Jesper Bruun 3/12/2020
This document is part of the supplement for: Bruun, J.; Evans, R.H. Network Analysis of Survey Data to Identify Non-Homogeneous Teacher Self-Efficacy Development in Using Formative Assessment Strategies. Educ. Sci. 2020, 10, 54. https://doi.org/10.3390/educsci10030054
It shows how to create similarity networks using our anonymised data and proceeds to show how we did the full analysis.
library(igraph)##
## Attaching package: 'igraph'
## The following objects are masked from 'package:stats':
##
## decompose, spectrum
## The following object is masked from 'package:base':
##
## union
library(PMCMRplus)
library(pgirmess)
library(effsize)
#library(rcompanion)
library(gplots)##
## Attaching package: 'gplots'
## The following object is masked from 'package:stats':
##
## lowess
source("R_scripts/backboneExtraction.r")
source("R_scripts/segregation.r")The full data set consists of 93 respondents, 64 of whom participated in the project. The data contains responses from pre intervention and post intervention to 12 questions about attributes of self-efficacy. See Bruun & Evans (2020) for details. Background variables are
- gender (however, the data is incomplete, so probably not very useful)
- years of teaching categories (1= less than 4 years, 2 = 5-10 years, 3 = 11-20 years, 4 = more than 20 years)
- local working group (LWG) number (the groups in which teachers worked during the intervention)
- STEM subjects taught by teacher (1 if they teach the subject, 0 if they do not)
## I5 Name pre38 pre39 pre40 pre41 pre42 pre43 pre44 pre45 pre46 pre47
## 1 1 Respondent 1 4 4 3 3 3 NA NA 3 3 3
## 2 2 Respondent 2 4 4 3 4 5 4 NA 2 4 5
## 3 3 Respondent 3 4 3 4 3 3 2 4 4 4 4
## 4 4 Respondent 4 4 NA 1 2 NA 4 2 1 NA 5
## 5 5 Respondent 5 4 2 3 4 4 4 5 3 4 3
## 6 6 Respondent 6 3 5 4 3 3 2 NA 2 3 NA
## 7 7 Respondent 7 4 5 4 3 2 3 3 4 3 3
## 8 8 Respondent 8 3 1 2 2 2 NA NA 2 NA 1
## 9 9 Respondent 9 5 5 5 5 2 4 2 5 2 3
## 10 10 Respondent 10 5 5 NA 5 5 5 5 4 NA 3
## 11 11 Respondent 11 4 5 1 4 3 3 2 3 NA 3
## 12 12 Respondent 12 5 5 3 NA 3 3 3 4 4 3
## 13 13 Respondent 13 4 5 3 4 4 NA NA 3 4 5
## 14 14 Respondent 14 5 3 3 5 5 1 1 3 NA 3
## 15 15 Respondent 15 5 5 3 4 4 2 4 3 5 4
## 16 16 Respondent 16 3 4 4 3 NA NA 5 3 NA 4
## 17 17 Respondent 17 1 4 3 1 3 2 2 2 NA NA
## 18 18 Respondent 18 NA NA 2 3 2 1 3 2 5 NA
## 19 19 Respondent 19 1 4 3 1 3 3 2 2 4 2
## 20 20 Respondent 20 2 5 3 1 2 3 2 4 5 1
## 21 21 Respondent 21 1 2 5 1 1 1 5 4 4 4
## 22 22 Respondent 22 4 1 5 1 1 2 3 2 5 1
## 23 23 Respondent 23 2 2 4 3 3 4 4 3 3 2
## 24 24 Respondent 24 1 4 4 1 NA 1 NA 1 5 3
## 25 25 Respondent 25 1 NA NA 1 2 1 NA 1 5 2
## 26 26 Respondent 26 1 NA NA 1 5 1 3 4 5 NA
## 27 27 Respondent 27 1 3 4 3 1 3 4 1 5 3
## 28 28 Respondent 28 1 NA NA 3 2 4 NA NA 5 3
## 29 29 Respondent 29 1 NA NA 1 4 4 2 NA 2 NA
## 30 30 Respondent 30 NA NA NA 3 2 3 3 NA NA 4
## 31 31 Respondent 31 NA 5 1 1 5 5 1 3 NA NA
## 32 32 Respondent 32 1 NA 1 3 4 4 1 NA NA NA
## 33 33 Respondent 33 NA NA NA NA NA NA NA NA NA NA
## 34 34 Respondent 34 2 1 NA 3 2 4 5 4 4 2
## 35 35 Respondent 35 NA NA NA 1 3 2 4 NA NA 2
## 36 36 Respondent 36 1 5 NA 1 NA 2 4 3 3 2
## 37 37 Respondent 37 1 5 3 1 3 3 NA NA NA 2
## 38 38 Respondent 38 1 5 NA 3 2 2 4 1 5 1
## 39 39 Respondent 39 4 2 4 3 4 4 3 3 5 NA
## 40 40 Respondent 40 4 3 3 NA 2 2 2 3 4 2
## 41 41 Respondent 41 1 4 2 1 5 NA 1 NA NA 4
## 42 42 Respondent 42 1 2 5 3 4 4 NA NA NA NA
## 43 43 Respondent 43 NA 3 2 NA NA 5 3 2 3 NA
## 44 44 Respondent 44 5 2 3 3 NA 2 2 3 NA 3
## 45 45 Respondent 45 5 2 2 3 3 2 3 2 2 3
## 46 46 Respondent 46 4 5 4 5 5 2 2 2 2 NA
## 47 47 Respondent 47 4 2 4 3 3 3 3 3 3 3
## 48 48 Respondent 48 5 2 3 4 4 2 4 4 2 4
## 49 49 Respondent 49 5 5 5 5 5 4 4 5 2 5
## 50 50 Respondent 50 2 4 4 2 3 3 1 2 3 2
## 51 51 Respondent 51 4 2 4 2 1 4 NA 2 NA 1
## 52 52 Respondent 52 NA NA 3 2 1 3 3 3 3 3
## 53 53 Respondent 53 5 5 NA 5 1 NA 5 NA 4 NA
## 54 54 Respondent 54 NA 1 1 1 1 NA 2 1 NA 2
## 55 55 Respondent 55 NA NA 1 1 1 4 NA NA NA 1
## 56 56 Respondent 56 5 3 3 1 1 5 5 4 1 1
## 57 57 Respondent 57 3 1 NA 4 1 1 2 3 2 1
## 58 58 Respondent 58 4 2 NA 2 2 NA NA 3 NA 2
## 59 59 Respondent 59 5 1 NA 1 1 3 4 NA 1 NA
## 60 60 Respondent 60 5 1 4 3 2 4 2 3 1 1
## 61 61 Respondent 61 3 2 4 4 3 3 2 2 4 2
## 62 62 Respondent 62 5 1 NA 1 1 5 5 NA 1 1
## 63 63 Respondent 63 NA NA NA NA NA NA NA NA NA NA
## 64 64 Respondent 64 4 2 2 2 2 NA 3 NA 4 2
## 65 65 Respondent 65 4 1 2 1 1 1 4 2 1 1
## 66 66 Respondent 66 4 1 4 1 1 4 4 4 1 4
## 67 67 Respondent 67 5 NA 3 3 NA 3 3 NA 4 4
## 68 68 Respondent 68 4 3 4 1 1 3 4 4 2 2
## 69 69 Respondent 69 3 2 NA NA 3 3 4 NA NA NA
## 70 70 Respondent 70 5 3 4 NA 1 NA 1 NA 2 NA
## 71 71 Respondent 71 5 3 NA 3 5 NA 2 2 NA NA
## 72 72 Respondent 72 5 5 3 2 4 5 5 4 4 NA
## 73 73 Respondent 73 5 5 3 2 5 2 2 5 5 5
## 74 74 Respondent 74 5 4 4 4 4 3 3 4 2 3
## 75 75 Respondent 75 5 5 4 5 5 3 5 4 5 5
## 76 76 Respondent 76 3 4 1 1 NA NA NA 2 NA 3
## 77 77 Respondent 77 5 4 1 4 5 5 NA 2 NA 4
## 78 78 Respondent 78 3 5 2 2 5 2 2 2 5 3
## 79 79 Respondent 79 4 4 NA NA 4 4 NA 3 4 5
## 80 80 Respondent 80 3 2 4 5 5 4 4 4 5 5
## 81 81 Respondent 81 5 5 2 5 5 2 NA 5 2 5
## 82 82 Respondent 82 4 4 2 2 4 5 5 3 4 2
## 83 83 Respondent 83 4 4 3 4 5 3 4 2 3 NA
## 84 84 Respondent 84 4 5 4 5 5 4 4 4 5 5
## 85 85 Respondent 85 3 5 5 5 5 1 3 4 4 2
## 86 86 Respondent 86 4 5 4 5 5 4 NA 4 5 5
## 87 87 Respondent 87 4 5 3 5 5 3 4 4 5 4
## 88 88 Respondent 88 NA 5 5 5 5 3 3 5 5 5
## 89 89 Respondent 89 4 4 2 3 4 4 3 4 NA 4
## 90 90 Respondent 90 4 4 4 5 5 5 4 4 5 4
## 91 91 Respondent 91 5 5 3 5 5 NA 3 3 1 5
## 92 92 Respondent 92 5 5 5 5 4 5 4 5 4 4
## 93 93 Respondent 93 3 5 3 5 4 4 3 3 4 2
## pre48 pre49 post38 post39 post40 post41 post42 post43 post44 post45 post46
## 1 3 3 4 4 3 3 3 3 4 3 3
## 2 3 2 5 4 4 4 5 5 4 4 4
## 3 5 4 4 4 3 NA 4 NA 3 4 4
## 4 4 2 3 4 3 NA 4 1 NA 2 3
## 5 4 3 4 1 4 3 4 3 4 4 4
## 6 4 4 4 5 3 NA 5 3 3 3 NA
## 7 3 4 3 2 4 2 5 4 2 4 4
## 8 NA 1 3 3 2 4 NA 2 1 2 2
## 9 5 5 5 5 4 4 4 3 4 5 4
## 10 NA NA 5 5 4 5 5 4 4 5 NA
## 11 3 4 5 5 5 5 5 3 5 5 NA
## 12 5 4 4 5 4 2 5 3 2 4 2
## 13 NA 2 5 4 4 5 5 4 4 4 4
## 14 3 3 5 4 3 3 3 1 1 3 3
## 15 NA 3 5 5 3 4 5 2 4 3 3
## 16 5 4 4 4 2 4 NA NA NA NA NA
## 17 3 4 NA 4 4 1 2 1 4 2 4
## 18 NA 3 2 2 4 3 1 2 5 3 3
## 19 2 5 2 4 3 3 4 4 5 5 5
## 20 1 3 1 5 4 3 2 1 4 1 5
## 21 2 1 3 1 5 3 1 1 5 4 4
## 22 NA 3 4 1 5 3 1 1 4 1 5
## 23 3 2 1 4 2 3 3 2 3 1 5
## 24 NA NA 1 5 4 1 2 1 NA NA 3
## 25 2 NA NA NA NA 1 3 1 4 1 5
## 26 NA 5 1 NA NA 1 3 2 4 3 1
## 27 2 2 3 2 4 1 1 2 5 2 5
## 28 4 2 NA NA NA 1 2 2 5 NA 5
## 29 NA 5 1 4 2 1 2 3 4 2 3
## 30 2 3 2 3 4 1 1 2 3 4 5
## 31 NA NA NA NA NA NA NA 5 NA NA 1
## 32 NA 5 NA NA NA 3 NA NA 1 NA NA
## 33 NA NA 1 4 2 3 4 4 1 NA 2
## 34 4 3 2 2 4 1 2 2 4 3 3
## 35 2 2 NA NA NA 1 2 2 4 4 5
## 36 NA 2 3 2 5 3 1 1 5 1 4
## 37 NA NA 1 5 1 1 3 2 NA NA NA
## 38 2 1 3 2 4 1 3 5 4 2 2
## 39 3 3 3 4 4 3 3 2 3 4 3
## 40 NA 4 NA NA NA NA NA NA NA NA NA
## 41 2 5 1 3 4 1 4 3 2 NA 2
## 42 2 4 1 3 4 3 NA 3 2 4 NA
## 43 NA 2 4 2 4 4 4 4 NA 3 1
## 44 1 2 5 3 4 5 5 3 NA 4 NA
## 45 4 2 5 2 3 5 3 3 2 2 2
## 46 NA 4 5 3 3 5 5 5 4 3 NA
## 47 3 3 4 2 4 3 3 2 3 4 2
## 48 5 3 4 4 4 4 4 3 3 4 2
## 49 5 5 5 5 5 5 5 5 4 5 2
## 50 5 5 3 2 4 2 2 4 1 5 2
## 51 3 4 NA 3 4 3 3 3 4 4 1
## 52 3 3 3 3 3 3 3 3 3 3 3
## 53 5 NA 3 NA 3 4 5 4 4 NA 5
## 54 4 5 3 4 3 5 4 4 NA NA 2
## 55 NA 3 3 4 3 4 5 4 1 NA NA
## 56 5 4 3 3 4 4 3 4 3 2 3
## 57 4 4 5 4 3 5 5 3 NA NA 5
## 58 4 NA 4 4 4 3 4 2 3 3 3
## 59 5 5 5 5 3 5 5 5 2 NA 5
## 60 4 2 NA 3 4 5 5 3 1 3 3
## 61 2 4 3 3 2 3 3 3 3 3 3
## 62 5 5 3 5 3 5 5 5 5 3 5
## 63 NA 5 NA NA NA 5 NA NA NA NA NA
## 64 4 4 3 NA 2 4 4 NA 3 2 4
## 65 3 3 3 2 1 2 5 NA 4 1 3
## 66 5 4 4 4 3 4 5 2 3 2 4
## 67 4 5 4 NA 3 4 4 4 4 NA 2
## 68 4 5 4 4 4 4 4 1 1 4 4
## 69 3 NA 4 3 3 3 4 4 4 3 4
## 70 NA 4 4 NA 3 4 4 NA 2 NA NA
## 71 1 4 3 4 2 NA 5 2 5 3 NA
## 72 5 5 5 5 4 3 4 3 5 4 NA
## 73 3 5 4 4 4 5 5 3 5 4 5
## 74 4 3 5 5 4 2 5 3 4 4 2
## 75 5 5 5 5 4 5 5 4 3 4 5
## 76 NA 3 4 2 5 5 5 4 3 4 4
## 77 3 2 3 5 1 5 5 3 NA 2 NA
## 78 5 3 5 5 4 5 5 2 NA 4 5
## 79 NA 2 4 4 3 4 5 4 2 4 4
## 80 4 5 5 5 5 5 5 4 5 5 5
## 81 NA 5 4 3 2 5 5 NA 1 2 NA
## 82 4 1 4 4 3 5 5 5 5 4 4
## 83 NA 3 NA 5 3 4 5 2 4 3 NA
## 84 4 5 5 5 4 5 5 5 5 5 5
## 85 3 5 4 4 4 4 4 2 4 4 NA
## 86 4 4 4 5 4 5 5 5 4 4 5
## 87 4 5 3 4 2 4 4 4 2 3 4
## 88 5 5 3 4 2 5 5 3 3 4 NA
## 89 3 3 3 4 2 3 4 4 2 3 4
## 90 5 2 4 5 4 4 4 5 4 4 4
## 91 5 5 5 5 5 5 4 4 2 5 3
## 92 5 5 4 5 5 5 5 4 3 5 4
## 93 5 5 5 5 4 5 5 4 3 4 5
## post47 post48 post49 control gender yearsTeaching LWG Physics Chemistry
## 1 3 3 2 n 1 3 1 1 1
## 2 4 4 3 n 2 4 1 1 1
## 3 5 5 4 n 1 2 1 0 0
## 4 5 3 3 n 1 3 1 1 0
## 5 4 4 3 n 1 3 1 1 1
## 6 5 4 3 n 2 3 1 1 0
## 7 5 5 4 n 1 3 1 0 0
## 8 2 3 3 n 2 1 1 0 0
## 9 5 4 5 n 1 4 1 0 0
## 10 5 4 5 n 2 4 1 1 1
## 11 4 4 5 n 2 2 1 0 0
## 12 4 4 4 n 2 2 1 0 1
## 13 5 4 5 n 1 2 1 0 0
## 14 3 3 4 y 1 2 1 0 0
## 15 5 NA 5 y 2 4 1 0 1
## 16 5 4 2 y 1 4 1 1 0
## 17 4 2 2 n 1 4 2 1 0
## 18 NA 2 3 n 2 2 2 0 0
## 19 2 2 3 n NA 1 2 0 0
## 20 2 2 2 n 2 4 2 0 0
## 21 3 3 2 n 2 3 2 0 0
## 22 NA NA 1 n 2 3 2 0 0
## 23 3 3 2 n 1 4 2 0 0
## 24 5 1 NA n 2 3 2 0 0
## 25 NA 1 3 n 1 2 2 1 0
## 26 5 1 2 n NA 2 2 1 0
## 27 4 1 2 n 1 4 2 0 0
## 28 NA NA 2 n 1 3 2 0 0
## 29 3 3 2 n 2 1 2 0 1
## 30 NA 2 2 n 1 2 2 0 1
## 31 NA NA 5 y 1 2 2 0 1
## 32 NA 1 5 y 2 2 2 0 0
## 33 4 2 5 y 1 2 2 0 0
## 34 3 3 2 y 2 2 2 0 0
## 35 2 NA 2 y 2 1 2 1 0
## 36 3 2 1 y 1 3 2 0 0
## 37 NA NA NA y 1 4 2 1 0
## 38 2 2 1 y 2 4 2 0 0
## 39 NA 3 3 y NA 2 2 0 0
## 40 NA NA NA y 2 3 2 1 1
## 41 3 2 4 y 1 3 2 0 1
## 42 NA 2 4 y 2 1 2 0 0
## 43 5 4 4 n 2 3 3 1 0
## 44 NA 4 5 n 2 3 3 0 0
## 45 3 4 2 n 1 3 3 0 0
## 46 5 4 4 n 2 4 3 0 0
## 47 3 4 3 n NA 3 3 1 1
## 48 4 4 4 n NA 3 3 0 0
## 49 5 5 5 n NA 3 3 0 0
## 50 2 5 NA y 1 4 3 0 0
## 51 5 4 2 n 2 4 4 0 0
## 52 3 3 3 n 2 4 4 0 0
## 53 5 5 1 n 2 1 4 0 0
## 54 2 5 1 n NA 4 4 0 0
## 55 5 NA 4 n 2 2 4 0 0
## 56 4 5 2 n 2 1 4 0 0
## 57 5 4 2 n NA 4 4 0 0
## 58 2 4 3 n 2 2 4 0 1
## 59 5 5 1 n 2 1 4 0 0
## 60 4 4 2 n 1 3 4 0 0
## 61 3 3 3 y 1 3 4 0 1
## 62 5 4 1 y 2 1 4 0 0
## 63 5 5 1 y 2 4 4 0 0
## 64 NA 4 2 y NA 4 4 0 0
## 65 5 2 NA y 2 4 4 0 0
## 66 3 4 3 y 2 4 4 0 0
## 67 2 4 2 y 2 4 4 0 0
## 68 4 4 2 y 2 4 4 0 0
## 69 4 5 3 y 2 4 4 0 0
## 70 4 4 2 y 2 1 4 1 1
## 71 2 1 3 n 2 3 6 1 1
## 72 4 5 5 n NA 3 6 1 1
## 73 4 2 2 n NA 3 6 1 1
## 74 3 4 4 n NA 3 6 1 1
## 75 5 5 3 n NA 2 6 0 0
## 76 2 3 4 n NA 4 6 0 0
## 77 5 4 3 n 2 2 6 0 0
## 78 5 3 4 n NA 2 6 0 0
## 79 4 NA 4 n 1 3 6 1 1
## 80 5 5 5 n 2 3 6 0 0
## 81 5 5 NA n 2 3 6 1 1
## 82 1 4 3 n NA 2 6 0 0
## 83 4 NA 3 n NA 3 6 0 0
## 84 1 5 5 n NA 3 6 0 0
## 85 5 4 5 n NA 3 6 1 1
## 86 5 4 4 n NA 4 6 0 0
## 87 3 4 4 y NA 4 6 0 0
## 88 NA 5 NA y NA 2 6 0 0
## 89 3 4 4 y NA 3 6 0 0
## 90 3 5 5 n NA 2 5 0 1
## 91 5 5 5 n NA 1 5 0 1
## 92 4 5 5 n NA 2 5 1 0
## 93 3 2 5 n NA 1 5 0 1
## Biology Technology Math Integrated X
## 1 0 0 0 0 1
## 2 1 0 1 0 2
## 3 0 1 0 0 3
## 4 0 0 1 0 4
## 5 1 0 1 0 5
## 6 0 0 1 0 6
## 7 1 0 0 0 7
## 8 0 0 1 0 8
## 9 0 1 0 0 9
## 10 1 0 1 0 10
## 11 1 0 0 0 11
## 12 1 0 0 0 12
## 13 1 0 0 0 13
## 14 1 0 0 0 14
## 15 0 1 1 0 15
## 16 0 0 1 0 16
## 17 0 0 0 0 17
## 18 0 0 1 1 18
## 19 0 0 1 1 19
## 20 0 0 1 1 20
## 21 1 0 0 0 21
## 22 0 0 0 1 22
## 23 0 0 1 1 23
## 24 1 0 0 0 24
## 25 0 0 1 0 25
## 26 0 0 1 0 26
## 27 1 0 0 0 27
## 28 1 0 1 1 28
## 29 0 0 0 0 29
## 30 0 0 1 0 30
## 31 1 0 0 0 31
## 32 0 0 1 1 32
## 33 1 0 0 0 33
## 34 1 0 0 0 34
## 35 0 0 1 0 35
## 36 1 0 0 0 36
## 37 0 0 1 0 37
## 38 0 0 1 1 38
## 39 0 0 1 1 39
## 40 1 0 0 0 40
## 41 1 0 0 0 41
## 42 1 0 0 0 42
## 43 0 0 0 0 43
## 44 1 0 1 0 44
## 45 0 0 1 0 45
## 46 0 0 1 0 46
## 47 0 0 1 0 47
## 48 0 0 1 0 48
## 49 0 0 1 0 49
## 50 0 0 1 0 50
## 51 0 0 1 0 51
## 52 0 0 1 0 52
## 53 0 0 1 0 53
## 54 1 0 0 0 54
## 55 0 0 1 0 55
## 56 1 1 1 0 56
## 57 1 0 1 0 57
## 58 1 0 0 0 58
## 59 0 0 1 0 59
## 60 1 0 1 0 60
## 61 1 0 0 0 61
## 62 0 0 1 0 62
## 63 0 0 1 0 63
## 64 1 0 1 0 64
## 65 0 0 1 0 65
## 66 1 0 1 0 66
## 67 1 0 1 0 67
## 68 1 0 1 0 68
## 69 0 0 1 0 69
## 70 1 0 0 0 70
## 71 0 0 0 0 71
## 72 0 0 0 0 72
## 73 0 0 0 0 73
## 74 0 0 0 0 74
## 75 0 0 1 0 75
## 76 1 0 0 0 76
## 77 0 0 1 0 77
## 78 1 0 0 0 78
## 79 0 0 0 0 79
## 80 0 0 0 1 80
## 81 0 0 0 0 81
## 82 0 1 0 0 82
## 83 1 0 0 0 83
## 84 1 0 0 1 84
## 85 0 0 0 0 85
## 86 0 1 0 0 86
## 87 0 1 0 0 87
## 88 1 0 0 0 88
## 89 0 0 1 0 89
## 90 1 0 1 1 90
## 91 0 0 1 0 91
## 92 0 0 1 1 92
## 93 1 0 0 0 93
Here is the overall idea behind the functions:
- Function ‘pmat’ replaces responses (here, 1, 2, 3, 4, 5 and NA) with
the information content in that response. E.g. if half had answered
1 and half had answered 5 on Q38 the probability of drawing a 1 at
ranom would be 0.5 and the information I = -log2(0.5) = 1. Then all
entries in the column corresonding to Q38 would be 1. Function
‘pmat’ uses function ‘probs’.
- Function ‘probs’ calculates the frequency of each question response. Here, a 1 on Q38, for example, is different from a 1 on Q39 and so on.
- Function ‘simRes’ calculates the similarity between two respondents.
It uses Lin’s (1998) information theoretical measure cited in Bruun
& Evans (2020). The function uses both the actual responses and
their information content as calculated by ‘pmat’.
- Function ‘simResk’ calculates the similarity between one respondent and all other respondents.
- Function ‘simMat’ runs ‘simResk’ for all respondents
#Function for calculating frequencies (here equated with probabilities) of responses
probs<-function(mydata,n){
a<-as.numeric(names(table(mydata[,n])))
p<-as.numeric(table(mydata[,n],useNA = "always")/length(resp))
x<-c(1:length(resp))
for(i in 1:length(a)){
x[which(mydata[,n]==a[i])]<-p[i]
}
x[which(is.na(mydata[,n]))]<-p[6]
return(x)
}
#Function which transforms frequencies/probabilities to information (bits)
pmat<-function(data){
pmat<-matrix(0,ncol=length(data),nrow=length(data[,1]))
for(j in 1:length(data)){
pmat[,j]<-probs(data,j)
}
infmat<--log2(pmat)
return(infmat)
}
#Function for calculating similarities between respondents
#The function uses Lin's (1998) information theoretical measure.
simRes<-function(i,j,infmat,d){
y<-infmat[i,]
overlap<-sum(y[which(d[i,1:12]==d[j,1:12])])
sinfi<-sum(infmat[i,])
sinfj<-sum(infmat[j,])
sim<-2*overlap/(sinfi+sinfj)
return(sim)
}
#Function for calculating similarity between k'th respondent and everyone else
simResk<-function(k,inf,d){
simVec<-vector()
for(i in 1:length(resp)){
simVec[i]<-simRes(k,i,inf,d)
}
return(simVec)
}
#Function for making similarity matrix. Really just a for-loop that uses simResk
simMatrix<-function(d){
inf<-pmat(d)
similarityMatrix<-matrix(data=0,ncol=length(d[,1]),nrow=length(d[,1]))
for(i in 1:length(resp)){
similarityMatrix[,i]<-simResk(i,inf,d)
}
return(similarityMatrix)
}Using the above fundtions, we make a pre intervention and a post intervention network for participating teacher. Then, we extract a backbone-version of those networks. The reasoning behind our use of backbone networks is:
- We use local adaptive networks sparsification (LANS) by Foti et al (2011). This algorithm evaluates links locally, via a threshold p-like value, and per node, rather than employing a global rule.
- We set the threshold value to the minimum value that still preserves overall network connectivity.
- A link is preserved if it is significant (below threshold) for at least one node.
#Name respondents
resp<-paste("R",c(1:length(mydata$X)),sep="")
#Identify which columns contain pre and which contain post responses.
names(mydata[3:14]) #Columns for pre## [1] "pre38" "pre39" "pre40" "pre41" "pre42" "pre43" "pre44" "pre45" "pre46"
## [10] "pre47" "pre48" "pre49"
names(mydata[15:26]) #Columns for post## [1] "post38" "post39" "post40" "post41" "post42" "post43" "post44" "post45"
## [9] "post46" "post47" "post48" "post49"
post<-mydata[15:26] #Responses to post survey questions
post[is.na(post)]<-100 #R does not like to perform calculations with NAs
pre<-mydata[3:14] # We will compare pre community structure with post community structure
pre[is.na(pre)]<-100
#Functions are now used to create a post similarity network
postSim<-simMatrix(post)
respTot<-resp
respT<-resp[mydata$control=="n"]
resp<-respT
preSimT<-simMatrix(pre[mydata$control=="n",])
postSimT<-simMatrix(post[mydata$control=="n",])
preNetT<-graph.adjacency(preSimT,diag=F,weighted=T)
postNetT<-graph.adjacency(postSimT,diag=F,weighted=T)
V(preNetT)$id<-respT
V(postNetT)$id<-respT
#Extract backbone networks
preNetBBT<-backboneNetwork(preNetT,0.0176,2) #Alpha value set to minimum value that keeps network connected
postNetBBT<-backboneNetwork(postNetT,0.0335,2)# This is the network we focus on in the article.
write.graph(postNetBBT,"postNetBBT.net",format=c("pajek"))
write.graph(preNetBBT,"preNetBBT.net",format=c("pajek"))For a simple comparison of raw and backbone post networks, the following code shows different representations of them
- The stored igraph objects with information about type, number of links and nodes.
- The cumulative degree distributions; the frequency of nodes with k connections or below.
- A force-based plot with LWG-labels.
postNetT## IGRAPH 5ea07e8 D-W- 64 3672 --
## + attr: id (v/c), weight (e/n)
## + edges from 5ea07e8:
## [1] 1-> 2 1-> 3 1-> 4 1-> 5 1-> 6 1-> 8 1-> 9 1->10 1->11 1->12 1->13 1->14
## [13] 1->15 1->16 1->17 1->18 1->19 1->20 1->21 1->22 1->23 1->24 1->25 1->26
## [25] 1->27 1->28 1->29 1->30 1->31 1->32 1->33 1->34 1->35 1->36 1->37 1->38
## [37] 1->39 1->40 1->41 1->42 1->43 1->44 1->45 1->46 1->47 1->48 1->50 1->51
## [49] 1->52 1->53 1->55 1->56 1->57 1->59 1->60 1->61 1->62 1->63 1->64 2-> 1
## [61] 2-> 3 2-> 4 2-> 5 2-> 6 2-> 7 2-> 8 2-> 9 2->10 2->11 2->12 2->13 2->14
## [73] 2->15 2->16 2->17 2->18 2->19 2->20 2->21 2->22 2->23 2->24 2->26 2->27
## [85] 2->28 2->29 2->30 2->31 2->32 2->33 2->34 2->35 2->36 2->37 2->38 2->39
## + ... omitted several edges
plot(postNetT, main="Post Net",sub="Labels show LWG-number",vertex.label=mydata$LWG[mydata$control=='n'])
plot(degree.distribution(postNetT,cumulative = T),log="xy", xlab="Degree, k",ylab="P(k>k')", main="Cumulative degree distribution")
postNetBBT## IGRAPH bb42f18 U-W- 64 106 --
## + attr: id (v/c), weight (e/n)
## + edges from bb42f18:
## [1] 1--20 1--26 1--30 1--35 1--36 2-- 5 2--13 2--56 2--61 3-- 6
## [11] 3--33 3--55 4--36 4--51 5--18 5--33 5--46 6--31 6--45 6--51
## [21] 6--57 7--12 7--50 7--53 8--45 8--55 9--10 9--13 9--46 9--59
## [31] 9--61 10--11 10--13 10--29 10--31 11--29 11--46 11--54 12--33 12--48
## [41] 13--29 13--64 14--17 14--26 15--16 15--24 15--27 16--42 17--19 17--20
## [51] 17--21 18--19 20--26 21--26 22--23 22--25 23--25 23--35 24--27 24--40
## [61] 28--33 28--59 29--41 29--51 30--32 30--41 31--60 32--42 33--47 33--48
## [71] 33--53 33--59 34--54 34--58 34--62 35--44 36--40 37--38 37--39 37--43
## + ... omitted several edges
plot(postNetBBT, main="Post Net Backbone",sub="Labels show LWG-number",vertex.label=mydata$LWG[mydata$control=='n'])
plot(degree.distribution(postNetBBT,cumulative = T),log="xy", xlab="Degree, k",ylab="P(k>k')", main="Cumulative degree distribution")
We used the version of infomap that can be downloaded from https://www.mapequation.org. Igraph also has a version of infomap installed, but we found that it was not as stable as the ones found on mapequation. Below we include the code we used to generate 1000 cluster solutions using a standard Mac terminal.
Code for running infomap 100 times and placing the results in a specific folder:
for i in {1..1000}; do ./pathToNetwork/[name].net /pathtoFolder/1000Infomaps[name]/
--out-name $i -2 --clu --map -s$i; done
The Data-folder contains the results of this code and we use those results for the further analysis. Below we evaluate the internal consistency of cluster solutions for the pre intervention and post intervention networks. Also, we compare the most frequent pre solution to the most frequent post solution.
files<-vector()
for (i in 1:1000){
files[i]<-paste("Data/1000InfomapsPreBBT/",i,".clu",sep = "")
}
#Read in cluster solutions
csvs<-lapply(files,read.csv,skip=2,header=F,sep="")
a<-matrix(data=0,nrow=1000,ncol=64)
for (i in 1:1000){
a[i,]<-csvs[[i]][ order(csvs[[i]][,1]),2 ]
}
comp<-function(j){
nmi<-vector()
for(i in 1:1000){
nmi[i]<-compare(a[i,],a[j,],method="nmi")
}
return(nmi)
}
nmiM<-matrix(data=0,nrow=1000,ncol=1000)
for(i in 1:1000){
nmiM[i,]<-comp(i)
}
mean(nmiM) #Normalized mutual information of pre-cluster solutions## [1] 0.9723268
sd(nmiM) #Standard deviation of NMI## [1] 0.02760185
files<-vector()
for (i in 1:1000){
files[i]<-paste("Data/1000InfomapsPostBBT/",i,".clu",sep = "")
}
#setwd("..") #go to where the files are
csvs<-lapply(files,read.csv,skip=2,header=F,sep="")
a<-matrix(data=0,nrow=1000,ncol=64)
for (i in 1:1000){
a[i,]<-csvs[[i]][ order(csvs[[i]][,1]),2 ]
}
comp<-function(j){
nmi<-vector()
for(i in 1:1000){
nmi[i]<-compare(a[i,],a[j,],method="nmi")
}
return(nmi)
}
nmiM<-matrix(data=0,nrow=1000,ncol=1000)
for(i in 1:1000){
nmiM[i,]<-comp(i)
}
mean(nmiM)#Normalized mutual information of post-cluster solutions## [1] 0.9455897
sd(nmiM)#Standard deviation of NMI## [1] 0.03625122
#Compare pre to post groupings
#Get most frequent groupings
postBBTgroup<-read.csv("Data/1000InfomapsPostBBT/1.clu",skip=2,header=F,sep="") #for us it was the first grouping.
postBBTgroup<-postBBTgroup[order(postBBTgroup$V1),]
preBBTgroup<-read.csv("Data/1000InfomapsPreBBT/2.clu",skip=2,header=F,sep="") #for us it was the first grouping.
preBBTgroup<-preBBTgroup[order(preBBTgroup$V1),]
compare(preBBTgroup$V2,postBBTgroup$V2,method="nmi") ## [1] 0.4346165
#Attach groupings to attributes data frame
attributesT<-read.csv("Data/attributesT.csv")
attributesT$preGroup<-preBBTgroup$V2
attributesT$postGroup<-postBBTgroup$V2## [1] 0.4854486
## [1] 0.5151299
## [1] 0.5151299
## N_teachers N_internal Mean_internal SD_internal N_external Mean_external
## A 22 28 0.4609278 0.07210353 4 0.4157937
## B 23 38 0.5646201 0.08324876 5 0.4724391
## C 19 25 0.4733391 0.08431360 6 0.4620622
## Total 64 91 0.5076376 0.09317196 15 0.4531829
## SD_external
## A 0.02169836
## B 0.07372601
## C 0.04990817
## Total 0.05575940
##
## Wilcoxon rank sum test with continuity correction
##
## data: allInt and allExt
## W = 925, p-value = 0.02827
## alternative hypothesis: true location shift is not equal to 0
##
## Welch Two Sample t-test
##
## data: allInt and allExt
## t = 3.13, df = 28.9, p-value = 0.003974
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 0.01886764 0.09004173
## sample estimates:
## mean of x mean of y
## 0.5076376 0.4531829
## Warning in kwAllPairsNemenyiTest.default(c(4L, 5L, 4L, 3L, 4L, 4L, 3L, 3L, :
## Ties are present. Chi-sq was corrected for ties.
##
## Pairwise comparisons using Nemenyi's all-pairs test with chi-square approximation
## data: newdata$post38 by supergroups
## alternative hypothesis: two.sided
## P value adjustment method: single-step
## H0
## X^2 value Pr(>|X^2|)
## B - A == 0 28.675 5.934e-07 ***
## C - A == 0 3.168 0.2051672
## C - B == 0 12.459 0.0019704 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Warning in kwAllPairsNemenyiTest.default(c(4L, 4L, 4L, 4L, 1L, 5L, 2L, 3L, :
## Ties are present. Chi-sq was corrected for ties.
##
## Pairwise comparisons using Nemenyi's all-pairs test with chi-square approximation
## data: newdata$post39 by supergroups
## alternative hypothesis: two.sided
## P value adjustment method: single-step
## H0
## X^2 value Pr(>|X^2|)
## B - A == 0 12.267 0.0021687 **
## C - A == 0 4.642 0.0981582 .
## C - B == 0 1.436 0.4876923
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Warning in kwAllPairsNemenyiTest.default(c(3L, 4L, 3L, 3L, 4L, 3L, 4L, 2L, :
## Ties are present. Chi-sq was corrected for ties.
##
## Pairwise comparisons using Nemenyi's all-pairs test with chi-square approximation
## data: newdata$post40 by supergroups
## alternative hypothesis: two.sided
## P value adjustment method: single-step
## H0
## X^2 value Pr(>|X^2|)
## B - A == 0 2.809 0.24544889
## C - A == 0 5.095 0.07826056 .
## C - B == 0 16.309 0.00028742 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Warning in kwAllPairsNemenyiTest.default(c(3L, 4L, 3L, 2L, 4L, 4L, 5L, 5L, :
## Ties are present. Chi-sq was corrected for ties.
##
## Pairwise comparisons using Nemenyi's all-pairs test with chi-square approximation
## data: newdata$post41 by supergroups
## alternative hypothesis: two.sided
## P value adjustment method: single-step
## H0
## X^2 value Pr(>|X^2|)
## B - A == 0 29.502 3.9233e-07 ***
## C - A == 0 6.966 0.030719 *
## C - B == 0 4.919 0.085493 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Warning in kwAllPairsNemenyiTest.default(c(3L, 5L, 4L, 4L, 4L, 5L, 5L, 4L, :
## Ties are present. Chi-sq was corrected for ties.
##
## Pairwise comparisons using Nemenyi's all-pairs test with chi-square approximation
## data: newdata$post42 by supergroups
## alternative hypothesis: two.sided
## P value adjustment method: single-step
## H0
## X^2 value Pr(>|X^2|)
## B - A == 0 34.767 2.8217e-08 ***
## C - A == 0 25.632 2.7176e-06 ***
## C - B == 0 0.225 0.89352
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Warning in kwAllPairsNemenyiTest.default(c(3L, 5L, 1L, 3L, 3L, 4L, 2L, 3L, :
## Ties are present. Chi-sq was corrected for ties.
##
## Pairwise comparisons using Nemenyi's all-pairs test with chi-square approximation
## data: newdata$post43 by supergroups
## alternative hypothesis: two.sided
## P value adjustment method: single-step
## H0
## X^2 value Pr(>|X^2|)
## B - A == 0 23.031 9.9745e-06 ***
## C - A == 0 5.765 0.055989 .
## C - B == 0 4.204 0.122218
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Warning in kwAllPairsNemenyiTest.default(c(4L, 4L, 3L, 4L, 3L, 2L, 1L, 4L, :
## Ties are present. Chi-sq was corrected for ties.
##
## Pairwise comparisons using Nemenyi's all-pairs test with chi-square approximation
## data: newdata$post44 by supergroups
## alternative hypothesis: two.sided
## P value adjustment method: single-step
## H0
## X^2 value Pr(>|X^2|)
## B - A == 0 0.639 0.726426
## C - A == 0 5.108 0.077760 .
## C - B == 0 8.811 0.012211 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Warning in kwAllPairsNemenyiTest.default(c(3L, 4L, 4L, 2L, 4L, 3L, 4L, 2L, :
## Ties are present. Chi-sq was corrected for ties.
##
## Pairwise comparisons using Nemenyi's all-pairs test with chi-square approximation
## data: newdata$post45 by supergroups
## alternative hypothesis: two.sided
## P value adjustment method: single-step
## H0
## X^2 value Pr(>|X^2|)
## B - A == 0 22.689 1.1835e-05 ***
## C - A == 0 1.272 0.5294416
## C - B == 0 10.528 0.0051758 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Warning in kwAllPairsNemenyiTest.default(c(3L, 4L, 4L, 3L, 4L, 4L, 2L, 4L, :
## Ties are present. Chi-sq was corrected for ties.
##
## Pairwise comparisons using Nemenyi's all-pairs test with chi-square approximation
## data: newdata$post46 by supergroups
## alternative hypothesis: two.sided
## P value adjustment method: single-step
## H0
## X^2 value Pr(>|X^2|)
## B - A == 0 2.874 0.237662
## C - A == 0 1.444 0.485741
## C - B == 0 6.775 0.033791 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Warning in kwAllPairsNemenyiTest.default(c(3L, 4L, 5L, 5L, 4L, 5L, 5L, 2L, :
## Ties are present. Chi-sq was corrected for ties.
##
## Pairwise comparisons using Nemenyi's all-pairs test with chi-square approximation
## data: newdata$post47 by supergroups
## alternative hypothesis: two.sided
## P value adjustment method: single-step
## H0
## X^2 value Pr(>|X^2|)
## B - A == 0 4.180 0.123683
## C - A == 0 5.501 0.063892 .
## C - B == 0 0.154 0.926003
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Warning in kwAllPairsNemenyiTest.default(c(3L, 4L, 5L, 3L, 4L, 4L, 5L, 3L, :
## Ties are present. Chi-sq was corrected for ties.
##
## Pairwise comparisons using Nemenyi's all-pairs test with chi-square approximation
## data: newdata$post48 by supergroups
## alternative hypothesis: two.sided
## P value adjustment method: single-step
## H0
## X^2 value Pr(>|X^2|)
## B - A == 0 13.046 0.0014693 **
## C - A == 0 10.983 0.0041214 **
## C - B == 0 0.000 0.9997512
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Warning in kwAllPairsNemenyiTest.default(c(2L, 3L, 4L, 3L, 3L, 3L, 4L, 3L, :
## Ties are present. Chi-sq was corrected for ties.
##
## Pairwise comparisons using Nemenyi's all-pairs test with chi-square approximation
## data: newdata$post49 by supergroups
## alternative hypothesis: two.sided
## P value adjustment method: single-step
## H0
## X^2 value Pr(>|X^2|)
## B - A == 0 28.343 7.0049e-07 ***
## C - A == 0 7.356 0.025278 *
## C - B == 0 5.465 0.065049 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1] 9.609773
## [1] 0.2486196
## [1] -0.04889402
## [1] -0.5642743
## [1] -0.51623
## [1] 1.35792
## [1] 2.985931
## [1] 0.05745959
## [1] 1.086237
## [1] 2.901326
## [1] 15.67396
This is the entropy analysis.
This is the single questions analyses.
## 4
## 1.863627
## 4
## 2.85216
## 3
## 2.589461
## 3
## -1.7826
## 5 - Agree
## 2.13912
## 5 - Agree
## 3.021038