 
 
dist.min <- as.matrix(dist) 
 
# removing zeroes in diagonale 
 
diag(dist.min) <- NA 
 
# write the name of each column into a vector (not strictly necessary since the 
# information is already contained in the column-names as well as the orginial 
# dataset and the names of concat_string_nat. However, this step makes it easier 
# to understand our further procedure) 
 
case_1 <- colnames(dist.min) 
 
# identify HD minvalue per column and push the actual value to new vector 
 
min_HD <- apply(dist.min[, ], 2, min, na.rm = TRUE) 
 
# identify the *row-wise position* of the HD min value per column in the matrix 
# and push to new vector. Remember we have pushed the school-id to the dimnames 
# of our matrix (line 106) 
 
case_2 <- apply(dist.min[, ], 2, function(x) names(which.min(x))) 
 
# Finally, merge the verctors in to a new dataframe 
 
df.dist.min <- as.data.frame(cbind(case_1, case_2, min_HD)) 
 
# plotting the frequencies of the *minimum* distance values for the subset 
 
plot(table(df.dist.min$min_HD), main = paste("Absolute Freq of HD Min for", i)) 
 
___________________________________________________________________________________________________________________ 
___________________________________________________________________________________________________________________ 
 
Data preprocessed in SPSS, only Hamming distance computed in R 
 
 
# This script is for importing the *preprocessed* SPSS Data  
# Applicable when concatenation has been done via SPSS Code 
# in file **** 
 
SPSS-SYNTAX 
 
count help=SC01Q01 to SC02Q01, SC04Q01, SC05Q01,SC11Q01 to  SC27Q01 (MISSING). 
fre help. 
 
temporary. 
select if (help le 39 and country='705'). 
WRITE OUTFILE='C:/****/pisa2009/writeout.txt' 
   /1 country (a9) schoolid (a10) SC01Q01 to SC02Q01, SC04Q01, SC05Q01,SC11Q01 to  SC27Q01 (202f1.0). 
EXECUTE. 
 
 
# This script requires the packages "readr" and "stringdist" 
# Please ensure those packages are installed on your system 
# or install them via  
# install.packages("<package-name>") 
 
 
library(readr) 
library(stringdist) 
 
# load dataset - make sure to adjust the variable "sav_file" to match the path of your spss-output file 
 
sav_file = "C:/****/pisa2009/writeout.txt" 
 
dataset_nat <- read_table2(sav_file, col_names = FALSE, col_types = "ccc") 
 
# rename the columns to match the structure of dataset_nat in Hammingdistance.R 
colnames(dataset_nat) <- c("CNT","SCHOOLID","concat_string") 
 
# necessary for generating the plots in Hammingdistance.R 
i = "Slovenia" 
 
# NEXT STEP: 
 
concat_string_nat <- dataset_nat$concat_string 
names(concat_string_nat) <- dataset_nat$SCHOOLID 
 
# compute distance matrix with the hamming method. This matrix is the basis 
# of all further analyses. By doing a "table(dist)"  you can already 
# take a quick look on the frequency patterns 
 
dist <- stringdistmatrix(concat_string_nat, method = "hamming", useNames = "names") 
 
 
# generate the plots ------------------------------------------------------ 
 
# plotting the frequencies of the distance values for the subset (intentionally 
# not as histogram since outliers are better to identify if bin width = 1) 
 
plot(table(dist), main = paste("Absolute Freq of HDs for", i)) 
 
# generating the qq plot for the subset 
 
qqnorm(dist, main = paste("Normal Dist. Q-Q Plot for", i)) 
 
# adding a reference line based on the mean and std-dev. of the distance matrix 
 
abline(mean(dist), sd(dist), col="Red") 
 
# Identify minimal distance pairs  
 
# In this step it is demonstrated how to identify the most similar match for each 
# case. To do so, isolate the lowest value per column and look up the 
# resepective row-name which contains the school-id (see line 106). In a second 
# step, write these case-combinations and the corresponding HD value into a 
# new dataframe 
 
# transform the numeric vector of the "distance matrix" into an actual matrix 
# (This is necessary since R stores symmetric distance matrix as a special 
# vector with the class "dist". For more information see the documentation on 
# dist() ) 
 
dist.min <- as.matrix(dist) 
 
# removing zeroes in diagonale 
 
diag(dist.min) <- NA 
 
# write the name of each column into a vector (not strictly necessary since the 
# information is already contained in the column-names as well as the orginial 
# dataset and the names of concat_string_nat. However, this step makes it easier 
# to understand our further procedure) 
 
case_1 <- colnames(dist.min) 
 
# identify HD minvalue per column and push the actual value to new vector 
 
min_HD <- apply(dist.min[, ], 2, min, na.rm = TRUE) 
 
# identify the *row-wise position* of the HD min value per column in the matrix 
# and push to new vector. Remember we have pushed the school-id to the dimnames 
# of our matrix (line 106) 
 
case_2 <- apply(dist.min[, ], 2, function(x) names(which.min(x))) 
 
# Finally, merge the verctors in to a new dataframe 
 
df.dist.min <- as.data.frame(cbind(case_1, case_2, min_HD)) 
 
# plotting the frequencies of the *minimum* distance values for the subset 
 
plot(table(df.dist.min$min_HD), main = paste("Absolute Freq of HD Min for", i))