Unit 3 Part 3
Research Questions
RQ1: What is the tie strength of School Leader 32’s two-step egocentric network?
RQ2: How does the tie strength of School Leader 32’s two-step egocentric network change from year 1 to year 3?
Data Source
Year 3 Data
I am choosing to use the School Leaders Data from Chapter 9_b. This is a directed, valued network. The possible values are a range of 0-4, and higher values indicate more frequently collaboration between school leaders. These data were collected in year-three of the three-year study; therefore, I anticipate that the tie strength for SL32 will be fairly high since they are three years into an initiative intended to increase collaboration among school leaders.
library(readxl)
School_Leaders_Data_Chapter_9_b <- read_excel("data/School Leaders Data Chapter 9_b.xlsx",
col_names = FALSE)## New names:
## * `` -> ...1
## * `` -> ...2
## * `` -> ...3
## * `` -> ...4
## * `` -> ...5
## * ...SchoolLeadersDataY3 <- School_Leaders_Data_Chapter_9_b| 2 | 2 | 2 | 2 | 0 | 1 | 0 | 2 | 1 | 0 | 1 | 1 | 0 | 0 | 2 | 1 | 0 | 2 | 0 | 0 | 0 | 1 | 2 | 3 | 4 | 0 | 4 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 2 | 1 | 1 | 0 | 0 | 0 | 1 | 1 |
|---|
| 1 | 0 | 0 | 0 | 1 | 1 | 0 | 2 | 1 | 1 | 0 | 0 | 0 | 1 | 1 |
|---|
Data Wrangling
rownames(SchoolLeadersDataY3) <- 1:43## Warning: Setting row names on a tibble is deprecated.colnames(SchoolLeadersDataY3) <- 1:43
SchoolLeadersDataY3## # A tibble: 43 × 43
## `1` `2` `3` `4` `5` `6` `7` `8` `9` `10` `11` `12` `13`
## * <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0 2 4 3 1 1 1 3 1 1 1 1 1
## 2 0 0 1 0 0 0 0 1 0 0 0 0 0
## 3 4 1 0 1 2 2 2 3 2 2 2 2 2
## 4 3 2 0 0 0 0 0 1 0 0 1 0 0
## 5 1 0 2 0 0 1 1 2 3 0 1 1 2
## 6 3 0 0 0 0 0 0 1 1 0 0 0 0
## 7 2 1 1 1 2 1 4 2 1 4 1 1 1
## 8 3 2 4 1 3 3 2 0 3 3 2 3 3
## 9 2 0 2 0 4 2 0 3 0 1 2 2 1
## 10 2 1 3 2 2 1 4 4 3 0 3 2 2
## # … with 33 more rows, and 30 more variables: `14` <dbl>, `15` <dbl>,
## # `16` <dbl>, `17` <dbl>, `18` <dbl>, `19` <dbl>, `20` <dbl>, `21` <dbl>,
## # `22` <dbl>, `23` <dbl>, `24` <dbl>, `25` <dbl>, `26` <dbl>, `27` <dbl>,
## # `28` <dbl>, `29` <dbl>, `30` <dbl>, `31` <dbl>, `32` <dbl>, `33` <dbl>,
## # `34` <dbl>, `35` <dbl>, `36` <dbl>, `37` <dbl>, `38` <dbl>, `39` <dbl>,
## # `40` <dbl>, `41` <dbl>, `42` <dbl>, `43` <dbl>SL32Y3 <- SchoolLeadersDataY3[32,]
SL32Y3 <- as.data.frame(t(SL32Y3))
colnames(SL32Y3) <- "SchoolLeader32"
SL32Y3## SchoolLeader32
## 1 2
## 2 2
## 3 2
## 4 2
## 5 0
## 6 1
## 7 0
## 8 2
## 9 1
## 10 0
## 11 1
## 12 1
## 13 0
## 14 0
## 15 2
## 16 1
## 17 0
## 18 2
## 19 0
## 20 0
## 21 0
## 22 1
## 23 2
## 24 3
## 25 4
## 26 0
## 27 4
## 28 1
## 29 1
## 30 0
## 31 0
## 32 0
## 33 1
## 34 1
## 35 0
## 36 2
## 37 1
## 38 1
## 39 0
## 40 0
## 41 0
## 42 1
## 43 1library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionSL32Y3 <- filter(SL32Y3, SchoolLeader32 >= 1)
SL32Y3## SchoolLeader32
## 1 2
## 2 2
## 3 2
## 4 2
## 6 1
## 8 2
## 9 1
## 11 1
## 12 1
## 15 2
## 16 1
## 18 2
## 22 1
## 23 2
## 24 3
## 25 4
## 27 4
## 28 1
## 29 1
## 33 1
## 34 1
## 36 2
## 37 1
## 38 1
## 42 1
## 43 1Standard Deviation
sd(SL32Y3$SchoolLeader32)## [1] 0.8918434Mean
mean(SL32Y3$SchoolLeader32)## [1] 1.653846Since this is a comparative analysis, I will also use the School Leaders Data from Chapter 9_a. This is also a directed, valued network with a value range of 0-4. However, this dataset was collected in year one of the three-year study. Therefore, as is immediately evident from looking at SL32’s row, tie strength is much lower than that found in Chapter 9_b.
Year 1 Data
library(readxl)
School_Leaders_Data_Chapter_9_a <- read_excel("data/School Leaders Data Chapter 9_a.xlsx",
col_names = FALSE)## New names:
## * `` -> ...1
## * `` -> ...2
## * `` -> ...3
## * `` -> ...4
## * `` -> ...5
## * ...SchoolLeadersDataY1 <- School_Leaders_Data_Chapter_9_aData Wrangling
rownames(SchoolLeadersDataY1) <- 1:43## Warning: Setting row names on a tibble is deprecated.colnames(SchoolLeadersDataY1) <- 1:43
SchoolLeadersDataY1 ## # A tibble: 43 × 43
## `1` `2` `3` `4` `5` `6` `7` `8` `9` `10` `11` `12` `13`
## * <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0 0 3 0 0 0 0 0 0 0 0 0 0
## 2 0 0 0 0 0 0 0 0 0 0 0 0 0
## 3 4 0 0 0 0 0 0 0 0 0 0 0 0
## 4 0 0 0 0 0 0 0 0 0 0 0 0 0
## 5 0 0 0 0 0 0 0 0 3 0 0 0 0
## 6 3 0 0 0 0 0 0 0 0 0 0 0 0
## 7 0 0 0 0 0 0 0 0 0 0 0 0 0
## 8 0 0 0 0 0 0 0 0 0 4 0 0 0
## 9 0 0 0 0 4 0 0 0 0 0 0 0 0
## 10 0 0 0 0 0 0 0 4 0 0 0 0 0
## # … with 33 more rows, and 30 more variables: `14` <dbl>, `15` <dbl>,
## # `16` <dbl>, `17` <dbl>, `18` <dbl>, `19` <dbl>, `20` <dbl>, `21` <dbl>,
## # `22` <dbl>, `23` <dbl>, `24` <dbl>, `25` <dbl>, `26` <dbl>, `27` <dbl>,
## # `28` <dbl>, `29` <dbl>, `30` <dbl>, `31` <dbl>, `32` <dbl>, `33` <dbl>,
## # `34` <dbl>, `35` <dbl>, `36` <dbl>, `37` <dbl>, `38` <dbl>, `39` <dbl>,
## # `40` <dbl>, `41` <dbl>, `42` <dbl>, `43` <dbl>| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
|---|
| 0 | 0 | 0 | 0 | 0 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
|---|
SL32Y1 <- SchoolLeadersDataY1[32,]
SL32Y1 <- as.data.frame(t(SL32Y1))
colnames(SL32Y1) <- "SchoolLeader32Y1"
SL32Y1## SchoolLeader32Y1
## 1 0
## 2 0
## 3 0
## 4 0
## 5 0
## 6 0
## 7 0
## 8 0
## 9 0
## 10 0
## 11 0
## 12 0
## 13 0
## 14 0
## 15 0
## 16 0
## 17 0
## 18 0
## 19 0
## 20 0
## 21 0
## 22 0
## 23 0
## 24 4
## 25 0
## 26 0
## 27 0
## 28 0
## 29 0
## 30 0
## 31 0
## 32 0
## 33 0
## 34 4
## 35 0
## 36 0
## 37 0
## 38 0
## 39 0
## 40 0
## 41 0
## 42 0
## 43 0library(dplyr)
SL32Y1 <- filter(SL32Y1, SchoolLeader32Y1 >= 1)
SL32Y1## SchoolLeader32Y1
## 24 4
## 34 4Standard Deviation
sd(SL32Y1$SchoolLeader32Y1)## [1] 0Mean
mean(SL32Y1$SchoolLeader32Y1)## [1] 4As the data show, there is a drastic difference in the network for School Leader 32 in year 1 compared to the network she (SL32 is female according to the demographics information collected in School_Leaders_Data_Chapter_9_e) has created in year 3. Interestingly, however, although her network is small in year 1, it is strong. SL32 rates both of her collaboration partners with a value of “4,” which is the highest possible value. This indicates that she collaborates with these two school leaders (SL24 and SL34) frequently. According to the dataset descriptions found on the Sage website, a score of 4 indicates collaboration 1-2 times per week. A quick visual scan of year 3 data indicates that while SL32 increased the breadth of her network significantly by year 3, she still only had two “level 4” collaboration partners. Interestingly, neither of these is the same as the level 4 partners noted in year 1.
Visualizations
Next, I wanted to visualize two-step egocentric networkw for School Leader 32 for both year 1 and year 3 in order to compare the tie-strength increase between these two years. Thus, I went back to my original datasets, which contain the complete network data for both year 1 and year 3. Then, I converted these datasets to matrices, then converted the matrices to graph objects so that I could create sociograms using the data.
According to Carolan (2014, p. 153), a “Two-Step Ego Network […] shows an ego […] and its relations with […] alters, as well as the valued, nondirectional relations among those […] alters.”
Year 3
SchoolLeadersDataY3_matrix <- as.matrix(SchoolLeadersDataY3)
SchoolLeadersDataY3_matrix## 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
## 1 0 2 4 3 1 1 1 3 1 1 1 1 1 1 1 2 1 2 1 1 1 2 1 2 1 1 2 4
## 2 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 2 0 1 0 0 0 2 0 0 1 0 0 4
## 3 4 1 0 1 2 2 2 3 2 2 2 2 2 2 2 3 1 2 2 2 2 1 2 2 2 2 4 3
## 4 3 2 0 0 0 0 0 1 0 0 1 0 0 0 0 4 0 3 0 0 0 3 0 1 2 0 2 4
## 5 1 0 2 0 0 1 1 2 3 0 1 1 2 1 1 0 1 1 1 1 2 1 2 2 1 2 2 2
## 6 3 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1
## 7 2 1 1 1 2 1 4 2 1 4 1 1 1 2 1 2 2 1 2 4 1 1 1 2 1 2 1 1
## 8 3 2 4 1 3 3 2 0 3 3 2 3 3 2 3 4 1 4 3 2 3 3 3 2 4 4 4 4
## 9 2 0 2 0 4 2 0 3 0 1 2 2 1 4 3 1 2 2 1 1 2 1 2 1 0 0 2 1
## 10 2 1 3 2 2 1 4 4 3 0 3 2 2 3 2 2 2 3 3 4 3 1 2 2 1 3 2 2
## 11 3 1 2 2 4 3 3 3 3 3 0 4 3 3 4 3 3 2 4 2 4 3 4 2 2 1 2 2
## 12 1 0 2 0 1 1 1 3 2 1 1 0 0 0 1 0 0 1 0 0 1 0 1 1 0 0 1 1
## 13 0 1 4 0 3 1 0 3 1 0 1 0 0 1 1 0 0 1 0 0 0 1 4 1 0 1 3 0
## 14 2 0 3 1 2 2 3 2 3 3 2 2 1 4 3 1 3 1 3 3 2 1 2 2 0 3 2 2
## 15 1 1 2 2 3 0 2 2 2 1 2 3 2 3 0 1 2 1 2 2 4 1 2 4 1 2 4 1
## 16 0 1 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0
## 17 1 1 1 1 2 1 2 1 1 2 1 1 1 2 1 1 4 1 2 2 1 1 1 1 1 4 1 2
## 18 4 2 2 2 2 2 2 3 2 3 2 2 1 1 2 2 1 0 2 2 1 4 1 1 2 3 2 4
## 19 0 0 2 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 4 0 0 0 0 0 0 0 0 0
## 20 3 1 2 1 3 1 4 2 2 4 2 1 1 2 1 1 1 3 3 0 1 2 1 2 1 2 1 1
## 21 1 0 2 0 2 1 1 2 2 0 3 2 2 3 3 1 1 0 1 1 0 0 2 0 2 1 0 1
## 22 1 2 1 1 1 1 1 3 1 1 1 1 1 1 1 4 1 3 1 1 1 0 1 1 1 1 2 4
## 23 3 0 2 2 2 2 2 3 2 0 3 2 2 0 2 0 0 1 0 0 2 0 0 0 0 0 1 1
## 24 2 0 3 0 1 1 1 4 1 2 2 1 1 1 3 1 1 1 1 1 1 2 1 0 2 2 4 1
## 25 1 2 3 2 0 2 0 4 0 0 0 1 1 0 1 1 0 3 0 0 2 2 0 3 4 0 0 1
## 26 1 0 2 0 0 0 0 2 0 1 0 0 0 1 0 1 4 2 0 0 0 1 0 1 0 0 1 1
## 27 0 0 4 0 1 0 1 3 1 0 1 1 1 0 3 0 0 1 0 0 0 0 2 4 4 1 0 0
## 28 4 4 4 4 4 3 3 4 4 3 3 3 4 3 3 4 3 4 3 3 4 4 3 3 3 4 4 4
## 29 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 4 0 0 0 1 0 0 0 0 0 0
## 30 1 1 2 1 2 1 1 2 1 1 1 1 1 1 1 1 1 1 2 1 1 2 1 2 1 1 2 1
## 31 0 0 0 0 2 0 2 0 0 0 0 0 0 0 2 0 0 0 4 1 0 0 1 0 0 0 0 0
## 32 2 2 2 2 0 1 0 2 1 0 1 1 0 0 2 1 0 2 0 0 0 1 2 3 4 0 4 1
## 33 1 2 2 1 2 3 1 3 3 1 2 3 2 2 2 1 1 2 2 1 4 1 2 2 2 1 2 2
## 34 4 3 4 4 2 2 1 4 2 2 2 2 2 1 2 3 1 4 1 1 1 4 1 3 2 2 4 4
## 35 1 1 2 2 1 0 1 2 0 0 1 0 4 0 0 0 0 2 0 0 2 2 1 0 0 0 1 2
## 36 4 2 4 4 1 0 1 4 1 0 1 0 0 0 0 4 0 4 1 0 1 4 0 1 2 2 4 4
## 37 1 1 4 1 3 3 3 3 3 3 3 3 3 4 3 1 3 3 3 3 3 2 3 2 3 3 3 3
## 38 4 2 4 2 3 3 2 4 3 3 3 3 3 3 3 2 2 4 3 3 3 3 3 2 2 4 4 4
## 39 1 0 2 0 1 2 0 2 1 0 1 1 1 0 1 1 0 1 1 0 1 1 1 1 1 0 1 1
## 40 0 0 1 0 1 1 2 2 0 0 0 0 1 2 0 0 2 1 2 2 2 0 0 2 1 0 2 1
## 41 1 0 2 4 2 2 1 2 1 2 4 1 1 2 1 1 4 2 2 2 1 2 1 1 2 4 2 2
## 42 2 0 2 0 1 1 0 2 4 0 2 2 2 0 4 0 0 1 2 0 2 2 0 4 3 0 4 2
## 43 1 1 1 1 2 1 2 3 2 2 2 2 1 2 3 1 2 2 2 2 3 2 3 2 1 2 1 2
## 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43
## 1 1 1 1 2 1 1 1 4 1 3 1 1 1 1 1
## 2 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0
## 3 1 2 1 2 2 2 3 3 3 3 3 2 2 2 2
## 4 0 0 0 2 0 4 0 4 0 2 0 0 0 0 0
## 5 0 2 1 0 1 1 0 1 2 2 2 1 1 1 2
## 6 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
## 7 1 1 2 1 1 1 1 1 1 2 1 2 2 1 2
## 8 2 2 1 3 2 2 1 4 3 4 2 4 1 2 2
## 9 0 1 1 1 2 1 0 1 1 2 1 0 0 3 2
## 10 2 3 2 1 2 3 1 1 2 4 0 3 3 1 3
## 11 1 1 1 2 3 3 3 1 2 3 1 1 4 2 4
## 12 0 0 0 0 2 0 0 0 2 1 1 0 0 0 0
## 13 1 0 0 1 0 1 4 0 3 1 1 1 0 3 1
## 14 2 3 3 0 2 2 0 2 4 3 2 3 3 1 2
## 15 1 2 4 2 3 2 2 1 3 2 3 2 2 4 4
## 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 17 1 2 2 1 1 1 1 1 2 1 1 2 4 0 2
## 18 4 1 1 3 1 4 1 4 3 4 1 2 2 1 2
## 19 0 0 4 0 0 0 0 0 2 2 0 0 0 2 0
## 20 1 2 3 1 1 2 1 1 2 2 1 2 1 1 2
## 21 0 1 1 0 3 1 4 0 0 1 2 1 1 2 2
## 22 3 1 1 2 1 3 1 1 1 3 1 1 1 1 1
## 23 1 0 0 1 0 0 0 0 1 0 0 0 0 2 2
## 24 0 2 1 4 2 1 1 0 1 2 1 1 1 4 1
## 25 2 0 0 4 3 3 2 2 1 1 1 0 0 3 1
## 26 1 1 0 0 0 2 0 1 1 2 0 0 4 0 0
## 27 0 3 0 4 0 0 1 2 0 2 1 0 0 4 0
## 28 4 3 3 4 3 4 3 4 4 4 3 3 3 3 3
## 29 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0
## 30 1 4 1 1 1 1 1 1 1 2 1 1 1 1 1
## 31 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0
## 32 1 0 0 0 1 1 0 2 1 1 0 0 0 1 1
## 33 2 1 1 2 0 2 1 1 2 3 2 1 1 1 3
## 34 4 1 1 3 2 0 3 4 4 4 1 2 2 2 2
## 35 2 0 1 1 0 2 0 0 2 0 0 0 0 2 1
## 36 2 0 0 2 1 4 0 0 4 4 0 0 0 1 0
## 37 1 0 3 2 3 3 3 2 0 4 3 3 3 3 3
## 38 2 3 2 2 4 4 2 4 4 0 4 3 2 2 3
## 39 0 0 1 0 1 0 0 0 1 2 0 0 0 2 1
## 40 1 2 2 0 0 1 0 0 2 2 0 4 2 0 2
## 41 1 2 2 1 1 1 1 1 2 2 1 2 4 2 1
## 42 0 0 2 0 0 2 2 0 0 3 2 0 2 4 4
## 43 2 1 2 3 3 3 1 1 3 1 3 1 1 4 0library("ggraph")## Loading required package: ggplot2library("tidygraph")##
## Attaching package: 'tidygraph'## The following object is masked from 'package:stats':
##
## filterSLY3_network <- as_tbl_graph(SchoolLeadersDataY3_matrix, directed = FALSE)
SLY3_network## # A tbl_graph: 43 nodes and 803 edges
## #
## # An undirected multigraph with 1 component
## #
## # Node Data: 43 × 1 (active)
## name
## <chr>
## 1 1
## 2 2
## 3 3
## 4 4
## 5 5
## 6 6
## # … with 37 more rows
## #
## # Edge Data: 803 × 3
## from to weight
## <int> <int> <dbl>
## 1 1 2 2
## 2 1 3 4
## 3 1 4 3
## # … with 800 more rowsOne-Step Visual
Just for fun, here is a visual of SL32’s one-step network.
SLY3_network |>
convert(to_local_neighborhood,
node = 32,
order = 1,
mode = "all") |>
ggraph(layout = "kk") +
geom_edge_link(aes(color = weight)) +
geom_node_point(aes(size = 2, alpha = 1.5, fill = "gray" ), shape = 23) +
geom_node_text(aes(label = name),family="serif") +
ggtitle("Year 3 One-Step Egocentric Network: SL32") +
ggthemes::theme_clean()
Two-Step Visual
As you can see, the two-step egocentric network is significantly more dense than the one-step network because this includes both her relationship with her alters and the relationships among those alters.
SLY3_network |>
convert(to_local_neighborhood,
node = 32,
order = 2,
mode = "all") |>
ggraph(layout = "kk") +
geom_edge_link(aes(color = weight)) +
geom_node_point(aes(size = 2, alpha = 1.5, fill = "gray" ), shape = 23) +
geom_node_text(aes(label = name),family="serif") +
ggtitle("Year 3 Two-Step Egocentric Network: SL32") +
ggthemes::theme_clean()
Year 1
Two-Step Visual
I then followed the same procedures to create a two-step egocentric network for SL32 based on data from year 1. I did not include the one-step sociogram for Year 1 because the primary purpose of showing that for Year 3 was to indicate the difference between a one-step and a two-step network. Also, since SL32 only sends two ties in year 1, it would be a very boring visual.
SchoolLeadersDataY1_matrix <- as.matrix(SchoolLeadersDataY1)
SchoolLeadersDataY1_matrix## 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
## 1 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 3 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0
## 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 5 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 6 3 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 3 0 0 0 0 0 0 0
## 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 8 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0
## 9 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 10 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 4 0 0 4 0 0 0 0 0
## 11 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0
## 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0
## 13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 14 3 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 15 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
## 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0
## 17 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0
## 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 20 0 0 0 0 0 0 0 0 0 4 0 0 0 0 3 0 0 0 0 0 0 0 4 0 0 0 0 0
## 21 3 0 2 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 23 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 24 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0
## 25 0 0 0 0 0 0 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 26 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 27 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0
## 28 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 4 0 0 0 0 0 0
## 29 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0
## 30 0 0 0 0 0 0 4 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 31 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0
## 32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0
## 33 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 34 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0
## 35 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 36 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0
## 37 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 38 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 39 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0
## 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 41 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 4 0 0
## 42 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0
## 43 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43
## 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 4 3 0 0 0 0 0 0 0 0 0 0 0 4 0 0
## 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 7 0 0 0 0 4 0 0 0 3 0 0 0 0 0 0
## 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 11 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0
## 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 14 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0
## 15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 16 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 17 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 18 0 4 0 0 0 0 0 0 0 0 4 0 0 0 0
## 19 0 0 0 0 0 0 4 0 3 0 0 0 0 0 0
## 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 21 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 22 4 0 0 0 0 0 0 0 0 0 3 0 0 0 0
## 23 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 24 0 0 4 0 0 4 0 0 0 0 0 0 0 0 0
## 25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 26 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 27 0 0 4 0 0 4 0 0 0 0 0 0 0 0 0
## 28 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0
## 29 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0
## 30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 31 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 32 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0
## 33 0 0 0 4 0 0 0 0 0 0 0 0 0 0 2
## 34 3 4 0 0 0 0 0 0 0 0 0 0 0 0 0
## 35 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 36 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 37 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 38 4 0 0 0 0 0 0 0 4 0 0 0 0 3 0
## 39 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0
## 40 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0
## 41 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 42 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## 43 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0library("ggraph")
library("tidygraph")
SLY1_network <- as_tbl_graph(SchoolLeadersDataY1_matrix, directed = FALSE)
SLY1_network## # A tbl_graph: 43 nodes and 75 edges
## #
## # An undirected simple graph with 3 components
## #
## # Node Data: 43 × 1 (active)
## name
## <chr>
## 1 1
## 2 2
## 3 3
## 4 4
## 5 5
## 6 6
## # … with 37 more rows
## #
## # Edge Data: 75 × 3
## from to weight
## <int> <int> <dbl>
## 1 1 3 4
## 2 1 6 3
## 3 1 14 3
## # … with 72 more rowsSLY1_network |>
convert(to_local_neighborhood,
node = 32,
order = 2,
mode = "all") |>
ggraph(layout = "kk") +
geom_edge_link(aes(color = weight)) +
geom_node_point(aes(size = 2, alpha = 1.5, fill = "gray" ), shape = 23) +
geom_node_text(aes(label = name),family="serif") +
ggtitle("Year 1 Two-Step Egocentric Network: SL32") +
ggthemes::theme_clean()
Comparing Year 1 to Year 3 makes it starkly apparent how much the tie strength increased for SL32 over the course of the study. Also, although the above sociogram is created using non-directional data, it is clear to see the “level 4” ties that SL32 sends to SL34 and SL24. Furthermore, although the directionality is not apparent, cross-referencing the sociogram with the dataset reveals that the tie between SL32 and SL33 is a level 4 tie that SL33 sends to SL32. SL32, however, does not reciprocate this tie, labeling SL33 “0” in her own evaluation.
Narrative
RQ1: What is the tie strength of School Leader 32’s two-step egocentric network?
In order to obtain the overall tie strength of School Leader 32 (SL32), I first calculated the mean and standard deviation of the one-step network (i.e. the collaboration nominations she “sent” to other school leaders) for years 1 and 3.
Mean, Year 1:
4Mean, Year 3:
1.653846Standard Deviation, Year 1:
0Standard Deviation, Year 3:
0.8918434I also simply calculated the number of ties that SL32 sent in both year 1 and year 3. In year 1, she sent two ties to other school leaders. In year 3, she sent 26 ties to other school leaders. This showed a dramatic (1300%) increase in quantity.
RQ2: How does the tie strength of School Leader 32’s two-step egocentric network change from year 1 to year 3?
In year 1, SL32 has two ties with other leaders, both valued “4,” which is the strongest value possible. In year 3, the quantity of SL32’s ties has increased significantly (she “sends” 26 ties to other school leaders), yet the quality has not. She continues to have only two level-4 ties. Although she has one level-3 tie, the other 23 ties are all levels 1 or 2. This is clearly shown in the precipitous drop in mean from year 1 to year 3. Thus, to use Carolan’s vernacular, the “strong ties” have increased only modestly—from 2 to 3, whereas the “weak ties” have increased from 0 to 23.
Conclusions: Based on the comparison of year 1 and year 3 tie strength as well as the two-step egocentric sociograms from years 1 and 3, I conclude that the school district’s reform initiative was effective in increasing collaboration among school leaders (at least according to their self-reports). However, if SL32 is indicative of the other school leaders within the network, then these collaborations were primarily “weak ties,” which makes me question the overall efficacy of the initiative. According to Carolan (2014, p. 152) “weak ties are important for transmitting information but less so for transmitting behavioral influence.” Thus, if the district’s motivation for implementing reforms was to create strong interpersonal connections among leaders that resulted in a tight network capable of affecting patterns of behaviors, beliefs, and commitments, they probably failed.
Reflection
I had two primary takeaways from conducting this analysis.
First, I concluded that the type of data analysis I completed, while interesting, would not be particularly useful in many contexts. If I were conducting a case study on a particular individual (or a few individuals) in order to provide specific depth to a broader study, then this type of in-depth analysis of a particular individual could prove useful. However, without conducting further analyses, I cannot determine if the conclusions that I drew are broadly applicable to the complete network. Therefore, as an isolated analysis, without any bigger portrait of network dynamics, my conclusions are of limited utility.
Second, I concluded that if SL32’s results are indicative of other school leaders within the network (a quick visual scan of the year 3 dataset suggests that they are), then I question whether the resources expended in implementing the district reforms versus the results garnered were justified. In other words, did the output (increased, but shallow, collaboration) justify the input (money, time, brainpower)? As I noted earlier, Carolan (2014) claims that “weak ties” are useful for information transfer. If this is an apt definition, then it seems that the district in question accomplished little through their reform initiative that could not have been achieved through a well crafted email listserv or text message chain. Without an increase in “strong ties,” I posit that there will be limited shift in mindset or action within school leaders.
Future Analysis: If I were to conduct further research of this type, I would want to conduct the same type of analysis (comparing year 1 and year 3 tie strength) for more of the school leaders within the network. Looking at School_Leaders_Data_Chapter_9_e, which contains attribute data for each of the 43 actors in this network, I would use representative sampling to choose a mix of male/female leaders and site/district based leaders. I don’t know that it would be necessary to conduct a two-step egocentric analysis for all 43 of the actors, but having a representative sample would enable me to better determine if the results I found for SL32 are generalizable to the network as a whole.
Reference:
Carolan, B. V. (2014). Measures for egocentric network analysis. In Social network analysis and education: Theory, methods & applications (pp. 139-168). SAGE Publications, Inc., https://dx.doi.org/10.4135/9781452270104