Pathways to Belonging Pilot
Samantha Grayson
2026-04-20
Load packages and data
library(qualtRics)
library(tidyverse)## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr 1.1.4 ✔ readr 2.1.5
## ✔ forcats 1.0.0 ✔ stringr 1.5.1
## ✔ ggplot2 3.5.1 ✔ tibble 3.2.1
## ✔ lubridate 1.9.4 ✔ tidyr 1.3.1
## ✔ purrr 1.0.4
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorslibrary(psych) # for reliability##
## Attaching package: 'psych'
##
## The following objects are masked from 'package:ggplot2':
##
## %+%, alphalibrary(broom) # for tidy model outputs
df <- read_survey("~/Google drive/My Drive/YEAR 3/PROJECTS/DANIEL/Belonging/belonging_pilot1.csv")##
## ── Column specification ────────────────────────────────────────────────────────
## cols(
## .default = col_double(),
## StartDate = col_character(),
## EndDate = col_character(),
## IPAddress = col_character(),
## RecordedDate = col_character(),
## ResponseId = col_character(),
## RecipientLastName = col_logical(),
## RecipientFirstName = col_logical(),
## RecipientEmail = col_logical(),
## ExternalReference = col_logical(),
## DistributionChannel = col_character(),
## UserLanguage = col_character(),
## open_1 = col_character(),
## open_2 = col_character(),
## industry = col_character(),
## attn_bots = col_character(),
## gender_4_TEXT = col_logical(),
## race = col_number(),
## race_8_TEXT = col_logical(),
## race_9_TEXT = col_logical(),
## ses_7_TEXT = col_logical()
## # ... with 12 more columns
## )
## ℹ Use `spec()` for the full column specifications.df_clean <- df %>%
filter(attn == 24)Demographic overview
Sample
table(df_clean$gender)##
## 1 2 3
## 54 44 1table(df_clean$race)##
## 1 2 3 4 5 15 25
## 72 13 7 1 2 3 1table(df_clean$ses)##
## 1 2 3 4 5 6
## 1 10 47 17 23 1table(df_clean$income_now)##
## 1 2 3 4 5 6 7
## 2 2 24 29 18 16 8table(df_clean$employment)##
## 1 3
## 98 1mean(df_clean$age, na.rm = T)## [1] 41.21212Team info
table(df_clean$team_info)##
## 1 2
## 95 41 = current team 2 = past team
Current
mean(df_clean$team_size_current, na.rm = T)## [1] 8.568421Former
mean(df_clean$team_size_former, na.rm = T)## [1] 12.75Clean data
Reverse coding
# Detect reverse-coded items (ending in R)
df_clean <- df_clean %>%
mutate(across(ends_with("R"),
~ 8 - ., # change 8 to (max+1)
.names = "{.col}_recoded"))df_clean <- df_clean %>%
mutate(across(ends_with("R"),
~ 8 - .)) # overwrite directly (simpler)Create composites
df_scales <- df_clean %>%
mutate(
idea_attachment = rowMeans(select(., starts_with("attach_")), na.rm = TRUE),
interactional_justice = rowMeans(select(., starts_with("colquitt_")), na.rm = TRUE),
personal_treatment = rowMeans(select(., starts_with("treat_")), na.rm = TRUE),
idea_inclusion = rowMeans(select(., starts_with("idea_")), na.rm = TRUE),
belonging = rowMeans(select(., starts_with("belong_")), na.rm = TRUE)
)Check reliability
psych::alpha(df_scales %>% select(starts_with("attach_")))## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done## In factor.stats, I could not find the RMSEA upper bound . Sorry about that## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0##
## Reliability analysis
## Call: psych::alpha(x = df_scales %>% select(starts_with("attach_")))
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.93 0.93 0.89 0.47 13 0.011 3.6 1 0.45
##
## 95% confidence boundaries
## lower alpha upper
## Feldt 0.90 0.93 0.95
## Duhachek 0.91 0.93 0.95
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r
## attach_1 0.93 0.93 0.88 0.48 13 0.011 0.035
## attach_2 0.93 0.93 0.88 0.49 13 0.011 0.032
## attach_3 0.92 0.92 0.88 0.46 12 0.012 0.039
## attach_4 0.93 0.93 0.88 0.48 13 0.011 0.035
## attach_5 0.93 0.93 0.88 0.48 13 0.011 0.039
## attach_6R 0.92 0.92 0.89 0.46 12 0.012 0.034
## attach_7R 0.92 0.92 0.89 0.46 12 0.012 0.036
## attach_8R 0.92 0.92 0.89 0.46 12 0.012 0.034
## attach_9R 0.92 0.92 0.89 0.47 12 0.011 0.033
## attach_10R 0.92 0.92 0.89 0.45 12 0.012 0.034
## attach_6R_recoded 0.92 0.92 0.89 0.46 12 0.012 0.034
## attach_7R_recoded 0.92 0.92 0.89 0.46 12 0.012 0.036
## attach_8R_recoded 0.92 0.92 0.89 0.46 12 0.012 0.034
## attach_9R_recoded 0.92 0.92 0.89 0.47 12 0.011 0.033
## attach_10R_recoded 0.92 0.92 0.89 0.45 12 0.012 0.034
## med.r
## attach_1 0.49
## attach_2 0.49
## attach_3 0.45
## attach_4 0.49
## attach_5 0.51
## attach_6R 0.45
## attach_7R 0.46
## attach_8R 0.45
## attach_9R 0.45
## attach_10R 0.44
## attach_6R_recoded 0.45
## attach_7R_recoded 0.46
## attach_8R_recoded 0.45
## attach_9R_recoded 0.45
## attach_10R_recoded 0.44
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## attach_1 99 0.56 0.55 0.53 0.49 4.9 1.5
## attach_2 99 0.52 0.50 0.47 0.44 4.9 1.5
## attach_3 99 0.77 0.76 0.76 0.72 4.2 1.8
## attach_4 99 0.58 0.56 0.55 0.51 4.8 1.4
## attach_5 99 0.62 0.62 0.60 0.55 4.0 1.5
## attach_6R 99 0.80 0.80 0.75 0.76 3.2 1.4
## attach_7R 99 0.78 0.76 0.71 0.73 3.7 1.5
## attach_8R 99 0.72 0.75 0.69 0.68 2.7 1.2
## attach_9R 99 0.67 0.69 0.63 0.62 2.5 1.2
## attach_10R 99 0.81 0.82 0.77 0.78 3.2 1.4
## attach_6R_recoded 99 0.80 0.80 0.75 0.76 3.2 1.4
## attach_7R_recoded 99 0.78 0.76 0.71 0.73 3.7 1.5
## attach_8R_recoded 99 0.72 0.75 0.69 0.68 2.7 1.2
## attach_9R_recoded 99 0.67 0.69 0.63 0.62 2.5 1.2
## attach_10R_recoded 99 0.81 0.82 0.77 0.78 3.2 1.4
##
## Non missing response frequency for each item
## 1 2 3 4 5 6 7 miss
## attach_1 0.03 0.04 0.12 0.07 0.36 0.26 0.11 0
## attach_2 0.03 0.04 0.14 0.09 0.33 0.24 0.12 0
## attach_3 0.09 0.14 0.15 0.05 0.31 0.20 0.05 0
## attach_4 0.03 0.03 0.12 0.12 0.39 0.20 0.10 0
## attach_5 0.09 0.07 0.17 0.21 0.31 0.12 0.02 0
## attach_6R 0.10 0.25 0.27 0.14 0.18 0.04 0.01 0
## attach_7R 0.07 0.19 0.21 0.15 0.25 0.10 0.02 0
## attach_8R 0.18 0.23 0.39 0.12 0.06 0.01 0.00 0
## attach_9R 0.22 0.36 0.20 0.12 0.08 0.01 0.00 0
## attach_10R 0.16 0.12 0.34 0.20 0.12 0.04 0.01 0
## attach_6R_recoded 0.10 0.25 0.27 0.14 0.18 0.04 0.01 0
## attach_7R_recoded 0.07 0.19 0.21 0.15 0.25 0.10 0.02 0
## attach_8R_recoded 0.18 0.23 0.39 0.12 0.06 0.01 0.00 0
## attach_9R_recoded 0.22 0.36 0.20 0.12 0.08 0.01 0.00 0
## attach_10R_recoded 0.16 0.12 0.34 0.20 0.12 0.04 0.01 0psych::alpha(df_scales %>% select(starts_with("colquitt_")))##
## Reliability analysis
## Call: psych::alpha(x = df_scales %>% select(starts_with("colquitt_")))
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.85 0.87 0.85 0.62 6.6 0.025 5.9 0.81 0.62
##
## 95% confidence boundaries
## lower alpha upper
## Feldt 0.8 0.85 0.89
## Duhachek 0.8 0.85 0.90
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## colquitt_1 0.79 0.81 0.78 0.59 4.3 0.038 0.02883 0.51
## colquitt_2 0.78 0.81 0.76 0.58 4.2 0.038 0.01765 0.51
## colquitt_3 0.78 0.80 0.75 0.57 4.0 0.039 0.01974 0.50
## colquitt_4 0.90 0.90 0.86 0.75 9.0 0.017 0.00093 0.74
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## colquitt_1 99 0.86 0.88 0.83 0.76 5.9 0.90
## colquitt_2 99 0.87 0.88 0.85 0.76 5.9 0.92
## colquitt_3 99 0.88 0.90 0.87 0.79 5.9 0.86
## colquitt_4 99 0.77 0.73 0.57 0.54 5.7 1.19
##
## Non missing response frequency for each item
## 1 2 3 4 5 6 7 miss
## colquitt_1 0.00 0.00 0.02 0.07 0.10 0.58 0.23 0
## colquitt_2 0.00 0.00 0.03 0.04 0.18 0.51 0.24 0
## colquitt_3 0.00 0.00 0.01 0.06 0.16 0.53 0.24 0
## colquitt_4 0.01 0.01 0.03 0.07 0.21 0.38 0.28 0psych::alpha(df_scales %>% select(starts_with("treat_")))##
## Reliability analysis
## Call: psych::alpha(x = df_scales %>% select(starts_with("treat_")))
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.88 0.89 0.89 0.53 7.8 0.018 5.6 0.81 0.54
##
## 95% confidence boundaries
## lower alpha upper
## Feldt 0.84 0.88 0.91
## Duhachek 0.84 0.88 0.92
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## treat_1 0.89 0.89 0.88 0.57 8.0 0.017 0.0062 0.60
## treat_2 0.85 0.86 0.86 0.51 6.2 0.023 0.0125 0.51
## treat_3 0.85 0.86 0.86 0.51 6.3 0.023 0.0132 0.51
## treat_4 0.86 0.87 0.86 0.52 6.6 0.022 0.0135 0.51
## treat_5 0.86 0.86 0.86 0.51 6.2 0.022 0.0112 0.49
## treat_6 0.87 0.87 0.87 0.54 6.9 0.021 0.0134 0.55
## treat_7 0.87 0.88 0.87 0.55 7.2 0.020 0.0094 0.58
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## treat_1 99 0.69 0.66 0.57 0.54 5.1 1.31
## treat_2 99 0.83 0.83 0.80 0.75 5.7 1.11
## treat_3 99 0.83 0.82 0.79 0.75 5.4 1.20
## treat_4 99 0.79 0.79 0.75 0.71 5.7 1.03
## treat_5 99 0.81 0.83 0.81 0.75 6.1 0.89
## treat_6 99 0.73 0.75 0.70 0.65 5.9 0.89
## treat_7 99 0.70 0.72 0.66 0.60 5.7 0.95
##
## Non missing response frequency for each item
## 2 3 4 5 6 7 miss
## treat_1 0.04 0.08 0.20 0.25 0.29 0.13 0
## treat_2 0.01 0.04 0.07 0.23 0.39 0.25 0
## treat_3 0.00 0.08 0.14 0.26 0.31 0.20 0
## treat_4 0.00 0.05 0.07 0.22 0.46 0.19 0
## treat_5 0.00 0.02 0.03 0.15 0.46 0.33 0
## treat_6 0.00 0.01 0.06 0.22 0.46 0.24 0
## treat_7 0.00 0.02 0.08 0.27 0.42 0.20 0psych::alpha(df_scales %>% select(starts_with("idea_")))## Number of categories should be increased in order to count frequencies.## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done## Warning in psych::alpha(df_scales %>% select(starts_with("idea_"))): Some items were negatively correlated with the first principal component and probably
## should be reversed.
## To do this, run the function again with the 'check.keys=TRUE' option## Some items ( idea_attachment ) were negatively correlated with the first principal component and
## probably should be reversed.
## To do this, run the function again with the 'check.keys=TRUE' option## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0##
## Reliability analysis
## Call: psych::alpha(x = df_scales %>% select(starts_with("idea_")))
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.87 0.88 0.88 0.41 7.7 0.019 5.3 0.76 0.48
##
## 95% confidence boundaries
## lower alpha upper
## Feldt 0.83 0.87 0.91
## Duhachek 0.84 0.87 0.91
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## idea_1 0.85 0.87 0.95 0.39 6.5 0.022 0.089 0.45
## idea_2 0.86 0.87 0.94 0.41 6.8 0.021 0.091 0.48
## idea_3 0.85 0.87 0.95 0.39 6.5 0.021 0.090 0.45
## idea_4 0.85 0.87 0.95 0.39 6.4 0.022 0.089 0.45
## idea_5 0.86 0.88 0.95 0.41 7.0 0.020 0.088 0.45
## idea_6 0.85 0.87 0.94 0.39 6.4 0.022 0.090 0.45
## idea_7 0.86 0.88 0.94 0.41 7.0 0.020 0.096 0.50
## idea_8R 0.87 0.88 0.88 0.42 7.3 0.019 0.087 0.51
## idea_8R_recoded 0.87 0.88 0.88 0.42 7.3 0.019 0.087 0.51
## idea_attachment 0.90 0.91 0.89 0.52 10.7 0.016 0.040 0.58
## idea_inclusion 0.84 0.85 0.86 0.36 5.6 0.023 0.076 0.37
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## idea_1 99 0.776 0.792 0.79 0.716 5.5 1.08
## idea_2 99 0.691 0.712 0.69 0.608 5.3 1.14
## idea_3 99 0.763 0.788 0.79 0.704 5.5 1.02
## idea_4 99 0.781 0.804 0.80 0.729 5.5 0.96
## idea_5 99 0.633 0.677 0.66 0.557 5.5 0.95
## idea_6 99 0.779 0.801 0.80 0.714 5.6 1.17
## idea_7 99 0.649 0.673 0.64 0.567 5.5 1.04
## idea_8R 99 0.682 0.611 0.51 0.561 5.1 1.55
## idea_8R_recoded 99 0.682 0.611 0.51 0.561 5.1 1.55
## idea_attachment 99 0.037 0.042 -0.09 -0.082 3.6 1.00
## idea_inclusion 99 0.993 0.988 0.91 0.991 5.4 0.84psych::alpha(df_scales %>% select(starts_with("belong_")))## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done## In factor.stats, I could not find the RMSEA upper bound . Sorry about that
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0
## In smc, smcs < 0 were set to .0##
## Reliability analysis
## Call: psych::alpha(x = df_scales %>% select(starts_with("belong_")))
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.97 0.97 0.92 0.72 30 0.0049 5.5 1.2 0.71
##
## 95% confidence boundaries
## lower alpha upper
## Feldt 0.95 0.97 0.97
## Duhachek 0.96 0.97 0.98
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r
## belong_1 0.96 0.97 0.90 0.72 29 0.0051 0.0093
## belong_2R 0.96 0.96 0.92 0.71 28 0.0054 0.0086
## belong_3 0.96 0.97 0.90 0.72 28 0.0053 0.0105
## belong_4R 0.96 0.97 0.92 0.72 28 0.0053 0.0086
## belong_5 0.96 0.97 0.90 0.72 28 0.0053 0.0095
## belong_6R 0.96 0.96 0.92 0.71 27 0.0056 0.0092
## belong_7 0.96 0.97 0.90 0.72 29 0.0052 0.0096
## belong_8R 0.96 0.96 0.92 0.71 27 0.0055 0.0092
## belong_2R_recoded 0.96 0.96 0.92 0.71 28 0.0054 0.0086
## belong_4R_recoded 0.96 0.97 0.92 0.72 28 0.0053 0.0086
## belong_6R_recoded 0.96 0.96 0.92 0.71 27 0.0056 0.0092
## belong_8R_recoded 0.96 0.96 0.92 0.71 27 0.0055 0.0092
## med.r
## belong_1 0.72
## belong_2R 0.71
## belong_3 0.72
## belong_4R 0.71
## belong_5 0.71
## belong_6R 0.71
## belong_7 0.72
## belong_8R 0.71
## belong_2R_recoded 0.71
## belong_4R_recoded 0.71
## belong_6R_recoded 0.71
## belong_8R_recoded 0.71
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## belong_1 99 0.81 0.82 0.83 0.77 5.3 1.28
## belong_2R 99 0.87 0.86 0.80 0.84 5.5 1.54
## belong_3 99 0.82 0.84 0.85 0.80 5.7 0.95
## belong_4R 99 0.85 0.85 0.79 0.82 5.8 1.10
## belong_5 99 0.83 0.84 0.85 0.80 5.4 1.27
## belong_6R 99 0.90 0.90 0.84 0.88 5.5 1.44
## belong_7 99 0.82 0.83 0.84 0.78 5.4 1.25
## belong_8R 99 0.89 0.88 0.82 0.86 5.2 1.64
## belong_2R_recoded 99 0.87 0.86 0.80 0.84 5.5 1.54
## belong_4R_recoded 99 0.85 0.85 0.79 0.82 5.8 1.10
## belong_6R_recoded 99 0.90 0.90 0.84 0.88 5.5 1.44
## belong_8R_recoded 99 0.89 0.88 0.82 0.86 5.2 1.64
##
## Non missing response frequency for each item
## 1 2 3 4 5 6 7 miss
## belong_1 0.00 0.03 0.09 0.08 0.29 0.33 0.17 0
## belong_2R 0.02 0.03 0.10 0.07 0.13 0.35 0.29 0
## belong_3 0.00 0.00 0.03 0.07 0.27 0.45 0.17 0
## belong_4R 0.00 0.02 0.02 0.07 0.20 0.42 0.26 0
## belong_5 0.01 0.01 0.09 0.08 0.27 0.36 0.17 0
## belong_6R 0.00 0.05 0.10 0.04 0.18 0.37 0.25 0
## belong_7 0.01 0.01 0.08 0.08 0.25 0.39 0.17 0
## belong_8R 0.02 0.05 0.15 0.07 0.17 0.30 0.23 0
## belong_2R_recoded 0.02 0.03 0.10 0.07 0.13 0.35 0.29 0
## belong_4R_recoded 0.00 0.02 0.02 0.07 0.20 0.42 0.26 0
## belong_6R_recoded 0.00 0.05 0.10 0.04 0.18 0.37 0.25 0
## belong_8R_recoded 0.02 0.05 0.15 0.07 0.17 0.30 0.23 0All alphas are above 0.80. Looks good to me!
Summary stats
df_scales %>%
summarise(
across(c(idea_attachment,
interactional_justice,
personal_treatment,
idea_inclusion,
belonging),
list(mean = ~mean(.x, na.rm = TRUE),
sd = ~sd(.x, na.rm = TRUE)))
)## # A tibble: 1 × 10
## idea_attachment_mean idea_attachment_sd interactional_justice_mean
## <dbl> <dbl> <dbl>
## 1 3.56 1.00 5.87
## # ℹ 7 more variables: interactional_justice_sd <dbl>,
## # personal_treatment_mean <dbl>, personal_treatment_sd <dbl>,
## # idea_inclusion_mean <dbl>, idea_inclusion_sd <dbl>, belonging_mean <dbl>,
## # belonging_sd <dbl>Correl matrix
df_scales %>%
select(idea_attachment,
interactional_justice,
personal_treatment,
idea_inclusion,
belonging) %>%
cor(use = "pairwise.complete.obs")## idea_attachment interactional_justice personal_treatment
## idea_attachment 1.00000000 -0.2118755 -0.1284202
## interactional_justice -0.21187545 1.0000000 0.7377405
## personal_treatment -0.12842018 0.7377405 1.0000000
## idea_inclusion -0.08241071 0.6494951 0.6936621
## belonging -0.13297661 0.6984000 0.7271349
## idea_inclusion belonging
## idea_attachment -0.08241071 -0.1329766
## interactional_justice 0.64949507 0.6984000
## personal_treatment 0.69366208 0.7271349
## idea_inclusion 1.00000000 0.6917183
## belonging 0.69171825 1.0000000Belonging is really highly correlated with personal treatment (scenarios and colquitt) and idea inclusion scenarios.
Testing conceptual model
Path 1: Personal treatment → Belonging
model1 <- lm(belonging ~ interactional_justice + personal_treatment,
data = df_scales)
summary(model1)##
## Call:
## lm(formula = belonging ~ interactional_justice + personal_treatment,
## data = df_scales)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.4557 -0.2195 0.1010 0.4217 1.4919
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.2952 0.5878 -2.203 0.02996 *
## interactional_justice 0.5097 0.1395 3.655 0.00042 ***
## personal_treatment 0.6679 0.1397 4.781 6.28e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7571 on 96 degrees of freedom
## Multiple R-squared: 0.5863, Adjusted R-squared: 0.5777
## F-statistic: 68.02 on 2 and 96 DF, p-value: < 2.2e-16library(ggplot2)
ggplot(df_scales, aes(x = personal_treatment, y = belonging)) +
geom_point(alpha = .6) +
geom_smooth(method = "lm", se = TRUE) +
labs(
x = "Personal Treatment",
y = "Belonging",
title = "Path 1: Personal Treatment → Belonging"
) +
theme_minimal()## `geom_smooth()` using formula = 'y ~ x'
ggplot(df_scales, aes(x = interactional_justice, y = belonging)) +
geom_point(alpha = .6) +
geom_smooth(method = "lm", se = TRUE) +
labs(
x = "Interactional Justice",
y = "Belonging",
title = "Interactional Justice → Belonging"
) +
theme_minimal()## `geom_smooth()` using formula = 'y ~ x'
Path 2: Felt idea inclusion → Belonging
model2 <- lm(belonging ~ idea_inclusion,
data = df_scales)
summary(model2)##
## Call:
## lm(formula = belonging ~ idea_inclusion, data = df_scales)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.9429 -0.3238 0.1165 0.4857 2.0332
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.2412 0.5606 0.430 0.668
## idea_inclusion 0.9642 0.1022 9.434 2.24e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8457 on 97 degrees of freedom
## Multiple R-squared: 0.4785, Adjusted R-squared: 0.4731
## F-statistic: 88.99 on 1 and 97 DF, p-value: 2.242e-15ggplot(df_scales, aes(x = idea_inclusion, y = belonging)) +
geom_point(alpha = .6) +
geom_smooth(method = "lm", se = TRUE) +
labs(
x = "Felt Idea Inclusion",
y = "Belonging",
title = "Path 2: Idea Inclusion → Belonging"
) +
theme_minimal()## `geom_smooth()` using formula = 'y ~ x'
Idea attachemnt to belonging
ggplot(df_scales, aes(x = idea_attachment, y = belonging)) +
geom_point(alpha = .6) +
geom_smooth(method = "lm", se = TRUE) +
labs(
x = "Idea Attachment (Importance)",
y = "Belonging",
title = "Extra: Idea Attachment → Belonging"
) +
theme_minimal()## `geom_smooth()` using formula = 'y ~ x'
Path 3: Both paths (idea importance and personal treatment) → Belonging
model_full <- lm(belonging ~ interactional_justice +
personal_treatment +
idea_inclusion,
data = df_scales)
summary(model_full)##
## Call:
## lm(formula = belonging ~ interactional_justice + personal_treatment +
## idea_inclusion, data = df_scales)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.59991 -0.17846 0.08155 0.43943 1.21427
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.6416 0.5719 -2.870 0.00505 **
## interactional_justice 0.3840 0.1389 2.764 0.00686 **
## personal_treatment 0.4718 0.1469 3.212 0.00180 **
## idea_inclusion 0.4042 0.1265 3.194 0.00190 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7233 on 95 degrees of freedom
## Multiple R-squared: 0.6264, Adjusted R-squared: 0.6146
## F-statistic: 53.1 on 3 and 95 DF, p-value: < 2.2e-16Mediation model
library(lavaan)## This is lavaan 0.6-18
## lavaan is FREE software! Please report any bugs.##
## Attaching package: 'lavaan'## The following object is masked from 'package:psych':
##
## cor2covmed_model <- '
# mediator
idea_attachment ~ a*idea_inclusion
# outcome
belonging ~ b*idea_attachment + c_prime*idea_inclusion
# indirect effect
indirect := a*b
# total effect
total := c_prime + indirect
'
fit_med <- sem(
med_model,
data = df_scales,
se = "bootstrap",
bootstrap = 1000,
missing = "fiml"
)
summary(fit_med, standardized = TRUE, fit.measures = TRUE)## lavaan 0.6-18 ended normally after 1 iteration
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 7
##
## Number of observations 99
## Number of missing patterns 1
##
## Model Test User Model:
##
## Test statistic 0.000
## Degrees of freedom 0
##
## Model Test Baseline Model:
##
## Test statistic 66.233
## Degrees of freedom 3
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000
## Tucker-Lewis Index (TLI) 1.000
##
## Robust Comparative Fit Index (CFI) 1.000
## Robust Tucker-Lewis Index (TLI) 1.000
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -261.931
## Loglikelihood unrestricted model (H1) -261.931
##
## Akaike (AIC) 537.863
## Bayesian (BIC) 556.028
## Sample-size adjusted Bayesian (SABIC) 533.922
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.000
## P-value H_0: RMSEA <= 0.050 NA
## P-value H_0: RMSEA >= 0.080 NA
##
## Robust RMSEA 0.000
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.000
## P-value H_0: Robust RMSEA <= 0.050 NA
## P-value H_0: Robust RMSEA >= 0.080 NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.000
##
## Parameter Estimates:
##
## Standard errors Bootstrap
## Number of requested bootstrap draws 1000
## Number of successful bootstrap draws 1000
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## idea_attachment ~
## id_ncls (a) -0.099 0.134 -0.735 0.462 -0.099 -0.082
## belonging ~
## id_ttch (b) -0.089 0.112 -0.794 0.427 -0.089 -0.076
## id_ncls (c_pr) 0.955 0.080 11.955 0.000 0.955 0.685
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .idea_attachmnt 4.091 0.697 5.865 0.000 4.091 4.112
## .belonging 0.606 0.725 0.835 0.404 0.606 0.523
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .idea_attachmnt 0.983 0.155 6.352 0.000 0.983 0.993
## .belonging 0.693 0.143 4.858 0.000 0.693 0.516
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## indirect 0.009 0.023 0.383 0.702 0.009 0.006
## total 0.964 0.079 12.277 0.000 0.964 0.692parameterEstimates(fit_med, standardized = TRUE, ci = TRUE)## lhs op rhs label est se z pvalue
## 1 idea_attachment ~ idea_inclusion a -0.099 0.134 -0.735 0.462
## 2 belonging ~ idea_attachment b -0.089 0.112 -0.794 0.427
## 3 belonging ~ idea_inclusion c_prime 0.955 0.080 11.955 0.000
## 4 idea_attachment ~~ idea_attachment 0.983 0.155 6.352 0.000
## 5 belonging ~~ belonging 0.693 0.143 4.858 0.000
## 6 idea_inclusion ~~ idea_inclusion 0.692 0.000 NA NA
## 7 idea_attachment ~1 4.091 0.697 5.865 0.000
## 8 belonging ~1 0.606 0.725 0.835 0.404
## 9 idea_inclusion ~1 5.422 0.000 NA NA
## 10 indirect := a*b indirect 0.009 0.023 0.383 0.702
## 11 total := c_prime+indirect total 0.964 0.079 12.277 0.000
## ci.lower ci.upper std.lv std.all std.nox
## 1 -0.343 0.163 -0.099 -0.082 -0.099
## 2 -0.302 0.157 -0.089 -0.076 -0.076
## 3 0.811 1.130 0.955 0.685 0.824
## 4 0.671 1.266 0.983 0.993 0.993
## 5 0.427 0.972 0.693 0.516 0.516
## 6 0.692 0.692 0.692 1.000 0.692
## 7 2.754 5.367 4.091 4.112 4.112
## 8 -0.901 1.942 0.606 0.523 0.523
## 9 5.422 5.422 5.422 6.520 5.422
## 10 -0.032 0.061 0.009 0.006 0.008
## 11 0.809 1.129 0.964 0.692 0.832A mediation analysis using bootstrapping revealed that idea attachment did not mediate the relationship between idea inclusion and belonging (indirect effect = 0.009, p = .691).
Instead, idea inclusion exerted a strong direct effect on belonging (β = .69, p < .001), suggesting that belonging is driven primarily by whether individuals feel their ideas are included, rather than by their attachment to those ideas.