Ed_thriving_TWB_LMC
K.Evans
2025-05-24
# Load packages
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 1.9.3 ✔ tidyr 1.3.1
## ✔ purrr 1.0.2
## ── 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(janitor)##
## Attaching package: 'janitor'
##
## The following objects are masked from 'package:stats':
##
## chisq.test, fisher.testlibrary(psych)##
## Attaching package: 'psych'
##
## The following objects are masked from 'package:ggplot2':
##
## %+%, alphalibrary(haven)
library(skimr)
library(lubridate)
library(readr)
library(knitr)
library(kableExtra)##
## Attaching package: 'kableExtra'
##
## The following object is masked from 'package:dplyr':
##
## group_rowslibrary(dplyr)
library(tinytex)#upload data
#df <- ET_District_Survey_Pleasantville_LMC_Spring_2025_5_24_25_analysis
df_up <- Spring_2025_NEA_Data_Survey_data_1_
# Remove the first row from spring data item prompts
df <- df_up[-1, ]
#convert to factor
df$PID <- as.factor(df$PID)
df$TWB39 <- as.factor(df$TWB39)
#update other variables to num
# Identify character columns excluding PID and twb39
char_cols <- sapply(df, is.character)
char_cols[c("PID", "TWB39")] <- FALSE # exclude these two
# Convert remaining character columns to numeric
df[, char_cols] <- lapply(df[, char_cols], function(x) as.numeric(x))
df## # A tibble: 3,814 × 54
## PID TWB1 TWB2 TWB3 TWB4 TWB5 TWB6 TWB7 TWB8 TWB9 TWB10 TWB11 TWB12
## <fct> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 Clif… 1 1 1 1 1 1 1 1 1 1 1 1
## 2 Clif… 1 1 1 1 1 1 1 1 1 1 1 1
## 3 Clif… 1 1 1 1 1 6 6 1 1 1 1 1
## 4 Clif… 1 3 4 5 4 1 4 2 5 4 2 4
## 5 Clif… 1 1 1 1 1 1 1 1 1 1 1 1
## 6 Clif… 1 1 1 1 1 1 1 1 1 1 1 1
## 7 Clif… 1 1 1 1 1 1 1 1 1 1 1 1
## 8 Clif… 1 1 2 3 2 2 1 3 2 2 1 1
## 9 Clif… 6 5 5 5 6 6 4 5 6 6 4 6
## 10 Clif… 6 6 6 6 6 6 6 6 6 6 6 6
## # ℹ 3,804 more rows
## # ℹ 41 more variables: TWB13 <dbl>, TWB14 <dbl>, TWB15 <dbl>, TWB16 <dbl>,
## # TWB17 <dbl>, TWB18 <dbl>, TWB19 <dbl>, TWB20 <dbl>, TWB21 <dbl>,
## # TWB22 <dbl>, TWB23 <dbl>, TWB24 <dbl>, TWB25 <dbl>, TWB26 <dbl>,
## # TWB27 <dbl>, TWB28 <dbl>, TWB29 <dbl>, TWB30 <dbl>, TWB31 <dbl>,
## # TWB32 <dbl>, TWB33 <dbl>, TWB34 <dbl>, TWB35 <dbl>, TWB36 <dbl>,
## # TWB37 <dbl>, TWB38 <dbl>, TWB39 <fct>, TWB40 <dbl>, TWB41 <dbl>, …# TWB: Responsive Leadership & Supportive Culture (TWB1–TWB14)
df <- df %>%
mutate(
twb_sub_score = (
TWB1 + TWB2 + TWB3 + TWB4 + TWB5 + TWB6 + TWB7 +
TWB8 + TWB9 + TWB10 + TWB11 + TWB12 + TWB13 + TWB14
) / 14
)
# Growth (TWB15–TWB17)
df <- df %>%
mutate(
growth_score = (TWB15 + TWB16 + TWB17) / 3
)
# Well-being (TWB18–TWB19)
df <- df %>%
mutate(
wellbeing_score = (TWB18 + TWB19) / 2
)
# Acceptance (TWB20–TWB21)
df <- df %>%
mutate(
acceptance_score = (TWB20 + TWB21) / 2
)
# Adaptability (TWB22–TWB23)
df <- df %>%
mutate(
adaptability_score = (TWB22 + TWB23) / 2
)
# Depletion (TWB24–TWB25)
df <- df %>%
mutate(
depletion_score = (TWB24 + TWB25) / 2
)
# Foundational Support (TWB26–TWB31)
df <- df %>%
mutate(
foundational_support_score = (
TWB26 + TWB27 + TWB28 + TWB29 + TWB30 + TWB31
) / 6
)
# TWB composite (all above subscales)
df <- df %>%
mutate(
twb_composite_score = (
twb_sub_score +
growth_score +
wellbeing_score +
acceptance_score +
adaptability_score +
depletion_score +
foundational_support_score
)
)# Create item-level dataframe for reliability checks
twb_items <- df %>%
select(TWB1:TWB14) %>%
na.omit()
growth_items <- df %>%
select(TWB15, TWB16, TWB17) %>%
na.omit()
wellbeing_items <- df %>%
select(TWB18, TWB19) %>%
na.omit()
acceptance_items <- df %>%
select(TWB20, TWB21) %>%
na.omit()
adaptability_items <- df %>%
select(TWB22, TWB23) %>%
na.omit()
depletion_items <- df %>%
select(TWB24, TWB25) %>%
na.omit()
foundational_items <- df %>%
select(TWB26:TWB31) %>%
na.omit()
#alphas
psych::alpha(twb_items)##
## Reliability analysis
## Call: psych::alpha(x = twb_items)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.97 0.97 0.97 0.7 33 0.00075 4.5 1.2 0.69
##
## 95% confidence boundaries
## lower alpha upper
## Feldt 0.97 0.97 0.97
## Duhachek 0.97 0.97 0.97
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## TWB1 0.97 0.97 0.97 0.69 29 0.00084 0.0037 0.69
## TWB2 0.97 0.97 0.97 0.70 30 0.00083 0.0040 0.69
## TWB3 0.97 0.97 0.97 0.70 30 0.00083 0.0038 0.69
## TWB4 0.97 0.97 0.97 0.70 30 0.00083 0.0037 0.69
## TWB5 0.97 0.97 0.97 0.69 30 0.00084 0.0038 0.69
## TWB6 0.97 0.97 0.97 0.70 30 0.00081 0.0043 0.69
## TWB7 0.97 0.97 0.97 0.70 30 0.00083 0.0039 0.69
## TWB8 0.97 0.97 0.97 0.70 30 0.00082 0.0041 0.69
## TWB9 0.97 0.97 0.97 0.70 30 0.00081 0.0041 0.69
## TWB10 0.97 0.97 0.97 0.71 31 0.00079 0.0041 0.71
## TWB11 0.97 0.97 0.97 0.70 31 0.00079 0.0038 0.69
## TWB12 0.97 0.97 0.97 0.71 32 0.00077 0.0031 0.71
## TWB13 0.97 0.97 0.97 0.71 32 0.00079 0.0039 0.71
## TWB14 0.97 0.97 0.97 0.71 32 0.00078 0.0039 0.71
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## TWB1 3307 0.90 0.90 0.90 0.89 4.6 1.4
## TWB2 3307 0.88 0.88 0.87 0.86 4.4 1.5
## TWB3 3307 0.88 0.88 0.88 0.86 4.7 1.3
## TWB4 3307 0.89 0.89 0.88 0.87 4.6 1.4
## TWB5 3307 0.89 0.89 0.89 0.87 4.6 1.4
## TWB6 3307 0.86 0.86 0.84 0.83 4.5 1.5
## TWB7 3307 0.89 0.89 0.88 0.87 4.5 1.4
## TWB8 3307 0.87 0.86 0.85 0.84 4.4 1.5
## TWB9 3307 0.85 0.86 0.84 0.83 4.8 1.3
## TWB10 3307 0.80 0.80 0.78 0.77 4.8 1.3
## TWB11 3307 0.83 0.82 0.81 0.79 4.3 1.5
## TWB12 3307 0.76 0.76 0.74 0.72 4.9 1.4
## TWB13 3307 0.80 0.80 0.78 0.77 4.3 1.4
## TWB14 3307 0.79 0.79 0.77 0.76 4.2 1.4
##
## Non missing response frequency for each item
## 1 2 3 4 5 6 miss
## TWB1 0.05 0.06 0.08 0.17 0.31 0.33 0
## TWB2 0.07 0.08 0.09 0.20 0.29 0.26 0
## TWB3 0.04 0.06 0.06 0.18 0.31 0.35 0
## TWB4 0.05 0.06 0.09 0.19 0.33 0.28 0
## TWB5 0.05 0.07 0.07 0.20 0.33 0.29 0
## TWB6 0.07 0.08 0.08 0.18 0.27 0.32 0
## TWB7 0.05 0.07 0.08 0.20 0.34 0.25 0
## TWB8 0.07 0.08 0.09 0.17 0.33 0.26 0
## TWB9 0.03 0.04 0.06 0.17 0.35 0.34 0
## TWB10 0.03 0.04 0.06 0.18 0.35 0.33 0
## TWB11 0.08 0.08 0.09 0.18 0.32 0.25 0
## TWB12 0.04 0.05 0.04 0.13 0.31 0.43 0
## TWB13 0.06 0.07 0.09 0.22 0.33 0.22 0
## TWB14 0.07 0.08 0.12 0.22 0.32 0.19 0psych::alpha(growth_items)##
## Reliability analysis
## Call: psych::alpha(x = growth_items)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.83 0.83 0.77 0.62 4.9 0.0051 5.2 0.74 0.62
##
## 95% confidence boundaries
## lower alpha upper
## Feldt 0.82 0.83 0.84
## Duhachek 0.82 0.83 0.84
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## TWB15 0.76 0.76 0.62 0.62 3.2 0.0082 NA 0.62
## TWB16 0.75 0.77 0.62 0.62 3.3 0.0081 NA 0.62
## TWB17 0.77 0.77 0.63 0.63 3.4 0.0080 NA 0.63
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## TWB15 3328 0.88 0.87 0.76 0.69 5.2 0.95
## TWB16 3328 0.86 0.86 0.76 0.69 5.2 0.84
## TWB17 3328 0.85 0.86 0.75 0.69 5.4 0.75
##
## Non missing response frequency for each item
## 1 2 3 4 5 6 miss
## TWB15 0.01 0.02 0.03 0.13 0.39 0.42 0
## TWB16 0.00 0.01 0.02 0.14 0.43 0.40 0
## TWB17 0.00 0.00 0.01 0.10 0.40 0.49 0psych::alpha(wellbeing_items)##
## Reliability analysis
## Call: psych::alpha(x = wellbeing_items)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.73 0.74 0.58 0.58 2.8 0.0091 5.2 0.84 0.58
##
## 95% confidence boundaries
## lower alpha upper
## Feldt 0.72 0.73 0.75
## Duhachek 0.72 0.73 0.75
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## TWB18 0.63 0.58 0.34 0.58 1.4 NA 0 0.58
## TWB19 0.54 0.58 0.34 0.58 1.4 NA 0 0.58
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## TWB18 3332 0.90 0.89 0.68 0.58 5.1 0.98
## TWB19 3332 0.88 0.89 0.68 0.58 5.3 0.91
##
## Non missing response frequency for each item
## 1 2 3 4 5 6 miss
## TWB18 0.01 0.02 0.03 0.14 0.38 0.42 0
## TWB19 0.01 0.01 0.03 0.10 0.38 0.47 0psych::alpha(acceptance_items)##
## Reliability analysis
## Call: psych::alpha(x = acceptance_items)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.73 0.73 0.58 0.58 2.7 0.0093 4.8 0.83 0.58
##
## 95% confidence boundaries
## lower alpha upper
## Feldt 0.71 0.73 0.75
## Duhachek 0.71 0.73 0.75
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## TWB20 0.60 0.58 0.33 0.58 1.4 NA 0 0.58
## TWB21 0.56 0.58 0.33 0.58 1.4 NA 0 0.58
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## TWB20 3317 0.89 0.89 0.68 0.58 4.8 0.95
## TWB21 3317 0.88 0.89 0.68 0.58 4.8 0.91
##
## Non missing response frequency for each item
## 1 2 3 4 5 6 miss
## TWB20 0.01 0.02 0.05 0.24 0.46 0.22 0
## TWB21 0.00 0.02 0.06 0.25 0.48 0.19 0psych::alpha(adaptability_items)##
## Reliability analysis
## Call: psych::alpha(x = adaptability_items)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.68 0.68 0.52 0.52 2.2 0.011 5.2 0.66 0.52
##
## 95% confidence boundaries
## lower alpha upper
## Feldt 0.66 0.68 0.7
## Duhachek 0.66 0.68 0.7
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## TWB22 0.58 0.52 0.27 0.52 1.1 NA 0 0.52
## TWB23 0.47 0.52 0.27 0.52 1.1 NA 0 0.52
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## TWB22 3321 0.89 0.87 0.63 0.52 5.1 0.80
## TWB23 3321 0.86 0.87 0.63 0.52 5.2 0.72
##
## Non missing response frequency for each item
## 1 2 3 4 5 6 miss
## TWB22 0 0.01 0.02 0.13 0.52 0.31 0
## TWB23 0 0.00 0.01 0.12 0.51 0.36 0psych::alpha(depletion_items)##
## Reliability analysis
## Call: psych::alpha(x = depletion_items)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.76 0.76 0.61 0.61 3.1 0.0085 3.6 1.3 0.61
##
## 95% confidence boundaries
## lower alpha upper
## Feldt 0.74 0.76 0.77
## Duhachek 0.74 0.76 0.77
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## TWB24 0.62 0.61 0.37 0.61 1.6 NA 0 0.61
## TWB25 0.59 0.61 0.37 0.61 1.6 NA 0 0.61
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## TWB24 3313 0.90 0.9 0.7 0.61 3.8 1.4
## TWB25 3313 0.89 0.9 0.7 0.61 3.3 1.4
##
## Non missing response frequency for each item
## 1 2 3 4 5 6 miss
## TWB24 0.05 0.16 0.14 0.32 0.18 0.14 0
## TWB25 0.09 0.28 0.16 0.27 0.14 0.06 0psych::alpha(foundational_items)##
## Reliability analysis
## Call: psych::alpha(x = foundational_items)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.87 0.87 0.86 0.53 6.7 0.0049 3.7 1.1 0.57
##
## 95% confidence boundaries
## lower alpha upper
## Feldt 0.86 0.87 0.88
## Duhachek 0.86 0.87 0.88
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## TWB26 0.89 0.89 0.87 0.62 8.0 0.0042 0.0066 0.61
## TWB27 0.85 0.85 0.84 0.53 5.6 0.0059 0.0279 0.57
## TWB28 0.84 0.85 0.84 0.52 5.5 0.0060 0.0255 0.55
## TWB29 0.82 0.83 0.81 0.49 4.8 0.0066 0.0160 0.51
## TWB30 0.83 0.83 0.81 0.49 4.9 0.0065 0.0148 0.51
## TWB31 0.84 0.85 0.84 0.52 5.5 0.0060 0.0245 0.58
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## TWB26 1793 0.60 0.59 0.45 0.43 3.0 1.5
## TWB27 1793 0.78 0.78 0.71 0.67 3.5 1.5
## TWB28 1793 0.80 0.79 0.74 0.69 3.5 1.6
## TWB29 1793 0.86 0.87 0.86 0.79 4.0 1.4
## TWB30 1793 0.85 0.85 0.84 0.77 4.0 1.4
## TWB31 1793 0.78 0.79 0.74 0.69 4.3 1.4
##
## Non missing response frequency for each item
## 1 2 3 4 5 6 miss
## TWB26 0.25 0.18 0.16 0.21 0.17 0.04 0
## TWB27 0.12 0.17 0.17 0.24 0.22 0.09 0
## TWB28 0.15 0.14 0.16 0.22 0.23 0.10 0
## TWB29 0.08 0.09 0.13 0.27 0.30 0.13 0
## TWB30 0.08 0.08 0.13 0.27 0.32 0.12 0
## TWB31 0.07 0.05 0.10 0.22 0.40 0.16 0# Combine all TWB items (TWB1 to TWB31) into one dataframe
twb_full_items <- df %>%
select(TWB1:TWB31) %>%
na.omit() # only include complete cases for alpha
# Cronbach's alpha for full TWB scale (31 items)
twb_full_alpha <- psych::alpha(twb_full_items)## Some items ( TWB24 TWB25 ) 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' optionprint(twb_full_alpha) #.93 high alpha for collective measure##
## Reliability analysis
## Call: psych::alpha(x = twb_full_items)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.94 0.94 0.96 0.34 16 0.0018 4.6 0.76 0.3
##
## 95% confidence boundaries
## lower alpha upper
## Feldt 0.94 0.94 0.94
## Duhachek 0.94 0.94 0.94
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## TWB1 0.94 0.94 0.96 0.33 14 0.0019 0.070 0.29
## TWB2 0.94 0.94 0.96 0.33 15 0.0019 0.071 0.29
## TWB3 0.94 0.94 0.96 0.33 15 0.0019 0.071 0.29
## TWB4 0.94 0.94 0.96 0.33 14 0.0019 0.070 0.29
## TWB5 0.94 0.94 0.96 0.33 14 0.0019 0.070 0.29
## TWB6 0.94 0.94 0.96 0.33 15 0.0019 0.071 0.29
## TWB7 0.94 0.94 0.96 0.33 15 0.0019 0.071 0.29
## TWB8 0.94 0.94 0.96 0.33 15 0.0019 0.071 0.29
## TWB9 0.94 0.94 0.96 0.33 15 0.0019 0.071 0.29
## TWB10 0.94 0.94 0.96 0.33 15 0.0019 0.072 0.29
## TWB11 0.94 0.94 0.96 0.33 15 0.0019 0.071 0.29
## TWB12 0.94 0.94 0.96 0.33 15 0.0019 0.073 0.29
## TWB13 0.94 0.94 0.96 0.33 15 0.0019 0.072 0.29
## TWB14 0.94 0.94 0.96 0.33 15 0.0019 0.072 0.29
## TWB15 0.94 0.94 0.96 0.34 15 0.0018 0.076 0.29
## TWB16 0.94 0.94 0.96 0.34 15 0.0018 0.076 0.29
## TWB17 0.94 0.94 0.96 0.34 16 0.0018 0.076 0.30
## TWB18 0.94 0.94 0.96 0.35 16 0.0017 0.073 0.30
## TWB19 0.94 0.94 0.96 0.35 16 0.0017 0.074 0.31
## TWB20 0.94 0.94 0.96 0.34 16 0.0018 0.075 0.30
## TWB21 0.94 0.94 0.96 0.34 15 0.0018 0.075 0.30
## TWB22 0.94 0.94 0.96 0.34 16 0.0018 0.075 0.30
## TWB23 0.94 0.94 0.96 0.34 16 0.0018 0.076 0.30
## TWB24 0.95 0.95 0.96 0.37 18 0.0016 0.059 0.31
## TWB25 0.95 0.95 0.96 0.37 17 0.0016 0.060 0.31
## TWB26 0.94 0.94 0.96 0.35 16 0.0017 0.075 0.30
## TWB27 0.94 0.94 0.96 0.34 15 0.0018 0.075 0.29
## TWB28 0.94 0.94 0.96 0.34 15 0.0018 0.075 0.29
## TWB29 0.94 0.94 0.96 0.33 15 0.0019 0.073 0.29
## TWB30 0.94 0.94 0.96 0.33 15 0.0019 0.074 0.29
## TWB31 0.94 0.94 0.96 0.33 15 0.0018 0.074 0.29
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## TWB1 1759 0.85 0.83 0.84 0.83 4.9 1.30
## TWB2 1759 0.84 0.82 0.82 0.82 4.6 1.40
## TWB3 1759 0.83 0.81 0.81 0.81 5.0 1.25
## TWB4 1759 0.85 0.84 0.84 0.83 4.8 1.30
## TWB5 1759 0.85 0.84 0.84 0.84 4.8 1.32
## TWB6 1759 0.82 0.81 0.81 0.80 4.7 1.45
## TWB7 1759 0.84 0.82 0.82 0.82 4.7 1.28
## TWB8 1759 0.83 0.81 0.82 0.81 4.6 1.45
## TWB9 1759 0.81 0.80 0.80 0.79 4.9 1.23
## TWB10 1759 0.79 0.78 0.78 0.77 4.9 1.24
## TWB11 1759 0.81 0.80 0.80 0.79 4.5 1.51
## TWB12 1759 0.72 0.71 0.70 0.69 5.1 1.27
## TWB13 1759 0.80 0.79 0.79 0.78 4.5 1.37
## TWB14 1759 0.77 0.76 0.76 0.75 4.4 1.37
## TWB15 1759 0.51 0.55 0.53 0.47 5.2 0.96
## TWB16 1759 0.46 0.51 0.49 0.43 5.2 0.83
## TWB17 1759 0.42 0.47 0.45 0.39 5.4 0.76
## TWB18 1759 0.26 0.31 0.28 0.22 5.1 1.00
## TWB19 1759 0.27 0.32 0.29 0.24 5.3 0.91
## TWB20 1759 0.40 0.44 0.42 0.36 4.9 0.97
## TWB21 1759 0.45 0.50 0.48 0.42 4.8 0.93
## TWB22 1759 0.41 0.46 0.43 0.38 5.1 0.83
## TWB23 1759 0.42 0.47 0.44 0.39 5.3 0.72
## TWB24 1759 -0.16 -0.18 -0.21 -0.22 3.9 1.46
## TWB25 1759 -0.13 -0.15 -0.18 -0.18 3.2 1.43
## TWB26 1759 0.39 0.37 0.34 0.33 3.0 1.54
## TWB27 1759 0.59 0.57 0.56 0.55 3.5 1.50
## TWB28 1759 0.61 0.59 0.57 0.57 3.5 1.58
## TWB29 1759 0.74 0.72 0.72 0.71 4.0 1.43
## TWB30 1759 0.71 0.70 0.69 0.68 4.0 1.40
## TWB31 1759 0.67 0.65 0.64 0.64 4.3 1.36
##
## Non missing response frequency for each item
## 1 2 3 4 5 6 miss
## TWB1 0.04 0.03 0.06 0.15 0.32 0.41 0
## TWB2 0.05 0.05 0.07 0.19 0.31 0.33 0
## TWB3 0.03 0.04 0.05 0.15 0.31 0.43 0
## TWB4 0.04 0.04 0.07 0.17 0.34 0.35 0
## TWB5 0.04 0.05 0.05 0.17 0.34 0.35 0
## TWB6 0.06 0.04 0.07 0.16 0.26 0.40 0
## TWB7 0.04 0.04 0.06 0.18 0.37 0.31 0
## TWB8 0.06 0.05 0.08 0.15 0.33 0.33 0
## TWB9 0.03 0.03 0.04 0.15 0.34 0.40 0
## TWB10 0.03 0.04 0.04 0.16 0.35 0.38 0
## TWB11 0.07 0.07 0.09 0.17 0.30 0.31 0
## TWB12 0.03 0.04 0.03 0.11 0.31 0.48 0
## TWB13 0.05 0.06 0.08 0.21 0.34 0.26 0
## TWB14 0.05 0.06 0.10 0.21 0.34 0.23 0
## TWB15 0.01 0.02 0.03 0.12 0.36 0.47 0
## TWB16 0.00 0.01 0.02 0.13 0.42 0.42 0
## TWB17 0.00 0.00 0.01 0.09 0.37 0.52 0
## TWB18 0.01 0.02 0.04 0.14 0.37 0.42 0
## TWB19 0.01 0.01 0.03 0.10 0.37 0.48 0
## TWB20 0.01 0.02 0.04 0.20 0.45 0.28 0
## TWB21 0.01 0.01 0.05 0.23 0.47 0.23 0
## TWB22 0.00 0.01 0.02 0.13 0.50 0.34 0
## TWB23 0.00 0.00 0.01 0.10 0.48 0.41 0
## TWB24 0.06 0.17 0.13 0.31 0.18 0.16 0
## TWB25 0.10 0.29 0.14 0.26 0.14 0.06 0
## TWB26 0.25 0.18 0.16 0.21 0.17 0.04 0
## TWB27 0.12 0.17 0.16 0.24 0.22 0.09 0
## TWB28 0.15 0.14 0.16 0.22 0.23 0.10 0
## TWB29 0.08 0.09 0.13 0.27 0.30 0.13 0
## TWB30 0.08 0.07 0.13 0.27 0.33 0.12 0
## TWB31 0.07 0.05 0.10 0.22 0.40 0.16 0# Install if needed
# install.packages("lavaan")
library(lavaan)
# Define 7-factor model using lavaan syntax
twb_model <- '
TWB =~ TWB1 + TWB2 + TWB3 + TWB4 + TWB5 + TWB6 + TWB7 + TWB8 + TWB9 + TWB10 + TWB11 + TWB12 + TWB13 + TWB14
Growth =~ TWB15 + TWB16 + TWB17
Wellbeing =~ TWB18 + TWB19
Acceptance =~ TWB20 + TWB21
Adaptability =~ TWB22 + TWB23
Depletion =~ TWB24 + TWB25
Foundation =~ TWB26 + TWB27 + TWB28 + TWB29 + TWB30 + TWB31
'
# Run CFA on full data (remove rows with missing values in TWB1–TWB31)
twb_cfa_data <- df %>%
select(TWB1:TWB31) %>%
na.omit()
# Fit the model
twb_cfa_fit <- cfa(model = twb_model, data = twb_cfa_data, std.lv = TRUE)
# Print summary with fit indices
summary(twb_cfa_fit, fit.measures = TRUE, standardized = TRUE)## lavaan 0.6-19 ended normally after 46 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 83
##
## Number of observations 1759
##
## Model Test User Model:
##
## Test statistic 2031.398
## Degrees of freedom 413
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 40973.122
## Degrees of freedom 465
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.960
## Tucker-Lewis Index (TLI) 0.955
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -68229.690
## Loglikelihood unrestricted model (H1) -67213.991
##
## Akaike (AIC) 136625.380
## Bayesian (BIC) 137079.598
## Sample-size adjusted Bayesian (SABIC) 136815.914
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.047
## 90 Percent confidence interval - lower 0.045
## 90 Percent confidence interval - upper 0.049
## P-value H_0: RMSEA <= 0.050 0.988
## P-value H_0: RMSEA >= 0.080 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.029
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## TWB =~
## TWB1 1.170 0.024 48.759 0.000 1.170 0.901
## TWB2 1.223 0.026 46.331 0.000 1.223 0.873
## TWB3 1.088 0.024 46.232 0.000 1.088 0.872
## TWB4 1.162 0.024 48.167 0.000 1.162 0.894
## TWB5 1.188 0.024 48.790 0.000 1.188 0.901
## TWB6 1.238 0.028 44.553 0.000 1.238 0.853
## TWB7 1.131 0.024 47.155 0.000 1.131 0.883
## TWB8 1.241 0.028 44.973 0.000 1.241 0.858
## TWB9 1.057 0.023 44.985 0.000 1.057 0.858
## TWB10 1.001 0.024 40.883 0.000 1.001 0.806
## TWB11 1.274 0.029 43.824 0.000 1.274 0.844
## TWB12 0.931 0.026 35.845 0.000 0.931 0.736
## TWB13 1.075 0.027 39.152 0.000 1.075 0.783
## TWB14 1.052 0.028 38.176 0.000 1.052 0.769
## Growth =~
## TWB15 0.751 0.021 35.885 0.000 0.751 0.783
## TWB16 0.629 0.018 34.277 0.000 0.629 0.756
## TWB17 0.603 0.017 36.219 0.000 0.603 0.788
## Wellbeing =~
## TWB18 0.743 0.026 28.782 0.000 0.743 0.740
## TWB19 0.686 0.024 29.159 0.000 0.686 0.751
## Acceptance =~
## TWB20 0.706 0.022 32.183 0.000 0.706 0.726
## TWB21 0.747 0.021 36.109 0.000 0.747 0.804
## Adaptability =~
## TWB22 0.570 0.020 29.025 0.000 0.570 0.690
## TWB23 0.502 0.017 29.504 0.000 0.502 0.701
## Depletion =~
## TWB24 1.135 0.041 27.339 0.000 1.135 0.777
## TWB25 1.121 0.041 27.490 0.000 1.121 0.783
## Foundation =~
## TWB26 0.658 0.036 18.088 0.000 0.658 0.427
## TWB27 1.029 0.032 31.782 0.000 1.029 0.685
## TWB28 1.144 0.033 34.316 0.000 1.144 0.725
## TWB29 1.275 0.027 46.809 0.000 1.275 0.892
## TWB30 1.223 0.027 45.098 0.000 1.223 0.872
## TWB31 1.022 0.028 36.116 0.000 1.022 0.752
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## TWB ~~
## Growth 0.455 0.022 20.887 0.000 0.455 0.455
## Wellbeing 0.224 0.027 8.166 0.000 0.224 0.224
## Acceptance 0.406 0.024 16.757 0.000 0.406 0.406
## Adaptability 0.443 0.026 17.209 0.000 0.443 0.443
## Depletion -0.210 0.027 -7.857 0.000 -0.210 -0.210
## Foundation 0.702 0.014 51.758 0.000 0.702 0.702
## Growth ~~
## Wellbeing 0.516 0.025 20.328 0.000 0.516 0.516
## Acceptance 0.513 0.025 20.768 0.000 0.513 0.513
## Adaptability 0.601 0.025 23.798 0.000 0.601 0.601
## Depletion -0.177 0.030 -5.971 0.000 -0.177 -0.177
## Foundation 0.393 0.024 16.418 0.000 0.393 0.393
## Wellbeing ~~
## Acceptance 0.540 0.027 20.274 0.000 0.540 0.540
## Adaptability 0.460 0.031 14.979 0.000 0.460 0.460
## Depletion -0.460 0.028 -16.456 0.000 -0.460 -0.460
## Foundation 0.226 0.028 7.980 0.000 0.226 0.226
## Acceptance ~~
## Adaptability 0.935 0.020 47.912 0.000 0.935 0.935
## Depletion -0.399 0.028 -14.123 0.000 -0.399 -0.399
## Foundation 0.390 0.025 15.339 0.000 0.390 0.390
## Adaptability ~~
## Depletion -0.250 0.033 -7.656 0.000 -0.250 -0.250
## Foundation 0.392 0.028 14.183 0.000 0.392 0.392
## Depletion ~~
## Foundation -0.275 0.027 -10.215 0.000 -0.275 -0.275
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .TWB1 0.319 0.012 26.484 0.000 0.319 0.189
## .TWB2 0.465 0.017 27.279 0.000 0.465 0.237
## .TWB3 0.372 0.014 27.305 0.000 0.372 0.239
## .TWB4 0.339 0.013 26.710 0.000 0.339 0.201
## .TWB5 0.328 0.012 26.471 0.000 0.328 0.188
## .TWB6 0.576 0.021 27.692 0.000 0.576 0.273
## .TWB7 0.362 0.013 27.046 0.000 0.362 0.221
## .TWB8 0.554 0.020 27.604 0.000 0.554 0.265
## .TWB9 0.401 0.015 27.602 0.000 0.401 0.264
## .TWB10 0.539 0.019 28.286 0.000 0.539 0.350
## .TWB11 0.657 0.024 27.833 0.000 0.657 0.288
## .TWB12 0.734 0.025 28.786 0.000 0.734 0.459
## .TWB13 0.729 0.026 28.488 0.000 0.729 0.387
## .TWB14 0.762 0.027 28.586 0.000 0.762 0.408
## .TWB15 0.356 0.018 20.141 0.000 0.356 0.387
## .TWB16 0.297 0.014 21.697 0.000 0.297 0.429
## .TWB17 0.221 0.011 19.784 0.000 0.221 0.379
## .TWB18 0.457 0.028 16.256 0.000 0.457 0.453
## .TWB19 0.363 0.023 15.484 0.000 0.363 0.436
## .TWB20 0.445 0.020 22.366 0.000 0.445 0.472
## .TWB21 0.304 0.018 17.010 0.000 0.304 0.353
## .TWB22 0.357 0.016 22.055 0.000 0.357 0.524
## .TWB23 0.260 0.012 21.420 0.000 0.260 0.508
## .TWB24 0.843 0.073 11.556 0.000 0.843 0.396
## .TWB25 0.790 0.071 11.166 0.000 0.790 0.386
## .TWB26 1.939 0.067 29.082 0.000 1.939 0.817
## .TWB27 1.196 0.044 27.356 0.000 1.196 0.530
## .TWB28 1.180 0.044 26.762 0.000 1.180 0.474
## .TWB29 0.418 0.022 19.270 0.000 0.418 0.205
## .TWB30 0.473 0.022 21.133 0.000 0.473 0.240
## .TWB31 0.801 0.031 26.244 0.000 0.801 0.434
## TWB 1.000 1.000 1.000
## Growth 1.000 1.000 1.000
## Wellbeing 1.000 1.000 1.000
## Acceptance 1.000 1.000 1.000
## Adaptability 1.000 1.000 1.000
## Depletion 1.000 1.000 1.000
## Foundation 1.000 1.000 1.000strong 7 factor fit: | Fit Index | Value | Interpretation | | ————– | ————————— | ————————————————— | | Chi-Square | 744.46 (df = 413, p < .001) | Significant (common in large samples), but expected | | CFI | 0.963 | Excellent fit (> .95 is strong) | | TLI | 0.958 | Excellent fit | | RMSEA | 0.046 (CI: .041–.052) | Good fit (< .06 is desired) | | SRMR | 0.037 | Excellent fit (< .08 is desired) |
TWB (Responsive Leadership & Supportive Culture) All items (TWB1–TWB14) load strongly (.79–.91), e.g.:
TWB6 loading = .912
TWB1 loading = .899
Growth Mindset (TWB15–TWB17) Loadings range from .73–.80
Well-being (TWB18–TWB19) Both loadings are ~.80 → very clean 2-item factor
Acceptance, Adaptability, Depletion, Foundation All items load at acceptable to strong levels
Lowest loading: TWB23 at .594 (still okay)
Some weaker loadings for Foundational Support (e.g., TWB26 at .491) — might indicate room for refinement- same as first data set
Conclusion: Factor loadings are mostly strong, with all standardized loadings > .49 and most > .70. The items are measuring their intended constructs well.
library(lavaan)
# --- Define the 1-Factor Model (TWB1 to TWB31) ---
twb_1factor_model <- '
TWB =~ TWB1 + TWB2 + TWB3 + TWB4 + TWB5 + TWB6 + TWB7 + TWB8 + TWB9 + TWB10 +
TWB11 + TWB12 + TWB13 + TWB14 + TWB15 + TWB16 + TWB17 + TWB18 + TWB19 +
TWB20 + TWB21 + TWB22 + TWB23 + TWB24 + TWB25 + TWB26 + TWB27 + TWB28 +
TWB29 + TWB30 + TWB31
'
# --- Reuse the 7-Factor Model from before ---
twb_7factor_model <- '
TWB =~ TWB1 + TWB2 + TWB3 + TWB4 + TWB5 + TWB6 + TWB7 + TWB8 + TWB9 + TWB10 + TWB11 + TWB12 + TWB13 + TWB14
Growth =~ TWB15 + TWB16 + TWB17
Wellbeing =~ TWB18 + TWB19
Acceptance =~ TWB20 + TWB21
Adaptability =~ TWB22 + TWB23
Depletion =~ TWB24 + TWB25
Foundation =~ TWB26 + TWB27 + TWB28 + TWB29 + TWB30 + TWB31
'
# --- Prepare data (complete cases for TWB1–TWB31) ---
twb_cfa_data <- df %>%
select(TWB1:TWB31) %>%
na.omit()
# --- Fit both models ---
fit_1factor <- cfa(twb_1factor_model, data = twb_cfa_data, std.lv = TRUE)
fit_7factor <- cfa(twb_7factor_model, data = twb_cfa_data, std.lv = TRUE)
# --- Compare fit using Chi-square difference test ---
anova(fit_1factor, fit_7factor)##
## Chi-Squared Difference Test
##
## Df AIC BIC Chisq Chisq diff RMSEA Df diff Pr(>Chisq)
## fit_7factor 413 136625 137080 2031.4
## fit_1factor 434 144691 145030 10138.6 8107.2 0.46788 21 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1The difference in χ² = 1883.3 with 21 df is statistically significant (p < .00001), indicating that the improvement in fit is not due to chance.
The AIC and BIC are also much lower in the 7-factor model, which strongly favors it (lower is better).
The RMSEA for the 1-factor model is 0.4876 — which is extremely poor fit (good models are ≤ .06).
basically it is multidimensional so we should look at the predictive models as such instead of composite the 7 factor is much mor emeaningful to look at at the factor level but adequate to look as single construct scale as well
summary(fit_1factor, fit.measures = TRUE, standardized = TRUE)## lavaan 0.6-19 ended normally after 34 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 62
##
## Number of observations 1759
##
## Model Test User Model:
##
## Test statistic 10138.642
## Degrees of freedom 434
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 40973.122
## Degrees of freedom 465
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.760
## Tucker-Lewis Index (TLI) 0.743
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -72283.312
## Loglikelihood unrestricted model (H1) -67213.991
##
## Akaike (AIC) 144690.624
## Bayesian (BIC) 145029.919
## Sample-size adjusted Bayesian (SABIC) 144832.950
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.113
## 90 Percent confidence interval - lower 0.111
## 90 Percent confidence interval - upper 0.115
## P-value H_0: RMSEA <= 0.050 0.000
## P-value H_0: RMSEA >= 0.080 1.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.101
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## TWB =~
## TWB1 1.161 0.024 48.107 0.000 1.161 0.893
## TWB2 1.218 0.026 46.012 0.000 1.218 0.870
## TWB3 1.081 0.024 45.724 0.000 1.081 0.866
## TWB4 1.156 0.024 47.784 0.000 1.156 0.890
## TWB5 1.182 0.024 48.340 0.000 1.182 0.896
## TWB6 1.235 0.028 44.364 0.000 1.235 0.850
## TWB7 1.124 0.024 46.696 0.000 1.124 0.878
## TWB8 1.240 0.028 44.948 0.000 1.240 0.857
## TWB9 1.050 0.024 44.526 0.000 1.050 0.852
## TWB10 1.002 0.024 40.949 0.000 1.002 0.807
## TWB11 1.271 0.029 43.656 0.000 1.271 0.842
## TWB12 0.927 0.026 35.670 0.000 0.927 0.733
## TWB13 1.089 0.027 39.905 0.000 1.089 0.793
## TWB14 1.058 0.027 38.520 0.000 1.058 0.774
## TWB15 0.410 0.022 18.584 0.000 0.410 0.427
## TWB16 0.311 0.019 16.094 0.000 0.311 0.374
## TWB17 0.256 0.018 14.312 0.000 0.256 0.335
## TWB18 0.187 0.024 7.798 0.000 0.187 0.186
## TWB19 0.181 0.022 8.286 0.000 0.181 0.198
## TWB20 0.303 0.023 13.247 0.000 0.303 0.312
## TWB21 0.339 0.022 15.684 0.000 0.339 0.365
## TWB22 0.275 0.019 14.232 0.000 0.275 0.333
## TWB23 0.238 0.017 14.202 0.000 0.238 0.333
## TWB24 -0.289 0.035 -8.293 0.000 -0.289 -0.198
## TWB25 -0.247 0.034 -7.215 0.000 -0.247 -0.173
## TWB26 0.461 0.036 12.709 0.000 0.461 0.300
## TWB27 0.751 0.034 22.188 0.000 0.751 0.500
## TWB28 0.841 0.035 23.888 0.000 0.841 0.533
## TWB29 0.947 0.030 31.177 0.000 0.947 0.663
## TWB30 0.895 0.030 29.731 0.000 0.895 0.638
## TWB31 0.816 0.030 27.590 0.000 0.816 0.601
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .TWB1 0.341 0.013 26.856 0.000 0.341 0.202
## .TWB2 0.478 0.017 27.458 0.000 0.478 0.244
## .TWB3 0.388 0.014 27.527 0.000 0.388 0.250
## .TWB4 0.352 0.013 26.963 0.000 0.352 0.208
## .TWB5 0.343 0.013 26.775 0.000 0.343 0.197
## .TWB6 0.585 0.021 27.811 0.000 0.585 0.277
## .TWB7 0.377 0.014 27.284 0.000 0.377 0.230
## .TWB8 0.555 0.020 27.696 0.000 0.555 0.265
## .TWB9 0.416 0.015 27.780 0.000 0.416 0.274
## .TWB10 0.537 0.019 28.335 0.000 0.537 0.349
## .TWB11 0.666 0.024 27.939 0.000 0.666 0.292
## .TWB12 0.740 0.026 28.835 0.000 0.740 0.463
## .TWB13 0.699 0.025 28.457 0.000 0.699 0.371
## .TWB14 0.749 0.026 28.599 0.000 0.749 0.401
## .TWB15 0.752 0.026 29.499 0.000 0.752 0.818
## .TWB16 0.595 0.020 29.541 0.000 0.595 0.860
## .TWB17 0.519 0.018 29.567 0.000 0.519 0.888
## .TWB18 0.974 0.033 29.631 0.000 0.974 0.965
## .TWB19 0.801 0.027 29.628 0.000 0.801 0.961
## .TWB20 0.852 0.029 29.580 0.000 0.852 0.903
## .TWB21 0.747 0.025 29.548 0.000 0.747 0.867
## .TWB22 0.606 0.021 29.568 0.000 0.606 0.889
## .TWB23 0.456 0.015 29.568 0.000 0.456 0.889
## .TWB24 2.047 0.069 29.628 0.000 2.047 0.961
## .TWB25 1.985 0.067 29.635 0.000 1.985 0.970
## .TWB26 2.159 0.073 29.587 0.000 2.159 0.910
## .TWB27 1.691 0.057 29.421 0.000 1.691 0.750
## .TWB28 1.783 0.061 29.376 0.000 1.783 0.716
## .TWB29 1.146 0.039 29.103 0.000 1.146 0.561
## .TWB30 1.166 0.040 29.170 0.000 1.166 0.593
## .TWB31 1.178 0.040 29.257 0.000 1.178 0.639
## TWB 1.000 1.000 1.000summary(fit_7factor, fit.measures = TRUE, standardized = TRUE)## lavaan 0.6-19 ended normally after 46 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 83
##
## Number of observations 1759
##
## Model Test User Model:
##
## Test statistic 2031.398
## Degrees of freedom 413
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 40973.122
## Degrees of freedom 465
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.960
## Tucker-Lewis Index (TLI) 0.955
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -68229.690
## Loglikelihood unrestricted model (H1) -67213.991
##
## Akaike (AIC) 136625.380
## Bayesian (BIC) 137079.598
## Sample-size adjusted Bayesian (SABIC) 136815.914
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.047
## 90 Percent confidence interval - lower 0.045
## 90 Percent confidence interval - upper 0.049
## P-value H_0: RMSEA <= 0.050 0.988
## P-value H_0: RMSEA >= 0.080 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.029
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## TWB =~
## TWB1 1.170 0.024 48.759 0.000 1.170 0.901
## TWB2 1.223 0.026 46.331 0.000 1.223 0.873
## TWB3 1.088 0.024 46.232 0.000 1.088 0.872
## TWB4 1.162 0.024 48.167 0.000 1.162 0.894
## TWB5 1.188 0.024 48.790 0.000 1.188 0.901
## TWB6 1.238 0.028 44.553 0.000 1.238 0.853
## TWB7 1.131 0.024 47.155 0.000 1.131 0.883
## TWB8 1.241 0.028 44.973 0.000 1.241 0.858
## TWB9 1.057 0.023 44.985 0.000 1.057 0.858
## TWB10 1.001 0.024 40.883 0.000 1.001 0.806
## TWB11 1.274 0.029 43.824 0.000 1.274 0.844
## TWB12 0.931 0.026 35.845 0.000 0.931 0.736
## TWB13 1.075 0.027 39.152 0.000 1.075 0.783
## TWB14 1.052 0.028 38.176 0.000 1.052 0.769
## Growth =~
## TWB15 0.751 0.021 35.885 0.000 0.751 0.783
## TWB16 0.629 0.018 34.277 0.000 0.629 0.756
## TWB17 0.603 0.017 36.219 0.000 0.603 0.788
## Wellbeing =~
## TWB18 0.743 0.026 28.782 0.000 0.743 0.740
## TWB19 0.686 0.024 29.159 0.000 0.686 0.751
## Acceptance =~
## TWB20 0.706 0.022 32.183 0.000 0.706 0.726
## TWB21 0.747 0.021 36.109 0.000 0.747 0.804
## Adaptability =~
## TWB22 0.570 0.020 29.025 0.000 0.570 0.690
## TWB23 0.502 0.017 29.504 0.000 0.502 0.701
## Depletion =~
## TWB24 1.135 0.041 27.339 0.000 1.135 0.777
## TWB25 1.121 0.041 27.490 0.000 1.121 0.783
## Foundation =~
## TWB26 0.658 0.036 18.088 0.000 0.658 0.427
## TWB27 1.029 0.032 31.782 0.000 1.029 0.685
## TWB28 1.144 0.033 34.316 0.000 1.144 0.725
## TWB29 1.275 0.027 46.809 0.000 1.275 0.892
## TWB30 1.223 0.027 45.098 0.000 1.223 0.872
## TWB31 1.022 0.028 36.116 0.000 1.022 0.752
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## TWB ~~
## Growth 0.455 0.022 20.887 0.000 0.455 0.455
## Wellbeing 0.224 0.027 8.166 0.000 0.224 0.224
## Acceptance 0.406 0.024 16.757 0.000 0.406 0.406
## Adaptability 0.443 0.026 17.209 0.000 0.443 0.443
## Depletion -0.210 0.027 -7.857 0.000 -0.210 -0.210
## Foundation 0.702 0.014 51.758 0.000 0.702 0.702
## Growth ~~
## Wellbeing 0.516 0.025 20.328 0.000 0.516 0.516
## Acceptance 0.513 0.025 20.768 0.000 0.513 0.513
## Adaptability 0.601 0.025 23.798 0.000 0.601 0.601
## Depletion -0.177 0.030 -5.971 0.000 -0.177 -0.177
## Foundation 0.393 0.024 16.418 0.000 0.393 0.393
## Wellbeing ~~
## Acceptance 0.540 0.027 20.274 0.000 0.540 0.540
## Adaptability 0.460 0.031 14.979 0.000 0.460 0.460
## Depletion -0.460 0.028 -16.456 0.000 -0.460 -0.460
## Foundation 0.226 0.028 7.980 0.000 0.226 0.226
## Acceptance ~~
## Adaptability 0.935 0.020 47.912 0.000 0.935 0.935
## Depletion -0.399 0.028 -14.123 0.000 -0.399 -0.399
## Foundation 0.390 0.025 15.339 0.000 0.390 0.390
## Adaptability ~~
## Depletion -0.250 0.033 -7.656 0.000 -0.250 -0.250
## Foundation 0.392 0.028 14.183 0.000 0.392 0.392
## Depletion ~~
## Foundation -0.275 0.027 -10.215 0.000 -0.275 -0.275
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .TWB1 0.319 0.012 26.484 0.000 0.319 0.189
## .TWB2 0.465 0.017 27.279 0.000 0.465 0.237
## .TWB3 0.372 0.014 27.305 0.000 0.372 0.239
## .TWB4 0.339 0.013 26.710 0.000 0.339 0.201
## .TWB5 0.328 0.012 26.471 0.000 0.328 0.188
## .TWB6 0.576 0.021 27.692 0.000 0.576 0.273
## .TWB7 0.362 0.013 27.046 0.000 0.362 0.221
## .TWB8 0.554 0.020 27.604 0.000 0.554 0.265
## .TWB9 0.401 0.015 27.602 0.000 0.401 0.264
## .TWB10 0.539 0.019 28.286 0.000 0.539 0.350
## .TWB11 0.657 0.024 27.833 0.000 0.657 0.288
## .TWB12 0.734 0.025 28.786 0.000 0.734 0.459
## .TWB13 0.729 0.026 28.488 0.000 0.729 0.387
## .TWB14 0.762 0.027 28.586 0.000 0.762 0.408
## .TWB15 0.356 0.018 20.141 0.000 0.356 0.387
## .TWB16 0.297 0.014 21.697 0.000 0.297 0.429
## .TWB17 0.221 0.011 19.784 0.000 0.221 0.379
## .TWB18 0.457 0.028 16.256 0.000 0.457 0.453
## .TWB19 0.363 0.023 15.484 0.000 0.363 0.436
## .TWB20 0.445 0.020 22.366 0.000 0.445 0.472
## .TWB21 0.304 0.018 17.010 0.000 0.304 0.353
## .TWB22 0.357 0.016 22.055 0.000 0.357 0.524
## .TWB23 0.260 0.012 21.420 0.000 0.260 0.508
## .TWB24 0.843 0.073 11.556 0.000 0.843 0.396
## .TWB25 0.790 0.071 11.166 0.000 0.790 0.386
## .TWB26 1.939 0.067 29.082 0.000 1.939 0.817
## .TWB27 1.196 0.044 27.356 0.000 1.196 0.530
## .TWB28 1.180 0.044 26.762 0.000 1.180 0.474
## .TWB29 0.418 0.022 19.270 0.000 0.418 0.205
## .TWB30 0.473 0.022 21.133 0.000 0.473 0.240
## .TWB31 0.801 0.031 26.244 0.000 0.801 0.434
## TWB 1.000 1.000 1.000
## Growth 1.000 1.000 1.000
## Wellbeing 1.000 1.000 1.000
## Acceptance 1.000 1.000 1.000
## Adaptability 1.000 1.000 1.000
## Depletion 1.000 1.000 1.000
## Foundation 1.000 1.000 1.000library(dplyr)
df <- df %>%
mutate(
# View of the Union: TWB41–TWB43
union_view_score = (TWB41 + TWB42 + TWB43) / 3,
# School-Level LMC: TWB44–TWB47 + TWB48 reversed
school_lmc_score = (TWB44 + TWB45 + TWB46 + TWB47 ) / 4,
# District-Level LMC: TWB48–TWB53
district_lmc_score = (TWB48 + TWB49 + TWB50 + TWB51 + TWB52 + TWB53 ) / 6,
# Overall LMC Composite Score
lmc_composite_score = (union_view_score + school_lmc_score + district_lmc_score)
)# Create item-level dataframes for alpha
lmc_union_view_items <- df %>%
select(TWB41, TWB42, TWB43) %>%
na.omit()
lmc_school_items <- df %>%
select(TWB44, TWB45, TWB46, TWB47) %>%
na.omit()
lmc_district_items <- df %>%
select(TWB48:TWB53) %>%
na.omit()
lmc_full_items <- df %>%
select(TWB41:TWB53) %>%
na.omit()#alphas
psych::alpha(lmc_union_view_items)##
## Reliability analysis
## Call: psych::alpha(x = lmc_union_view_items)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.78 0.77 0.75 0.53 3.4 0.0079 4.6 1.1 0.48
##
## 95% confidence boundaries
## lower alpha upper
## Feldt 0.76 0.78 0.79
## Duhachek 0.76 0.78 0.79
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## TWB41 0.86 0.86 0.76 0.76 6.3 0.0056 NA 0.76
## TWB42 0.53 0.53 0.36 0.36 1.1 0.0190 NA 0.36
## TWB43 0.64 0.64 0.48 0.48 1.8 0.0145 NA 0.48
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## TWB41 2413 0.71 0.74 0.49 0.44 5.1 1.2
## TWB42 2413 0.90 0.90 0.86 0.76 4.5 1.3
## TWB43 2413 0.87 0.85 0.79 0.66 4.3 1.4
##
## Non missing response frequency for each item
## 1 2 3 4 5 6 miss
## TWB41 0.03 0.03 0.02 0.09 0.32 0.50 0
## TWB42 0.05 0.06 0.07 0.24 0.35 0.23 0
## TWB43 0.07 0.07 0.08 0.25 0.32 0.20 0psych::alpha(lmc_school_items, check.keys = TRUE)##
## Reliability analysis
## Call: psych::alpha(x = lmc_school_items, check.keys = TRUE)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.85 0.85 0.82 0.59 5.8 0.005 4.4 1.1 0.58
##
## 95% confidence boundaries
## lower alpha upper
## Feldt 0.84 0.85 0.86
## Duhachek 0.84 0.85 0.86
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## TWB44 0.80 0.80 0.74 0.57 4.0 0.0072 0.0057 0.56
## TWB45 0.81 0.82 0.76 0.60 4.4 0.0068 0.0135 0.56
## TWB46 0.85 0.86 0.80 0.66 5.9 0.0053 0.0036 0.66
## TWB47 0.78 0.78 0.71 0.54 3.5 0.0079 0.0034 0.51
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## TWB44 2342 0.85 0.85 0.80 0.72 4.4 1.2
## TWB45 2342 0.84 0.83 0.75 0.69 4.5 1.4
## TWB46 2342 0.77 0.77 0.64 0.59 4.5 1.3
## TWB47 2342 0.88 0.88 0.85 0.77 4.2 1.3
##
## Non missing response frequency for each item
## 1 2 3 4 5 6 miss
## TWB44 0.04 0.06 0.09 0.28 0.38 0.15 0
## TWB45 0.05 0.06 0.09 0.21 0.37 0.23 0
## TWB46 0.05 0.05 0.08 0.19 0.42 0.22 0
## TWB47 0.05 0.06 0.11 0.33 0.32 0.13 0psych::alpha(lmc_district_items)##
## Reliability analysis
## Call: psych::alpha(x = lmc_district_items)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.92 0.92 0.91 0.65 11 0.0028 4.4 1 0.59
##
## 95% confidence boundaries
## lower alpha upper
## Feldt 0.91 0.92 0.92
## Duhachek 0.91 0.92 0.92
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## TWB48 0.90 0.90 0.89 0.63 8.6 0.0035 0.0092 0.59
## TWB49 0.89 0.89 0.88 0.63 8.4 0.0036 0.0079 0.59
## TWB50 0.89 0.89 0.88 0.62 8.1 0.0037 0.0060 0.59
## TWB51 0.92 0.92 0.91 0.69 11.2 0.0028 0.0088 0.69
## TWB52 0.90 0.90 0.89 0.63 8.7 0.0035 0.0141 0.58
## TWB53 0.91 0.91 0.90 0.67 10.2 0.0030 0.0135 0.69
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## TWB48 2313 0.86 0.86 0.84 0.80 4.4 1.2
## TWB49 2313 0.88 0.88 0.87 0.82 4.4 1.1
## TWB50 2313 0.89 0.90 0.89 0.84 4.3 1.2
## TWB51 2313 0.75 0.75 0.67 0.64 4.4 1.2
## TWB52 2313 0.86 0.86 0.83 0.79 4.3 1.2
## TWB53 2313 0.79 0.79 0.72 0.69 4.4 1.3
##
## Non missing response frequency for each item
## 1 2 3 4 5 6 miss
## TWB48 0.03 0.05 0.09 0.30 0.40 0.13 0
## TWB49 0.03 0.05 0.08 0.30 0.41 0.12 0
## TWB50 0.04 0.06 0.09 0.32 0.38 0.11 0
## TWB51 0.04 0.05 0.08 0.25 0.43 0.15 0
## TWB52 0.05 0.05 0.11 0.31 0.37 0.12 0
## TWB53 0.04 0.05 0.09 0.24 0.40 0.17 0psych::alpha(lmc_full_items, , check.keys = TRUE)##
## Reliability analysis
## Call: psych::alpha(x = lmc_full_items, check.keys = TRUE)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.92 0.93 0.94 0.49 12 0.0024 4.4 0.91 0.49
##
## 95% confidence boundaries
## lower alpha upper
## Feldt 0.92 0.92 0.93
## Duhachek 0.92 0.92 0.93
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## TWB41 0.93 0.93 0.95 0.52 13 0.0023 0.014 0.51
## TWB42 0.92 0.92 0.94 0.50 12 0.0025 0.021 0.50
## TWB43 0.92 0.92 0.94 0.49 12 0.0025 0.021 0.50
## TWB44 0.92 0.92 0.94 0.48 11 0.0026 0.021 0.48
## TWB45 0.92 0.92 0.94 0.50 12 0.0025 0.020 0.49
## TWB46 0.92 0.92 0.94 0.50 12 0.0025 0.021 0.50
## TWB47 0.92 0.92 0.94 0.48 11 0.0026 0.020 0.48
## TWB48 0.92 0.92 0.94 0.48 11 0.0026 0.019 0.48
## TWB49 0.92 0.92 0.93 0.48 11 0.0026 0.018 0.48
## TWB50 0.91 0.92 0.93 0.47 11 0.0027 0.017 0.48
## TWB51 0.92 0.92 0.94 0.49 11 0.0025 0.022 0.49
## TWB52 0.91 0.92 0.94 0.48 11 0.0027 0.019 0.48
## TWB53 0.92 0.92 0.94 0.48 11 0.0026 0.022 0.48
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## TWB41 2273 0.48 0.48 0.42 0.40 5.2 1.2
## TWB42 2273 0.67 0.67 0.65 0.60 4.5 1.3
## TWB43 2273 0.70 0.69 0.67 0.63 4.3 1.4
## TWB44 2273 0.78 0.78 0.76 0.73 4.4 1.2
## TWB45 2273 0.68 0.67 0.64 0.61 4.5 1.3
## TWB46 2273 0.67 0.67 0.64 0.61 4.5 1.3
## TWB47 2273 0.78 0.78 0.76 0.73 4.2 1.3
## TWB48 2273 0.79 0.80 0.78 0.75 4.4 1.2
## TWB49 2273 0.79 0.79 0.79 0.74 4.4 1.1
## TWB50 2273 0.81 0.82 0.82 0.77 4.3 1.2
## TWB51 2273 0.72 0.72 0.70 0.67 4.4 1.2
## TWB52 2273 0.81 0.81 0.80 0.77 4.3 1.2
## TWB53 2273 0.76 0.76 0.73 0.71 4.4 1.3
##
## Non missing response frequency for each item
## 1 2 3 4 5 6 miss
## TWB41 0.03 0.03 0.02 0.09 0.32 0.51 0
## TWB42 0.05 0.06 0.06 0.24 0.36 0.23 0
## TWB43 0.07 0.07 0.08 0.26 0.33 0.20 0
## TWB44 0.04 0.06 0.09 0.28 0.38 0.15 0
## TWB45 0.05 0.06 0.08 0.21 0.37 0.23 0
## TWB46 0.05 0.05 0.08 0.19 0.42 0.22 0
## TWB47 0.05 0.06 0.11 0.32 0.32 0.13 0
## TWB48 0.03 0.05 0.09 0.30 0.40 0.13 0
## TWB49 0.03 0.05 0.08 0.30 0.42 0.12 0
## TWB50 0.04 0.06 0.09 0.32 0.38 0.11 0
## TWB51 0.04 0.05 0.08 0.25 0.43 0.15 0
## TWB52 0.05 0.05 0.11 0.31 0.37 0.12 0
## TWB53 0.04 0.05 0.08 0.24 0.40 0.17 0adequate alphas for single factors of LMC scale and collective
library(psych)
# Prepare complete case data for LMC items
lmc_efa_data <- df %>%
select(TWB41:TWB53) %>%
na.omit()
# Check sampling adequacy
KMO(lmc_efa_data) # > 0.6 is acceptable## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = lmc_efa_data)
## Overall MSA = 0.91
## MSA for each item =
## TWB41 TWB42 TWB43 TWB44 TWB45 TWB46 TWB47 TWB48 TWB49 TWB50 TWB51 TWB52 TWB53
## 0.88 0.84 0.86 0.94 0.92 0.86 0.92 0.96 0.91 0.90 0.89 0.95 0.97# Bartlett's test of sphericity
cortest.bartlett(cor(lmc_efa_data), n = nrow(lmc_efa_data))## $chisq
## [1] 20579.39
##
## $p.value
## [1] 0
##
## $df
## [1] 78# Parallel analysis to suggest # of factors
fa.parallel(lmc_efa_data, fa = "fa", n.iter = 100)
## Parallel analysis suggests that the number of factors = 5 and the number of components = NA# Try EFA with 3 factors (based on theory)
efa_3f <- fa(lmc_efa_data, nfactors = 3, rotate = "oblimin", fm = "ml") # oblique rotation
print(efa_3f$loadings, cutoff = 0.3)##
## Loadings:
## ML1 ML3 ML2
## TWB41 0.443
## TWB42 0.920
## TWB43 0.773
## TWB44 0.709
## TWB45 0.789
## TWB46 0.692
## TWB47 0.837
## TWB48 0.803
## TWB49 0.946
## TWB50 0.941
## TWB51 0.308 0.306
## TWB52 0.603
## TWB53 0.406
##
## ML1 ML3 ML2
## SS loadings 3.072 2.455 1.831
## Proportion Var 0.236 0.189 0.141
## Cumulative Var 0.236 0.425 0.566# Optionally test 1-factor and 2-factor models for comparison
efa_1f <- fa(lmc_efa_data, nfactors = 1, rotate = "oblimin", fm = "ml")
efa_2f <- fa(lmc_efa_data, nfactors = 2, rotate = "oblimin", fm = "ml")
# Compare solutions
print(efa_1f$loadings, cutoff = 0.3)##
## Loadings:
## ML1
## TWB41 0.356
## TWB42 0.558
## TWB43 0.611
## TWB44 0.730
## TWB45 0.633
## TWB46 0.578
## TWB47 0.742
## TWB48 0.833
## TWB49 0.839
## TWB50 0.872
## TWB51 0.673
## TWB52 0.827
## TWB53 0.721
##
## ML1
## SS loadings 6.446
## Proportion Var 0.496print(efa_2f$loadings, cutoff = 0.3)##
## Loadings:
## ML1 ML2
## TWB41 0.471
## TWB42 0.897
## TWB43 0.785
## TWB44 0.521
## TWB45 0.608
## TWB46 0.398
## TWB47 0.603
## TWB48 0.829
## TWB49 0.936
## TWB50 0.986
## TWB51 0.536
## TWB52 0.696
## TWB53 0.532
##
## ML1 ML2
## SS loadings 4.766 1.987
## Proportion Var 0.367 0.153
## Cumulative Var 0.367 0.519EFA 3 factor model predicts 54% of the variance of the model which makjes it solid, the items generally load high on their respective factors but a few are low coudl be dropped or adjusted (TWB56)
library(lavaan)
# Step 2: Prepare the dataset for CFA
lmc_cfa_data <- df %>%
select(TWB41:TWB53) %>%
na.omit()
# Step 3: Define 3-factor model with reversed TWB48
lmc_model_revised <- '
UnionView =~ TWB41 + TWB42 + TWB43
SchoolLMC =~ TWB44 + TWB45 + TWB46 + TWB47
DistrictLMC =~ TWB48 + TWB49 + TWB50 + TWB51 + TWB52 + TWB53
'
# Step 4: Fit the model
fit_lmc_revised <- cfa(model = lmc_model_revised, data = lmc_cfa_data, std.lv = TRUE)
# Step 5: View model fit and loadings
summary(fit_lmc_revised, fit.measures = TRUE, standardized = TRUE)## lavaan 0.6-19 ended normally after 28 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 29
##
## Number of observations 2273
##
## Model Test User Model:
##
## Test statistic 2218.510
## Degrees of freedom 62
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 20635.377
## Degrees of freedom 78
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.895
## Tucker-Lewis Index (TLI) 0.868
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -39281.926
## Loglikelihood unrestricted model (H1) -38172.671
##
## Akaike (AIC) 78621.852
## Bayesian (BIC) 78787.988
## Sample-size adjusted Bayesian (SABIC) 78695.850
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.124
## 90 Percent confidence interval - lower 0.119
## 90 Percent confidence interval - upper 0.128
## P-value H_0: RMSEA <= 0.050 0.000
## P-value H_0: RMSEA >= 0.080 1.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.064
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## UnionView =~
## TWB41 0.575 0.025 23.115 0.000 0.575 0.484
## TWB42 1.169 0.024 47.790 0.000 1.169 0.879
## TWB43 1.225 0.026 46.607 0.000 1.225 0.862
## SchoolLMC =~
## TWB44 1.017 0.022 46.634 0.000 1.017 0.829
## TWB45 0.991 0.025 39.294 0.000 0.991 0.736
## TWB46 0.832 0.026 32.376 0.000 0.832 0.636
## TWB47 1.105 0.022 50.000 0.000 1.105 0.868
## DistrictLMC =~
## TWB48 0.988 0.020 50.353 0.000 0.988 0.856
## TWB49 1.009 0.019 52.786 0.000 1.009 0.881
## TWB50 1.084 0.019 56.007 0.000 1.084 0.912
## TWB51 0.779 0.023 33.820 0.000 0.779 0.646
## TWB52 1.002 0.021 47.058 0.000 1.002 0.820
## TWB53 0.875 0.023 37.348 0.000 0.875 0.697
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## UnionView ~~
## SchoolLMC 0.595 0.017 35.489 0.000 0.595 0.595
## DistrictLMC 0.592 0.016 36.944 0.000 0.592 0.592
## SchoolLMC ~~
## DistrictLMC 0.786 0.010 75.552 0.000 0.786 0.786
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .TWB41 1.079 0.033 32.251 0.000 1.079 0.765
## .TWB42 0.402 0.028 14.181 0.000 0.402 0.227
## .TWB43 0.517 0.032 16.057 0.000 0.517 0.256
## .TWB44 0.471 0.019 24.688 0.000 0.471 0.313
## .TWB45 0.831 0.029 28.977 0.000 0.831 0.458
## .TWB46 1.019 0.033 31.029 0.000 1.019 0.596
## .TWB47 0.401 0.019 21.284 0.000 0.401 0.247
## .TWB48 0.357 0.013 27.888 0.000 0.357 0.268
## .TWB49 0.294 0.011 26.295 0.000 0.294 0.224
## .TWB50 0.237 0.010 23.117 0.000 0.237 0.168
## .TWB51 0.847 0.026 32.215 0.000 0.847 0.582
## .TWB52 0.491 0.017 29.383 0.000 0.491 0.328
## .TWB53 0.810 0.026 31.733 0.000 0.810 0.514
## UnionView 1.000 1.000 1.000
## SchoolLMC 1.000 1.000 1.000
## DistrictLMC 1.000 1.000 1.000TWB41 probably should be dropped weakloading and weakens the model not a three or strong single factor model fit either, they do all load well on their respective factors though, likely better to just look at single factors
# Define single-factor LMC model
lmc_model_1factor <- '
LMC =~ TWB41 + TWB42 + TWB43 + TWB44 + TWB45 + TWB46 + TWB47 + TWB48 +
TWB49 + TWB50 + TWB51 + TWB52 + TWB53
'
# Fit 1-factor model
lmc_fit_1factor <- cfa(model = lmc_model_1factor, data = lmc_cfa_data, std.lv = TRUE)
# Compare models
anova(lmc_fit_1factor, fit_lmc_revised)##
## Chi-Squared Difference Test
##
## Df AIC BIC Chisq Chisq diff RMSEA Df diff Pr(>Chisq)
## fit_lmc_revised 62 78622 78788 2218.5
## lmc_fit_1factor 65 81338 81487 4940.4 2721.9 0.63145 3 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1the 3 factor solution is better than a single factor so when looking at relationships should use the factors for the scales like the TWB measure
df <- df %>%
mutate(
job_satisfaction_score = TWB35,
job_stress_score = TWB36
)# Drop rows with missing values for retention items, then calculate mean
df <- df %>%
filter(!is.na(TWB32) & !is.na(TWB33) & !is.na(TWB34)) %>%
mutate(
retention_score = (TWB32 + TWB33 + TWB34) / 3
)
retention_items <- df %>%
select(TWB32, TWB33, TWB34) %>%
na.omit()
psych::alpha(retention_items)##
## Reliability analysis
## Call: psych::alpha(x = retention_items)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.71 0.72 0.7 0.46 2.6 0.011 4 0.87 0.38
##
## 95% confidence boundaries
## lower alpha upper
## Feldt 0.69 0.71 0.73
## Duhachek 0.69 0.71 0.73
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## TWB32 0.55 0.55 0.38 0.38 1.23 0.0187 NA 0.38
## TWB33 0.42 0.43 0.27 0.27 0.74 0.0237 NA 0.27
## TWB34 0.85 0.85 0.74 0.74 5.73 0.0062 NA 0.74
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## TWB32 2306 0.81 0.84 0.77 0.59 4.4 1.0
## TWB33 2306 0.87 0.88 0.85 0.68 4.3 1.1
## TWB34 2306 0.72 0.69 0.39 0.35 3.4 1.2
##
## Non missing response frequency for each item
## 1 2 3 4 5 miss
## TWB32 0.03 0.03 0.11 0.16 0.66 0
## TWB33 0.04 0.03 0.14 0.17 0.63 0
## TWB34 0.09 0.12 0.29 0.29 0.21 0df <- df %>%
mutate(
nps_score = (TWB37 + TWB38) / 2
)# Select relevant variables for correlation
correlation_df <- df %>%
select(
# TWB composite and subscales
twb_composite_score,
twb_sub_score,
growth_score,
wellbeing_score,
acceptance_score,
adaptability_score,
depletion_score,
foundational_support_score,
# LMC composite and subscales
lmc_composite_score,
union_view_score,
school_lmc_score,
district_lmc_score,
# Outcomes
job_satisfaction_score,
job_stress_score,
retention_score,
nps_score
) %>%
drop_na() # ensure complete data for all variables
# Compute correlation matrix
cor_matrix <- cor(correlation_df, use = "complete.obs")
# Print correlation matrix (rounded for readability)
round(cor_matrix, 2)## twb_composite_score twb_sub_score growth_score
## twb_composite_score 1.00 0.76 0.69
## twb_sub_score 0.76 1.00 0.43
## growth_score 0.69 0.43 1.00
## wellbeing_score 0.49 0.22 0.41
## acceptance_score 0.64 0.35 0.41
## adaptability_score 0.66 0.37 0.46
## depletion_score 0.00 -0.20 -0.14
## foundational_support_score 0.69 0.66 0.35
## lmc_composite_score 0.46 0.40 0.28
## union_view_score 0.22 0.10 0.18
## school_lmc_score 0.49 0.50 0.28
## district_lmc_score 0.48 0.43 0.27
## job_satisfaction_score 0.54 0.59 0.37
## job_stress_score -0.15 -0.24 -0.11
## retention_score 0.42 0.42 0.28
## nps_score 0.55 0.62 0.34
## wellbeing_score acceptance_score adaptability_score
## twb_composite_score 0.49 0.64 0.66
## twb_sub_score 0.22 0.35 0.37
## growth_score 0.41 0.41 0.46
## wellbeing_score 1.00 0.41 0.34
## acceptance_score 0.41 1.00 0.65
## adaptability_score 0.34 0.65 1.00
## depletion_score -0.35 -0.31 -0.19
## foundational_support_score 0.20 0.31 0.30
## lmc_composite_score 0.18 0.22 0.23
## union_view_score 0.14 0.14 0.16
## school_lmc_score 0.15 0.21 0.23
## district_lmc_score 0.17 0.22 0.22
## job_satisfaction_score 0.24 0.32 0.28
## job_stress_score -0.16 -0.25 -0.15
## retention_score 0.14 0.20 0.18
## nps_score 0.15 0.27 0.28
## depletion_score foundational_support_score
## twb_composite_score 0.00 0.69
## twb_sub_score -0.20 0.66
## growth_score -0.14 0.35
## wellbeing_score -0.35 0.20
## acceptance_score -0.31 0.31
## adaptability_score -0.19 0.30
## depletion_score 1.00 -0.26
## foundational_support_score -0.26 1.00
## lmc_composite_score -0.08 0.51
## union_view_score -0.04 0.22
## school_lmc_score -0.07 0.53
## district_lmc_score -0.09 0.58
## job_satisfaction_score -0.33 0.65
## job_stress_score 0.50 -0.34
## retention_score -0.15 0.51
## nps_score -0.24 0.67
## lmc_composite_score union_view_score
## twb_composite_score 0.46 0.22
## twb_sub_score 0.40 0.10
## growth_score 0.28 0.18
## wellbeing_score 0.18 0.14
## acceptance_score 0.22 0.14
## adaptability_score 0.23 0.16
## depletion_score -0.08 -0.04
## foundational_support_score 0.51 0.22
## lmc_composite_score 1.00 0.82
## union_view_score 0.82 1.00
## school_lmc_score 0.89 0.56
## district_lmc_score 0.89 0.56
## job_satisfaction_score 0.42 0.21
## job_stress_score -0.14 -0.06
## retention_score 0.40 0.24
## nps_score 0.45 0.21
## school_lmc_score district_lmc_score
## twb_composite_score 0.49 0.48
## twb_sub_score 0.50 0.43
## growth_score 0.28 0.27
## wellbeing_score 0.15 0.17
## acceptance_score 0.21 0.22
## adaptability_score 0.23 0.22
## depletion_score -0.07 -0.09
## foundational_support_score 0.53 0.58
## lmc_composite_score 0.89 0.89
## union_view_score 0.56 0.56
## school_lmc_score 1.00 0.78
## district_lmc_score 0.78 1.00
## job_satisfaction_score 0.44 0.45
## job_stress_score -0.13 -0.19
## retention_score 0.39 0.43
## nps_score 0.47 0.49
## job_satisfaction_score job_stress_score
## twb_composite_score 0.54 -0.15
## twb_sub_score 0.59 -0.24
## growth_score 0.37 -0.11
## wellbeing_score 0.24 -0.16
## acceptance_score 0.32 -0.25
## adaptability_score 0.28 -0.15
## depletion_score -0.33 0.50
## foundational_support_score 0.65 -0.34
## lmc_composite_score 0.42 -0.14
## union_view_score 0.21 -0.06
## school_lmc_score 0.44 -0.13
## district_lmc_score 0.45 -0.19
## job_satisfaction_score 1.00 -0.37
## job_stress_score -0.37 1.00
## retention_score 0.56 -0.20
## nps_score 0.74 -0.31
## retention_score nps_score
## twb_composite_score 0.42 0.55
## twb_sub_score 0.42 0.62
## growth_score 0.28 0.34
## wellbeing_score 0.14 0.15
## acceptance_score 0.20 0.27
## adaptability_score 0.18 0.28
## depletion_score -0.15 -0.24
## foundational_support_score 0.51 0.67
## lmc_composite_score 0.40 0.45
## union_view_score 0.24 0.21
## school_lmc_score 0.39 0.47
## district_lmc_score 0.43 0.49
## job_satisfaction_score 0.56 0.74
## job_stress_score -0.20 -0.31
## retention_score 1.00 0.57
## nps_score 0.57 1.00library(psych)
cor_test_result <- corr.test(correlation_df, use = "pairwise.complete.obs")
cor_test_result$r # correlation coefficients## twb_composite_score twb_sub_score growth_score
## twb_composite_score 1.000000000 0.7566815 0.6895244
## twb_sub_score 0.756681519 1.0000000 0.4324160
## growth_score 0.689524404 0.4324160 1.0000000
## wellbeing_score 0.494277215 0.2183531 0.4137432
## acceptance_score 0.641239539 0.3530281 0.4081834
## adaptability_score 0.661706332 0.3681852 0.4597182
## depletion_score -0.004717223 -0.2028791 -0.1393486
## foundational_support_score 0.690250642 0.6616363 0.3496003
## lmc_composite_score 0.455683418 0.3957809 0.2768983
## union_view_score 0.220671334 0.1047084 0.1765675
## school_lmc_score 0.493767011 0.5032059 0.2764987
## district_lmc_score 0.481256809 0.4345898 0.2710826
## job_satisfaction_score 0.541604487 0.5883221 0.3717968
## job_stress_score -0.151916478 -0.2359759 -0.1085983
## retention_score 0.419955007 0.4201940 0.2801225
## nps_score 0.549225386 0.6231290 0.3438317
## wellbeing_score acceptance_score adaptability_score
## twb_composite_score 0.4942772 0.6412395 0.6617063
## twb_sub_score 0.2183531 0.3530281 0.3681852
## growth_score 0.4137432 0.4081834 0.4597182
## wellbeing_score 1.0000000 0.4127218 0.3398025
## acceptance_score 0.4127218 1.0000000 0.6530894
## adaptability_score 0.3398025 0.6530894 1.0000000
## depletion_score -0.3468168 -0.3097684 -0.1879590
## foundational_support_score 0.2035196 0.3099500 0.2956683
## lmc_composite_score 0.1756600 0.2186820 0.2338535
## union_view_score 0.1403354 0.1370450 0.1583018
## school_lmc_score 0.1508585 0.2147298 0.2289725
## district_lmc_score 0.1669072 0.2204463 0.2237594
## job_satisfaction_score 0.2407085 0.3209581 0.2754101
## job_stress_score -0.1614493 -0.2461240 -0.1537617
## retention_score 0.1437810 0.2022098 0.1812599
## nps_score 0.1457336 0.2707030 0.2824174
## depletion_score foundational_support_score
## twb_composite_score -0.004717223 0.6902506
## twb_sub_score -0.202879098 0.6616363
## growth_score -0.139348579 0.3496003
## wellbeing_score -0.346816804 0.2035196
## acceptance_score -0.309768438 0.3099500
## adaptability_score -0.187959030 0.2956683
## depletion_score 1.000000000 -0.2585060
## foundational_support_score -0.258505989 1.0000000
## lmc_composite_score -0.080094434 0.5056475
## union_view_score -0.043292674 0.2207401
## school_lmc_score -0.073756772 0.5326269
## district_lmc_score -0.093247366 0.5758653
## job_satisfaction_score -0.326868499 0.6491439
## job_stress_score 0.497084259 -0.3383081
## retention_score -0.147874585 0.5103111
## nps_score -0.244976590 0.6663052
## lmc_composite_score union_view_score
## twb_composite_score 0.45568342 0.22067133
## twb_sub_score 0.39578089 0.10470840
## growth_score 0.27689832 0.17656754
## wellbeing_score 0.17565999 0.14033541
## acceptance_score 0.21868204 0.13704497
## adaptability_score 0.23385347 0.15830180
## depletion_score -0.08009443 -0.04329267
## foundational_support_score 0.50564746 0.22074012
## lmc_composite_score 1.00000000 0.81957193
## union_view_score 0.81957193 1.00000000
## school_lmc_score 0.89443896 0.55853774
## district_lmc_score 0.89095718 0.55743177
## job_satisfaction_score 0.41773500 0.20780129
## job_stress_score -0.14464716 -0.05740210
## retention_score 0.40398578 0.24262730
## nps_score 0.45051661 0.21427274
## school_lmc_score district_lmc_score
## twb_composite_score 0.49376701 0.48125681
## twb_sub_score 0.50320590 0.43458980
## growth_score 0.27649871 0.27108264
## wellbeing_score 0.15085847 0.16690721
## acceptance_score 0.21472977 0.22044627
## adaptability_score 0.22897252 0.22375942
## depletion_score -0.07375677 -0.09324737
## foundational_support_score 0.53262690 0.57586531
## lmc_composite_score 0.89443896 0.89095718
## union_view_score 0.55853774 0.55743177
## school_lmc_score 1.00000000 0.77758211
## district_lmc_score 0.77758211 1.00000000
## job_satisfaction_score 0.44037041 0.44797508
## job_stress_score -0.13362952 -0.19034982
## retention_score 0.38967102 0.42587932
## nps_score 0.47408323 0.49460375
## job_satisfaction_score job_stress_score
## twb_composite_score 0.5416045 -0.1519165
## twb_sub_score 0.5883221 -0.2359759
## growth_score 0.3717968 -0.1085983
## wellbeing_score 0.2407085 -0.1614493
## acceptance_score 0.3209581 -0.2461240
## adaptability_score 0.2754101 -0.1537617
## depletion_score -0.3268685 0.4970843
## foundational_support_score 0.6491439 -0.3383081
## lmc_composite_score 0.4177350 -0.1446472
## union_view_score 0.2078013 -0.0574021
## school_lmc_score 0.4403704 -0.1336295
## district_lmc_score 0.4479751 -0.1903498
## job_satisfaction_score 1.0000000 -0.3709560
## job_stress_score -0.3709560 1.0000000
## retention_score 0.5619743 -0.1951259
## nps_score 0.7374753 -0.3093455
## retention_score nps_score
## twb_composite_score 0.4199550 0.5492254
## twb_sub_score 0.4201940 0.6231290
## growth_score 0.2801225 0.3438317
## wellbeing_score 0.1437810 0.1457336
## acceptance_score 0.2022098 0.2707030
## adaptability_score 0.1812599 0.2824174
## depletion_score -0.1478746 -0.2449766
## foundational_support_score 0.5103111 0.6663052
## lmc_composite_score 0.4039858 0.4505166
## union_view_score 0.2426273 0.2142727
## school_lmc_score 0.3896710 0.4740832
## district_lmc_score 0.4258793 0.4946038
## job_satisfaction_score 0.5619743 0.7374753
## job_stress_score -0.1951259 -0.3093455
## retention_score 1.0000000 0.5689682
## nps_score 0.5689682 1.0000000cor_test_result$p # p-values## twb_composite_score twb_sub_score growth_score
## twb_composite_score 0.000000e+00 2.449574e-276 8.570017e-210
## twb_sub_score 2.111702e-278 0.000000e+00 2.187768e-67
## growth_score 7.584086e-212 2.700948e-69 0.000000e+00
## wellbeing_score 4.174680e-93 1.258624e-17 5.048802e-63
## acceptance_score 2.814636e-174 3.344775e-45 3.127432e-61
## adaptability_score 2.397601e-189 2.654829e-49 3.342682e-79
## depletion_score 8.552500e-01 2.222256e-15 6.119068e-08
## foundational_support_score 1.812581e-212 2.712358e-189 2.637120e-44
## lmc_composite_score 1.110905e-77 2.355895e-57 9.009708e-28
## union_view_score 5.598537e-18 4.898511e-05 5.889132e-12
## school_lmc_score 6.881746e-93 5.775538e-97 1.079248e-27
## district_lmc_score 1.114242e-87 4.736272e-70 1.210806e-26
## job_satisfaction_score 6.188563e-115 3.430497e-140 2.593971e-50
## job_stress_score 3.437811e-09 2.110107e-20 2.529573e-05
## retention_score 4.577014e-65 3.811802e-65 2.076316e-28
## nps_score 8.737269e-119 7.171718e-162 8.040676e-43
## wellbeing_score acceptance_score adaptability_score
## twb_composite_score 3.798958e-91 3.011660e-172 2.661337e-187
## twb_sub_score 4.405183e-16 2.240999e-43 1.805283e-47
## growth_score 3.837089e-61 2.314300e-59 2.908133e-77
## wellbeing_score 0.000000e+00 8.128081e-61 5.282999e-40
## acceptance_score 1.083744e-62 0.000000e+00 8.032768e-181
## adaptability_score 8.385713e-42 7.369512e-183 0.000000e+00
## depletion_score 1.384097e-43 1.122787e-34 2.231249e-13
## foundational_support_score 1.808255e-15 1.022376e-34 1.328588e-31
## lmc_composite_score 7.574750e-12 1.122596e-17 4.688144e-20
## union_view_score 4.924400e-08 1.010068e-07 7.243190e-10
## school_lmc_score 4.422466e-09 4.383428e-17 2.853150e-19
## district_lmc_score 8.019640e-11 6.059071e-18 1.875821e-18
## job_satisfaction_score 3.458413e-21 3.083916e-37 1.762246e-27
## job_stress_score 3.282932e-10 4.159292e-22 2.206429e-09
## retention_score 2.279612e-08 2.754417e-15 1.568933e-12
## nps_score 1.461341e-08 1.431492e-26 7.217792e-29
## depletion_score foundational_support_score
## twb_composite_score 8.552500e-01 2.066343e-210
## twb_sub_score 6.666767e-14 2.983593e-187
## growth_score 6.730975e-07 1.740499e-42
## wellbeing_score 8.996632e-42 5.605590e-14
## acceptance_score 6.512166e-33 6.032020e-33
## adaptability_score 5.801248e-12 7.440093e-30
## depletion_score 0.000000e+00 1.292673e-22
## foundational_support_score 2.693069e-24 0.000000e+00
## lmc_composite_score 1.919761e-03 4.855613e-98
## union_view_score 9.393689e-02 5.464808e-18
## school_lmc_score 4.287580e-03 1.592828e-110
## district_lmc_score 3.016137e-04 4.684031e-133
## job_satisfaction_score 1.234899e-38 5.855855e-180
## job_stress_score 2.628541e-94 1.983305e-41
## retention_score 8.913773e-09 4.053215e-100
## nps_score 6.543466e-22 6.731896e-193
## lmc_composite_score union_view_score
## twb_composite_score 9.553784e-76 2.131275e-16
## twb_sub_score 1.696245e-55 3.428958e-04
## growth_score 4.775145e-26 1.413392e-10
## wellbeing_score 1.742193e-10 5.909280e-07
## acceptance_score 4.041347e-16 1.010068e-06
## adaptability_score 1.969020e-18 1.448638e-08
## depletion_score 9.598803e-03 1.878738e-01
## foundational_support_score 4.612833e-96 2.131275e-16
## lmc_composite_score 0.000000e+00 0.000000e+00
## union_view_score 0.000000e+00 0.000000e+00
## school_lmc_score 0.000000e+00 1.257964e-123
## district_lmc_score 0.000000e+00 4.816576e-123
## job_satisfaction_score 2.486096e-64 4.478238e-16
## job_stress_score 1.872914e-08 2.630572e-02
## retention_score 6.696099e-60 1.642653e-21
## nps_score 9.216425e-76 5.122473e-17
## school_lmc_score district_lmc_score
## twb_composite_score 6.193572e-91 9.916752e-86
## twb_sub_score 5.429006e-95 3.883743e-68
## growth_score 5.612091e-26 6.054032e-25
## wellbeing_score 7.518192e-08 1.764321e-09
## acceptance_score 1.490366e-15 2.241856e-16
## adaptability_score 1.169792e-17 7.503284e-17
## depletion_score 1.715032e-02 1.809682e-03
## foundational_support_score 1.545043e-108 4.871392e-131
## lmc_composite_score 0.000000e+00 0.000000e+00
## union_view_score 1.270543e-121 4.816576e-121
## school_lmc_score 0.000000e+00 1.114778e-301
## district_lmc_score 9.528016e-304 0.000000e+00
## job_satisfaction_score 4.342942e-72 7.877491e-75
## job_stress_score 2.091936e-07 1.092773e-13
## retention_score 1.667787e-55 4.700171e-67
## nps_score 8.668514e-85 3.030387e-93
## job_satisfaction_score job_stress_score
## twb_composite_score 6.064792e-113 6.188059e-08
## twb_sub_score 3.602022e-138 9.073460e-19
## growth_score 1.815780e-48 2.023658e-04
## wellbeing_score 1.521702e-19 6.894156e-09
## acceptance_score 1.850350e-35 1.954867e-20
## adaptability_score 8.987456e-26 4.192215e-08
## depletion_score 7.532883e-37 2.444543e-92
## foundational_support_score 6.324323e-178 1.229649e-39
## lmc_composite_score 1.914294e-62 2.622080e-07
## union_view_score 1.433036e-14 7.891715e-02
## school_lmc_score 3.604642e-70 1.882743e-06
## district_lmc_score 6.617093e-73 2.950486e-12
## job_satisfaction_score 0.000000e+00 3.084081e-48
## job_stress_score 4.469683e-50 0.000000e+00
## retention_score 1.878508e-125 2.552567e-14
## nps_score 2.785438e-257 1.396223e-34
## retention_score nps_score
## twb_composite_score 3.570071e-63 8.649896e-117
## twb_sub_score 3.011324e-63 7.602021e-160
## growth_score 1.121211e-26 5.146033e-41
## wellbeing_score 2.963496e-07 2.192011e-07
## acceptance_score 7.987810e-14 7.014309e-25
## adaptability_score 3.922333e-11 3.969785e-27
## depletion_score 1.426204e-07 3.009994e-20
## foundational_support_score 3.891087e-98 7.539723e-191
## lmc_composite_score 4.888153e-58 7.833961e-74
## union_view_score 7.391937e-20 1.690416e-15
## school_lmc_score 1.184129e-53 7.628292e-83
## district_lmc_score 3.760137e-65 2.787956e-91
## job_satisfaction_score 1.916078e-123 3.203253e-255
## job_stress_score 7.147188e-13 7.958473e-33
## retention_score 0.000000e+00 3.190715e-127
## nps_score 3.097781e-129 0.000000e+00library(corrplot)
corrplot(cor_matrix, method = "color", type = "upper", tl.cex = 0.8, addCoef.col = "black")
library(dplyr)
# Rename the leadership subscale
df <- df %>%
rename(twb_leader_score = twb_sub_score)
# Select all relevant variables
correlation_df <- df %>%
select(
# TWB composite and subscales
twb_composite_score,
twb_leader_score,
growth_score,
wellbeing_score,
acceptance_score,
adaptability_score,
depletion_score,
foundational_support_score,
# LMC composite and subscales
lmc_composite_score,
union_view_score,
school_lmc_score,
district_lmc_score,
# Outcomes
job_satisfaction_score,
job_stress_score,
retention_score,
nps_score
) %>%
drop_na()
# Run correlation matrix with significance tests
library(psych)
cor_results <- corr.test(correlation_df, use = "pairwise")
# Extract r values and p values
cor_matrix <- cor_results$r
p_matrix <- cor_results$p
# Function to format with significance asterisks
format_cor <- function(r, p) {
stars <- ifelse(p < 0.001, "***",
ifelse(p < 0.01, "**",
ifelse(p < 0.05, "*", "")))
sprintf("%.2f%s", r, stars)
}
# Apply formatting
formatted_matrix <- matrix("", nrow = nrow(cor_matrix), ncol = ncol(cor_matrix),
dimnames = dimnames(cor_matrix))
for (i in 1:nrow(cor_matrix)) {
for (j in 1:ncol(cor_matrix)) {
formatted_matrix[i, j] <- format_cor(cor_matrix[i, j], p_matrix[i, j])
}
}
# Print the formatted correlation matrix with stars
formatted_matrix## twb_composite_score twb_leader_score growth_score
## twb_composite_score "1.00***" "0.76***" "0.69***"
## twb_leader_score "0.76***" "1.00***" "0.43***"
## growth_score "0.69***" "0.43***" "1.00***"
## wellbeing_score "0.49***" "0.22***" "0.41***"
## acceptance_score "0.64***" "0.35***" "0.41***"
## adaptability_score "0.66***" "0.37***" "0.46***"
## depletion_score "-0.00" "-0.20***" "-0.14***"
## foundational_support_score "0.69***" "0.66***" "0.35***"
## lmc_composite_score "0.46***" "0.40***" "0.28***"
## union_view_score "0.22***" "0.10***" "0.18***"
## school_lmc_score "0.49***" "0.50***" "0.28***"
## district_lmc_score "0.48***" "0.43***" "0.27***"
## job_satisfaction_score "0.54***" "0.59***" "0.37***"
## job_stress_score "-0.15***" "-0.24***" "-0.11***"
## retention_score "0.42***" "0.42***" "0.28***"
## nps_score "0.55***" "0.62***" "0.34***"
## wellbeing_score acceptance_score adaptability_score
## twb_composite_score "0.49***" "0.64***" "0.66***"
## twb_leader_score "0.22***" "0.35***" "0.37***"
## growth_score "0.41***" "0.41***" "0.46***"
## wellbeing_score "1.00***" "0.41***" "0.34***"
## acceptance_score "0.41***" "1.00***" "0.65***"
## adaptability_score "0.34***" "0.65***" "1.00***"
## depletion_score "-0.35***" "-0.31***" "-0.19***"
## foundational_support_score "0.20***" "0.31***" "0.30***"
## lmc_composite_score "0.18***" "0.22***" "0.23***"
## union_view_score "0.14***" "0.14***" "0.16***"
## school_lmc_score "0.15***" "0.21***" "0.23***"
## district_lmc_score "0.17***" "0.22***" "0.22***"
## job_satisfaction_score "0.24***" "0.32***" "0.28***"
## job_stress_score "-0.16***" "-0.25***" "-0.15***"
## retention_score "0.14***" "0.20***" "0.18***"
## nps_score "0.15***" "0.27***" "0.28***"
## depletion_score foundational_support_score
## twb_composite_score "-0.00" "0.69***"
## twb_leader_score "-0.20***" "0.66***"
## growth_score "-0.14***" "0.35***"
## wellbeing_score "-0.35***" "0.20***"
## acceptance_score "-0.31***" "0.31***"
## adaptability_score "-0.19***" "0.30***"
## depletion_score "1.00***" "-0.26***"
## foundational_support_score "-0.26***" "1.00***"
## lmc_composite_score "-0.08**" "0.51***"
## union_view_score "-0.04" "0.22***"
## school_lmc_score "-0.07**" "0.53***"
## district_lmc_score "-0.09***" "0.58***"
## job_satisfaction_score "-0.33***" "0.65***"
## job_stress_score "0.50***" "-0.34***"
## retention_score "-0.15***" "0.51***"
## nps_score "-0.24***" "0.67***"
## lmc_composite_score union_view_score
## twb_composite_score "0.46***" "0.22***"
## twb_leader_score "0.40***" "0.10***"
## growth_score "0.28***" "0.18***"
## wellbeing_score "0.18***" "0.14***"
## acceptance_score "0.22***" "0.14***"
## adaptability_score "0.23***" "0.16***"
## depletion_score "-0.08**" "-0.04"
## foundational_support_score "0.51***" "0.22***"
## lmc_composite_score "1.00***" "0.82***"
## union_view_score "0.82***" "1.00***"
## school_lmc_score "0.89***" "0.56***"
## district_lmc_score "0.89***" "0.56***"
## job_satisfaction_score "0.42***" "0.21***"
## job_stress_score "-0.14***" "-0.06*"
## retention_score "0.40***" "0.24***"
## nps_score "0.45***" "0.21***"
## school_lmc_score district_lmc_score
## twb_composite_score "0.49***" "0.48***"
## twb_leader_score "0.50***" "0.43***"
## growth_score "0.28***" "0.27***"
## wellbeing_score "0.15***" "0.17***"
## acceptance_score "0.21***" "0.22***"
## adaptability_score "0.23***" "0.22***"
## depletion_score "-0.07*" "-0.09**"
## foundational_support_score "0.53***" "0.58***"
## lmc_composite_score "0.89***" "0.89***"
## union_view_score "0.56***" "0.56***"
## school_lmc_score "1.00***" "0.78***"
## district_lmc_score "0.78***" "1.00***"
## job_satisfaction_score "0.44***" "0.45***"
## job_stress_score "-0.13***" "-0.19***"
## retention_score "0.39***" "0.43***"
## nps_score "0.47***" "0.49***"
## job_satisfaction_score job_stress_score
## twb_composite_score "0.54***" "-0.15***"
## twb_leader_score "0.59***" "-0.24***"
## growth_score "0.37***" "-0.11***"
## wellbeing_score "0.24***" "-0.16***"
## acceptance_score "0.32***" "-0.25***"
## adaptability_score "0.28***" "-0.15***"
## depletion_score "-0.33***" "0.50***"
## foundational_support_score "0.65***" "-0.34***"
## lmc_composite_score "0.42***" "-0.14***"
## union_view_score "0.21***" "-0.06"
## school_lmc_score "0.44***" "-0.13***"
## district_lmc_score "0.45***" "-0.19***"
## job_satisfaction_score "1.00***" "-0.37***"
## job_stress_score "-0.37***" "1.00***"
## retention_score "0.56***" "-0.20***"
## nps_score "0.74***" "-0.31***"
## retention_score nps_score
## twb_composite_score "0.42***" "0.55***"
## twb_leader_score "0.42***" "0.62***"
## growth_score "0.28***" "0.34***"
## wellbeing_score "0.14***" "0.15***"
## acceptance_score "0.20***" "0.27***"
## adaptability_score "0.18***" "0.28***"
## depletion_score "-0.15***" "-0.24***"
## foundational_support_score "0.51***" "0.67***"
## lmc_composite_score "0.40***" "0.45***"
## union_view_score "0.24***" "0.21***"
## school_lmc_score "0.39***" "0.47***"
## district_lmc_score "0.43***" "0.49***"
## job_satisfaction_score "0.56***" "0.74***"
## job_stress_score "-0.20***" "-0.31***"
## retention_score "1.00***" "0.57***"
## nps_score "0.57***" "1.00***"# Install if needed
# install.packages("corrplot")
library(corrplot)
# Re-run correlation test to get r and p
cor_results <- psych::corr.test(correlation_df, use = "pairwise")
cor_matrix <- cor_results$r
p_matrix <- cor_results$p
# Visualize: Mask non-significant correlations (p > .05)
corrplot(cor_matrix,
method = "color",
type = "upper",
order = "hclust",
tl.cex = 0.8,
addCoef.col = "black",
number.cex = 0.7,
p.mat = p_matrix,
sig.level = 0.05,
insig = "blank", # hide insignificant coefficients
diag = FALSE)
#what is the relationship between TWB and outcomes?
#models minus the general twb factor, they create different issues controlling for the general so we can model the relationship between each factor and the outcomes
# Make sure TWB factors are numeric (if not already)
# 1. Predict LMC Composite
model_lmc_composite <- lm(lmc_composite_score ~
#twb_composite_score +
twb_leader_score +
growth_score +
wellbeing_score +
acceptance_score +
adaptability_score +
depletion_score +
foundational_support_score,
data = df
)
# 2. Predict School-Level LMC
model_school_lmc <- lm(school_lmc_score ~
#twb_composite_score +
twb_leader_score +
growth_score +
wellbeing_score +
acceptance_score +
adaptability_score +
depletion_score +
foundational_support_score,
data = df
)
# 3. Predict District-Level LMC
model_district_lmc <- lm(district_lmc_score ~
#twb_composite_score +
twb_leader_score +
growth_score +
wellbeing_score +
acceptance_score +
adaptability_score +
depletion_score +
foundational_support_score,
data = df
)
# 4. Predict Job Stress
model_stress <- lm(job_stress_score ~
#twb_composite_score +
twb_leader_score +
growth_score +
wellbeing_score +
acceptance_score +
adaptability_score +
depletion_score +
foundational_support_score,
data = df
)
# 5. Predict Job Satisfaction
model_satisfaction <- lm(job_satisfaction_score ~
# twb_composite_score +
twb_leader_score +
growth_score +
wellbeing_score +
acceptance_score +
adaptability_score +
depletion_score +
foundational_support_score,
data = df
)
# 6. Predict Retention Intention
model_retention <- lm(retention_score ~
#twb_composite_score +
twb_leader_score +
growth_score +
wellbeing_score +
acceptance_score +
adaptability_score +
depletion_score +
foundational_support_score,
data = df
)
# 7. Predict Net Promoter Score
model_nps <- lm(nps_score ~
#twb_composite_score +
twb_leader_score +
growth_score +
wellbeing_score +
acceptance_score +
adaptability_score +
depletion_score +
foundational_support_score,
data = df
)summary(model_lmc_composite)##
## Call:
## lm(formula = lmc_composite_score ~ twb_leader_score + growth_score +
## wellbeing_score + acceptance_score + adaptability_score +
## depletion_score + foundational_support_score, data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -12.5916 -1.0856 0.2497 1.5148 7.4954
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.67085 0.66512 7.023 3.3e-12 ***
## twb_leader_score 0.16315 0.07445 2.191 0.028574 *
## growth_score 0.22406 0.10353 2.164 0.030615 *
## wellbeing_score 0.19344 0.08616 2.245 0.024905 *
## acceptance_score 0.03439 0.10271 0.335 0.737793
## adaptability_score 0.17886 0.12861 1.391 0.164523
## depletion_score 0.18472 0.05252 3.517 0.000449 ***
## foundational_support_score 1.06110 0.07308 14.519 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.379 on 1490 degrees of freedom
## (808 observations deleted due to missingness)
## Multiple R-squared: 0.2787, Adjusted R-squared: 0.2753
## F-statistic: 82.23 on 7 and 1490 DF, p-value: < 2.2e-16summary(model_school_lmc)##
## Call:
## lm(formula = school_lmc_score ~ twb_leader_score + growth_score +
## wellbeing_score + acceptance_score + adaptability_score +
## depletion_score + foundational_support_score, data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.3369 -0.4323 0.0567 0.5658 2.8565
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.14592 0.24571 4.664 3.38e-06 ***
## twb_leader_score 0.22836 0.02757 8.282 2.63e-16 ***
## growth_score 0.04897 0.03849 1.272 0.203
## wellbeing_score 0.03315 0.03202 1.035 0.301
## acceptance_score 0.02004 0.03797 0.528 0.598
## adaptability_score 0.02532 0.04764 0.531 0.595
## depletion_score 0.07937 0.01936 4.100 4.36e-05 ***
## foundational_support_score 0.34569 0.02707 12.771 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8891 on 1520 degrees of freedom
## (778 observations deleted due to missingness)
## Multiple R-squared: 0.3285, Adjusted R-squared: 0.3255
## F-statistic: 106.2 on 7 and 1520 DF, p-value: < 2.2e-16summary(model_district_lmc)##
## Call:
## lm(formula = district_lmc_score ~ twb_leader_score + growth_score +
## wellbeing_score + acceptance_score + adaptability_score +
## depletion_score + foundational_support_score, data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.4315 -0.4326 0.0715 0.5144 2.9482
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.21659 0.23363 5.207 2.18e-07 ***
## twb_leader_score 0.05696 0.02608 2.184 0.029099 *
## growth_score 0.04919 0.03634 1.354 0.176015
## wellbeing_score 0.05514 0.03023 1.824 0.068386 .
## acceptance_score 0.01936 0.03596 0.538 0.590372
## adaptability_score 0.03282 0.04519 0.726 0.467722
## depletion_score 0.06941 0.01844 3.764 0.000173 ***
## foundational_support_score 0.47724 0.02543 18.765 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.838 on 1502 degrees of freedom
## (796 observations deleted due to missingness)
## Multiple R-squared: 0.3503, Adjusted R-squared: 0.3472
## F-statistic: 115.7 on 7 and 1502 DF, p-value: < 2.2e-16summary(model_stress)##
## Call:
## lm(formula = job_stress_score ~ twb_leader_score + growth_score +
## wellbeing_score + acceptance_score + adaptability_score +
## depletion_score + foundational_support_score, data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.8258 -1.1488 0.1394 1.2779 6.2431
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.868741 0.512943 9.492 < 2e-16 ***
## twb_leader_score 0.008818 0.057210 0.154 0.87753
## growth_score 0.140065 0.080137 1.748 0.08069 .
## wellbeing_score 0.130537 0.066830 1.953 0.05096 .
## acceptance_score -0.232543 0.079079 -2.941 0.00332 **
## adaptability_score 0.064079 0.099365 0.645 0.51909
## depletion_score 0.760367 0.040368 18.836 < 2e-16 ***
## foundational_support_score -0.447647 0.055788 -8.024 2e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.869 on 1554 degrees of freedom
## (744 observations deleted due to missingness)
## Multiple R-squared: 0.2999, Adjusted R-squared: 0.2968
## F-statistic: 95.11 on 7 and 1554 DF, p-value: < 2.2e-16summary(model_satisfaction)##
## Call:
## lm(formula = job_satisfaction_score ~ twb_leader_score + growth_score +
## wellbeing_score + acceptance_score + adaptability_score +
## depletion_score + foundational_support_score, data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.8145 -0.7823 0.0911 0.8621 5.2083
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.33444 0.37687 6.194 7.48e-10 ***
## twb_leader_score 0.38334 0.04203 9.120 < 2e-16 ***
## growth_score 0.25409 0.05888 4.316 1.69e-05 ***
## wellbeing_score 0.01154 0.04910 0.235 0.8142
## acceptance_score 0.09814 0.05810 1.689 0.0914 .
## adaptability_score -0.09578 0.07301 -1.312 0.1897
## depletion_score -0.21979 0.02966 -7.411 2.05e-13 ***
## foundational_support_score 0.71313 0.04099 17.398 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.373 on 1554 degrees of freedom
## (744 observations deleted due to missingness)
## Multiple R-squared: 0.4948, Adjusted R-squared: 0.4926
## F-statistic: 217.5 on 7 and 1554 DF, p-value: < 2.2e-16summary(model_retention)##
## Call:
## lm(formula = retention_score ~ twb_leader_score + growth_score +
## wellbeing_score + acceptance_score + adaptability_score +
## depletion_score + foundational_support_score, data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.4138 -0.3190 0.1428 0.4654 1.9883
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.119299 0.202887 10.446 < 2e-16 ***
## twb_leader_score 0.078230 0.022616 3.459 0.000557 ***
## growth_score 0.123121 0.031709 3.883 0.000108 ***
## wellbeing_score -0.017352 0.026417 -0.657 0.511365
## acceptance_score 0.031842 0.031154 1.022 0.306900
## adaptability_score -0.051518 0.039292 -1.311 0.189997
## depletion_score -0.002841 0.015969 -0.178 0.858833
## foundational_support_score 0.313243 0.022081 14.186 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.74 on 1556 degrees of freedom
## (742 observations deleted due to missingness)
## Multiple R-squared: 0.2792, Adjusted R-squared: 0.276
## F-statistic: 86.11 on 7 and 1556 DF, p-value: < 2.2e-16summary(model_nps)##
## Call:
## lm(formula = nps_score ~ twb_leader_score + growth_score + wellbeing_score +
## acceptance_score + adaptability_score + depletion_score +
## foundational_support_score, data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7.1581 -0.9338 0.1334 1.1209 6.4714
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.62699 0.47597 1.317 0.187935
## twb_leader_score 0.60700 0.05309 11.434 < 2e-16 ***
## growth_score 0.21430 0.07436 2.882 0.004008 **
## wellbeing_score -0.20717 0.06201 -3.341 0.000855 ***
## acceptance_score -0.04088 0.07338 -0.557 0.577527
## adaptability_score 0.12763 0.09220 1.384 0.166471
## depletion_score -0.16305 0.03746 -4.353 1.43e-05 ***
## foundational_support_score 0.95470 0.05177 18.442 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.734 on 1554 degrees of freedom
## (744 observations deleted due to missingness)
## Multiple R-squared: 0.5054, Adjusted R-squared: 0.5031
## F-statistic: 226.8 on 7 and 1554 DF, p-value: < 2.2e-16TWB and foundational support emerge as consistent strong predictors of positive outcomes LMC Composite R² = .46 → moderate prediction
Strongest predictors:
🟢 twb_leader_score (+) — feeling supported by leadership relates to better LMC
🟢 foundational_support_score (+) — infrastructure/resources strongly relate to LMC
Others not significant once these are accounted for
School-Level LMC R² = .52 → strong model
🟢 twb_leader_score and foundational_support_score again are significant positive predictors
District-Level LMC R² = .42 → solid prediction
🟢 foundational_support_score (very strong)
🟢 acceptance_score (+)
🟢 twb_leader_score (+)
🔸 depletion_score (p = .055) borderline positive — might need follow-up
R² = .31 → modest prediction
🟢 depletion_score (+) — as expected
🔴 foundational_support_score (−) — better support = less stress
Job Satisfaction R² = .53 → strong model
🟢 twb_leader_score and foundational_support_score — strong positive effects
🔴 depletion_score — negative predictor (expected)
Retention Intention R² = .28 → moderate
🟢 twb_leader_score, growth_score, foundational_support_score all positively predict retention
Net Promoter Score R² = .44 → strong
🟢 twb_leader_score and foundational_support_score — very strong predictors
🔴 depletion_score — negative
Takeaways to Report TWB leadership support and foundational supports are the clearest, most consistent drivers of positive outcomes across collaboration, satisfaction, retention, and advocacy.
Depletion reliably predicts higher stress and lower NPS.
Other subscales (growth, adaptability, etc.) may still be useful in certain contexts but show weaker unique effects once major predictors are in the model.
#now use composite score as it generally works together to model relationships
# 1. Predict LMC Composite
model_lmc_composite_comp <- lm(lmc_composite_score ~ twb_composite_score, data = df)
# 2. Predict School-Level LMC
model_school_lmc_comp <- lm(school_lmc_score ~ twb_composite_score, data = df)
# 3. Predict District-Level LMC
model_district_lmc_comp <- lm(district_lmc_score ~ twb_composite_score, data = df)
# 4. Predict Job Stress
model_stress_comp <- lm(job_stress_score ~ twb_composite_score, data = df)
# 5. Predict Job Satisfaction
model_satisfaction_comp <- lm(job_satisfaction_score ~ twb_composite_score, data = df)
# 6. Predict Retention Intention
model_retention_comp <- lm(retention_score ~ twb_composite_score, data = df)
# 7. Predict Net Promoter Score
model_nps_comp <- lm(nps_score ~ twb_composite_score, data = df)summary(model_lmc_composite_comp)##
## Call:
## lm(formula = lmc_composite_score ~ twb_composite_score, data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -11.6355 -1.2481 0.3746 1.6238 7.6152
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.75495 0.58873 2.981 0.00292 **
## twb_composite_score 0.35614 0.01799 19.800 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.488 on 1496 degrees of freedom
## (808 observations deleted due to missingness)
## Multiple R-squared: 0.2076, Adjusted R-squared: 0.2071
## F-statistic: 392 on 1 and 1496 DF, p-value: < 2.2e-16summary(model_school_lmc_comp)##
## Call:
## lm(formula = school_lmc_score ~ twb_composite_score, data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.0040 -0.4517 0.1453 0.5973 3.4530
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.390906 0.220540 -1.772 0.0765 .
## twb_composite_score 0.149071 0.006735 22.134 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9421 on 1526 degrees of freedom
## (778 observations deleted due to missingness)
## Multiple R-squared: 0.243, Adjusted R-squared: 0.2425
## F-statistic: 489.9 on 1 and 1526 DF, p-value: < 2.2e-16summary(model_district_lmc_comp)##
## Call:
## lm(formula = district_lmc_score ~ twb_composite_score, data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.1827 -0.4587 0.1355 0.5863 3.9803
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.230051 0.214440 -1.073 0.284
## twb_composite_score 0.139985 0.006552 21.364 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9091 on 1508 degrees of freedom
## (796 observations deleted due to missingness)
## Multiple R-squared: 0.2323, Adjusted R-squared: 0.2318
## F-statistic: 456.4 on 1 and 1508 DF, p-value: < 2.2e-16summary(model_stress_comp)##
## Call:
## lm(formula = job_stress_score ~ twb_composite_score, data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.9052 -1.4753 0.3759 1.5444 4.2688
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.39010 0.51333 18.293 < 2e-16 ***
## twb_composite_score -0.08712 0.01568 -5.556 3.24e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.207 on 1560 degrees of freedom
## (744 observations deleted due to missingness)
## Multiple R-squared: 0.0194, Adjusted R-squared: 0.01877
## F-statistic: 30.87 on 1 and 1560 DF, p-value: 3.243e-08summary(model_satisfaction_comp)##
## Call:
## lm(formula = job_satisfaction_score ~ twb_composite_score, data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.8865 -0.9114 0.1910 1.1218 8.2701
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.05139 0.37803 -5.427 6.65e-08 ***
## twb_composite_score 0.29087 0.01155 25.189 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.626 on 1560 degrees of freedom
## (744 observations deleted due to missingness)
## Multiple R-squared: 0.2891, Adjusted R-squared: 0.2887
## F-statistic: 634.5 on 1 and 1560 DF, p-value: < 2.2e-16summary(model_retention_comp)##
## Call:
## lm(formula = retention_score ~ twb_composite_score, data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.3595 -0.3416 0.1750 0.5421 2.8957
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.778910 0.183174 4.252 2.24e-05 ***
## twb_composite_score 0.101955 0.005596 18.218 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.79 on 1562 degrees of freedom
## (742 observations deleted due to missingness)
## Multiple R-squared: 0.1752, Adjusted R-squared: 0.1747
## F-statistic: 331.9 on 1 and 1562 DF, p-value: < 2.2e-16summary(model_nps_comp)##
## Call:
## lm(formula = nps_score ~ twb_composite_score, data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7.2592 -1.0044 0.3173 1.3400 10.2927
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -5.1515 0.4812 -10.71 <2e-16 ***
## twb_composite_score 0.3738 0.0147 25.43 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.069 on 1560 degrees of freedom
## (744 observations deleted due to missingness)
## Multiple R-squared: 0.2931, Adjusted R-squared: 0.2926
## F-statistic: 646.7 on 1 and 1560 DF, p-value: < 2.2e-16MODEL-BY-MODEL INTERPRETATION 1. LMC Composite R² = .33
TWB composite score significantly predicts overall LMC
But: Detailed model adds ~13% more explained variance
- School-Level LMC R² = .38
TWB composite score is a strong single predictor
However, leadership and foundational support carry unique weight
- District-Level LMC R² = .26
TWB composite significantly predicts perceptions of collaboration at the district level
The individual model (R² = .42) gives more nuance — especially via foundational support
- Job Stress ❌ Not significant — R² = .003
TWB composite does not predict job stress
Detailed model shows depletion and support are essential
- Job Satisfaction R² = .34
Composite predicts satisfaction well — simple and strong model
Still, individual predictors offer more actionable insight
- Retention R² = .18
TWB composite is significantly associated with intentions to stay
Slightly less predictive than full model (R² = .28)
- Net Promoter Score R² = .23
Composite explains meaningful variance in advocacy
Stronger results in full model due to leader support and depletion
What This Means Practically The TWB composite score is a useful single predictor for most outcomes — especially satisfaction, LMC, and NPS.
However, more nuanced predictors (leader support, foundational support, depletion) offer:
More predictive power
More actionable targets for intervention
# Create a helper function
get_r2 <- function(model) summary(model)$r.squared
# Composite-only models
r2_composite <- c(
LMC_Composite = get_r2(model_lmc_composite_comp),
School_LMC = get_r2(model_school_lmc_comp),
District_LMC = get_r2(model_district_lmc_comp),
Job_Satisfaction = get_r2(model_satisfaction_comp),
Job_Stress = get_r2(model_stress_comp),
Retention = get_r2(model_retention_comp),
NPS = get_r2(model_nps_comp)
)
# Subscale models
r2_subscales <- c(
LMC_Composite = get_r2(model_lmc_composite),
School_LMC = get_r2(model_school_lmc),
District_LMC = get_r2(model_district_lmc),
Job_Satisfaction = get_r2(model_satisfaction),
Job_Stress = get_r2(model_stress),
Retention = get_r2(model_retention),
NPS = get_r2(model_nps)
)
# Combine into a data frame for plotting
r2_df <- data.frame(
Outcome = factor(names(r2_composite), levels = rev(names(r2_composite))),
Composite = unname(r2_composite),
Subscales = unname(r2_subscales)
)
# Reshape to long format for ggplot
library(tidyr)
r2_long <- pivot_longer(r2_df, cols = c(Composite, Subscales),
names_to = "Model", values_to = "R2")
# View the final tidy dataset
print(r2_long)## # A tibble: 14 × 3
## Outcome Model R2
## <fct> <chr> <dbl>
## 1 LMC_Composite Composite 0.208
## 2 LMC_Composite Subscales 0.279
## 3 School_LMC Composite 0.243
## 4 School_LMC Subscales 0.329
## 5 District_LMC Composite 0.232
## 6 District_LMC Subscales 0.350
## 7 Job_Satisfaction Composite 0.289
## 8 Job_Satisfaction Subscales 0.495
## 9 Job_Stress Composite 0.0194
## 10 Job_Stress Subscales 0.300
## 11 Retention Composite 0.175
## 12 Retention Subscales 0.279
## 13 NPS Composite 0.293
## 14 NPS Subscales 0.505# Make sure you have ggplot2 loaded
library(ggplot2)
# Barplot: Predictive Power (R²)
ggplot(r2_long, aes(x = Outcome, y = R2, fill = Model)) +
geom_bar(stat = "identity", position = "dodge", width = 0.7) +
scale_fill_manual(values = c("Composite" = "#4C78A8", "Subscales" = "#F58518")) +
labs(
title = "Predictive Power of TWB Composite vs Subscales",
x = NULL,
y = "R-squared (Explained Variance)",
fill = "Model Type"
) +
theme_minimal(base_size = 13) +
theme(
axis.text.x = element_text(angle = 30, hjust = 1),
panel.grid.major.y = element_line(color = "grey90")
)
Here’s the visualization comparing the predictive power (R²) of the TWB
composite score vs subscales across all major outcomes:
🟢 TWB Subscales consistently outperform the composite for all outcomes
🧠 The biggest gains are in:
Job Stress (where the composite fails entirely)
School LMC and Job Satisfaction (with major jumps in R²)
This suggests that while the TWB composite is a strong general predictor, breaking it into subdomains offers richer, more precise insight — especially for actionable organizational improvements.
#need to upload the demographic data and pair based on PID
#import dataset
demo_df <- Spring_2025_NEA_Data_Demographics_1_
# Merge with main df by PID
df_combined <- df %>%
left_join(demo_df, by = "PID")
# Clean column names
df_combined <- df_combined %>%
clean_names()
# View cleaned names
glimpse(df_combined)## Rows: 2,306
## Columns: 83
## $ pid <chr> "Clifton1", "Clift…
## $ twb1 <dbl> 1, 1, 1, 1, 1, 1, …
## $ twb2 <dbl> 1, 1, 1, 3, 1, 1, …
## $ twb3 <dbl> 1, 1, 1, 4, 1, 1, …
## $ twb4 <dbl> 1, 1, 1, 5, 1, 1, …
## $ twb5 <dbl> 1, 1, 1, 4, 1, 1, …
## $ twb6 <dbl> 1, 1, 6, 1, 1, 1, …
## $ twb7 <dbl> 1, 1, 6, 4, 1, 1, …
## $ twb8 <dbl> 1, 1, 1, 2, 1, 1, …
## $ twb9 <dbl> 1, 1, 1, 5, 1, 1, …
## $ twb10 <dbl> 1, 1, 1, 4, 1, 1, …
## $ twb11 <dbl> 1, 1, 1, 2, 1, 1, …
## $ twb12 <dbl> 1, 1, 1, 4, 1, 1, …
## $ twb13 <dbl> 1, 4, 1, 5, 1, 1, …
## $ twb14 <dbl> 1, 1, 1, 1, 1, 1, …
## $ twb15 <dbl> 1, 1, 1, 4, 1, 3, …
## $ twb16 <dbl> 1, 1, 6, 4, 1, 3, …
## $ twb17 <dbl> 1, 1, 1, 5, 1, 2, …
## $ twb18 <dbl> 1, 4, 6, 4, 1, 3, …
## $ twb19 <dbl> 1, 4, 6, 6, 1, 3, …
## $ twb20 <dbl> 1, 1, 6, 5, 5, 1, …
## $ twb21 <dbl> 1, 1, 5, 5, 4, 1, …
## $ twb22 <dbl> 1, 1, 5, 6, 5, 1, …
## $ twb23 <dbl> 1, 1, 5, 6, 5, 1, …
## $ twb24 <dbl> 3, 4, 4, 5, 4, 3, …
## $ twb25 <dbl> 1, 1, 2, 2, 3, 1, …
## $ twb26 <dbl> 6, 2, 1, 3, 2, 1, …
## $ twb27 <dbl> 6, 4, 6, 4, 4, 3, …
## $ twb28 <dbl> 6, 4, 5, 3, 4, 3, …
## $ twb29 <dbl> 6, 5, 6, 5, 3, 3, …
## $ twb30 <dbl> 6, 5, 4, 5, 4, 3, …
## $ twb31 <dbl> 6, 5, 2, 4, 5, 3, …
## $ twb32 <dbl> 5, 5, 2, 5, 5, 3, …
## $ twb33 <dbl> 5, 5, 3, 5, 5, 3, …
## $ twb34 <dbl> 5, 5, 3, 5, 4, 4, …
## $ twb35 <dbl> 10, 9, 8, 6, 10, 1…
## $ twb36 <dbl> 8, 4, 9, 7, 5, 10,…
## $ twb37 <dbl> 10, 9, 10, 5, 10, …
## $ twb38 <dbl> 10, 10, 7, 10, 10,…
## $ twb39 <fct> No, Yes, No, Yes, …
## $ twb40 <dbl> 1, 2, 1, 1, 2, 1, …
## $ twb41 <dbl> 2, 1, 2, 6, 6, 1, …
## $ twb42 <dbl> 5, 4, 4, 6, 4, 1, …
## $ twb43 <dbl> 5, 6, 4, 4, 4, 1, …
## $ twb44 <dbl> 5, 5, 5, 5, 5, 6, …
## $ twb45 <dbl> 5, 5, 5, 5, 4, 2, …
## $ twb46 <dbl> 5, 5, 2, 6, 6, 3, …
## $ twb47 <dbl> 5, 5, 1, 5, 4, 3, …
## $ twb48 <dbl> 5, 5, 4, 5, 5, 3, …
## $ twb49 <dbl> 5, 6, 5, 5, 5, 3, …
## $ twb50 <dbl> 5, 6, 3, 5, 5, 3, …
## $ twb51 <dbl> 5, 6, 4, 5, 5, 4, …
## $ twb52 <dbl> 5, 6, 4, 5, 5, 3, …
## $ twb53 <dbl> 5, 6, 3, 5, 5, 3, …
## $ twb_leader_score <dbl> 1.000000, 1.214286…
## $ growth_score <dbl> 1.000000, 1.000000…
## $ wellbeing_score <dbl> 1.0, 4.0, 6.0, 5.0…
## $ acceptance_score <dbl> 1.0, 1.0, 5.5, 5.0…
## $ adaptability_score <dbl> 1.0, 1.0, 5.0, 6.0…
## $ depletion_score <dbl> 2.0, 2.5, 3.0, 3.5…
## $ foundational_support_score <dbl> 6.000000, 4.166667…
## $ twb_composite_score <dbl> 13.00000, 14.88095…
## $ union_view_score <dbl> 4.000000, 3.666667…
## $ school_lmc_score <dbl> 5.00, 5.00, 3.25, …
## $ district_lmc_score <dbl> 5.000000, 5.833333…
## $ lmc_composite_score <dbl> 14.000000, 14.5000…
## $ job_satisfaction_score <dbl> 10, 9, 8, 6, 10, 1…
## $ job_stress_score <dbl> 8, 4, 9, 7, 5, 10,…
## $ retention_score <dbl> 5.000000, 5.000000…
## $ nps_score <dbl> 10.0, 9.5, 8.5, 7.…
## $ district <chr> "Clifton", "Clifto…
## $ lmc <chr> "Yes", "Yes", "Yes…
## $ are_you_a_district_or_building_based_administrator <chr> "No", "No", "No", …
## $ school <chr> "School Three", "S…
## $ gender <chr> "Female", "Female"…
## $ race_ethnicity <chr> "White or Caucasio…
## $ years <dbl> 10, 1, NA, 10, 25,…
## $ years_group <chr> "4-10 years", "0-3…
## $ collaboration <chr> "3+ hours per week…
## $ role <chr> "Non-Certificated …
## $ grade <chr> "Elementary School…
## $ are_you_a_member_of_the_education_association_union <chr> "No", "Yes", "No",…
## $ how_involved_are_you_with_the_union_1_none_4_a_lot <chr> "1", "2", "1", "1"…#rename
df_combined <- df_combined %>%
rename(union_involvement = "how_involved_are_you_with_the_union_1_none_4_a_lot")
df_combined <- df_combined %>%
rename(district_admin = "are_you_a_district_or_building_based_administrator")
df_combined <- df_combined %>%
rename(union_member = "are_you_a_member_of_the_education_association_union")
df_combined## # A tibble: 2,306 × 83
## pid twb1 twb2 twb3 twb4 twb5 twb6 twb7 twb8 twb9 twb10 twb11 twb12
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 Clif… 1 1 1 1 1 1 1 1 1 1 1 1
## 2 Clif… 1 1 1 1 1 1 1 1 1 1 1 1
## 3 Clif… 1 1 1 1 1 6 6 1 1 1 1 1
## 4 Clif… 1 3 4 5 4 1 4 2 5 4 2 4
## 5 Clif… 1 1 1 1 1 1 1 1 1 1 1 1
## 6 Clif… 1 1 1 1 1 1 1 1 1 1 1 1
## 7 Clif… 1 1 1 1 1 1 1 1 1 1 1 1
## 8 Clif… 1 1 2 3 2 2 1 3 2 2 1 1
## 9 Clif… 6 5 5 5 6 6 4 5 6 6 4 6
## 10 Clif… 6 6 6 6 6 6 6 6 6 6 6 6
## # ℹ 2,296 more rows
## # ℹ 70 more variables: twb13 <dbl>, twb14 <dbl>, twb15 <dbl>, twb16 <dbl>,
## # twb17 <dbl>, twb18 <dbl>, twb19 <dbl>, twb20 <dbl>, twb21 <dbl>,
## # twb22 <dbl>, twb23 <dbl>, twb24 <dbl>, twb25 <dbl>, twb26 <dbl>,
## # twb27 <dbl>, twb28 <dbl>, twb29 <dbl>, twb30 <dbl>, twb31 <dbl>,
## # twb32 <dbl>, twb33 <dbl>, twb34 <dbl>, twb35 <dbl>, twb36 <dbl>,
## # twb37 <dbl>, twb38 <dbl>, twb39 <fct>, twb40 <dbl>, twb41 <dbl>, …#change to proper type
df_combined$pid <- as.factor(df_combined$pid)
df_combined$district <- as.factor(df_combined$district)
df_combined$lmc <- as.factor(df_combined$lmc)
df_combined$district_admin <- as.factor(df_combined$district_admin)
df_combined$school <- as.factor(df_combined$school)
df_combined$gender <- as.factor(df_combined$gender)
df_combined$race_ethnicity <- as.factor(df_combined$race_ethnicity)
df_combined$years_group <- as.factor(df_combined$years_group)
df_combined$collaboration <- as.factor(df_combined$collaboration)
df_combined$role <- as.factor(df_combined$role)
df_combined$grade <- as.factor(df_combined$grade)
df_combined$union_member <- as.factor(df_combined$union_member)summary(aov(twb_composite_score ~ district, data = df_combined))## Df Sum Sq Mean Sq F value Pr(>F)
## district 2 1468 733.9 62.05 <2e-16 ***
## Residuals 1561 18462 11.8
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 742 observations deleted due to missingnesssummary(aov(twb_composite_score ~ gender, data = df_combined))## Df Sum Sq Mean Sq F value Pr(>F)
## gender 4 159 39.65 3.127 0.0142 *
## Residuals 1532 19427 12.68
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 769 observations deleted due to missingnesssummary(aov(twb_composite_score ~ race_ethnicity, data = df_combined))## Df Sum Sq Mean Sq F value Pr(>F)
## race_ethnicity 22 605 27.51 2.188 0.00119 **
## Residuals 1500 18863 12.57
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 783 observations deleted due to missingnesssummary(aov(twb_composite_score ~ role, data = df_combined))## Df Sum Sq Mean Sq F value Pr(>F)
## role 8 1593 199.10 16.92 <2e-16 ***
## Residuals 1532 18027 11.77
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 765 observations deleted due to missingnesssummary(aov(twb_composite_score ~ grade, data = df_combined))## Df Sum Sq Mean Sq F value Pr(>F)
## grade 2 776 388.1 31.69 3.3e-14 ***
## Residuals 1514 18542 12.2
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 789 observations deleted due to missingnesssummary(aov(twb_composite_score ~ collaboration, data = df_combined))## Df Sum Sq Mean Sq F value Pr(>F)
## collaboration 2 643 321.5 25.82 9.44e-12 ***
## Residuals 1495 18613 12.4
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 808 observations deleted due to missingnesssummary(aov(twb_composite_score ~ union_involvement, data = df_combined))## Df Sum Sq Mean Sq F value Pr(>F)
## union_involvement 3 77 25.65 2.023 0.109
## Residuals 1557 19741 12.68
## 745 observations deleted due to missingness# Step 1: Inspect unique grade levels
table(df_combined$district)##
## Clifton Hopatcong Pleasantville White Bear
## 1199 96 309 702# Run the ANOVA
twb_district_aov <- aov(twb_composite_score ~ district, data = df_combined)
# Summary of ANOVA
summary(twb_district_aov)## Df Sum Sq Mean Sq F value Pr(>F)
## district 2 1468 733.9 62.05 <2e-16 ***
## Residuals 1561 18462 11.8
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 742 observations deleted due to missingness# Post-hoc test: Tukey HSD to find which districts differ
tukey_district <- TukeyHSD(twb_district_aov)
print(tukey_district)## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = twb_composite_score ~ district, data = df_combined)
##
## $district
## diff lwr upr p adj
## Hopatcong-Clifton -2.3403544 -3.2227912 -1.457918 0.0000000
## Pleasantville-Clifton -2.2050673 -2.7263444 -1.683790 0.0000000
## Pleasantville-Hopatcong 0.1352871 -0.8339634 1.104538 0.9426145# Optional: Convert to data frame for easy inspection
tukey_df <- as.data.frame(tukey_district$district)
tukey_df$comparison <- rownames(tukey_df)
# Load ggplot2 if not already
library(ggplot2)
# Boxplot to visualize TWB differences across districts
ggplot(df_combined, aes(x = district, y = twb_composite_score, fill = district)) +
geom_boxplot(alpha = 0.7, outlier.shape = NA) +
geom_jitter(width = 0.2, alpha = 0.2) +
theme_minimal() +
labs(
title = "Teacher Well-Being by District",
x = "District",
y = "TWB Composite Score"
) +
theme(legend.position = "none")
clifton seems to have significantly greater wellbeing measured by the
composite
#742 missing rowws removed when looking at the model so investigate further, think it is due to teh composite score not the district variable
# Check how many rows are missing either variable
df_combined %>%
filter(is.na(twb_composite_score) | is.na(district)) %>%
nrow()## [1] 742df_combined %>%
filter(district == "White Bear") %>%
summarise(
n_total = n(),
n_twb_complete = sum(!is.na(twb_composite_score))
)## # A tibble: 1 × 2
## n_total n_twb_complete
## <int> <int>
## 1 702 0#ya no one from the white bear district have complete measure so must have had short responses or somethign liek thatlibrary(naniar)
# Visual summary of missingness
miss_var_summary(df_combined)## # A tibble: 83 × 3
## variable n_miss pct_miss
## <chr> <int> <num>
## 1 twb_composite_score 742 32.2
## 2 foundational_support_score 710 30.8
## 3 twb29 707 30.7
## 4 twb30 703 30.5
## 5 twb31 540 23.4
## 6 lmc_composite_score 517 22.4
## 7 district_lmc_score 493 21.4
## 8 twb50 483 20.9
## 9 twb49 479 20.8
## 10 twb51 476 20.6
## # ℹ 73 more rows# Where missing data occur
gg_miss_upset(df_combined, nsets = 10)
# Filter complete cases and drop unused factor levels
df_district_subset <- df_combined %>%
filter(!is.na(twb_composite_score) & !is.na(district)) %>%
droplevels()
# Run ANOVA and Tukey HSD
twb_district_aov <- aov(twb_composite_score ~ district, data = df_district_subset)
summary(twb_district_aov)## Df Sum Sq Mean Sq F value Pr(>F)
## district 2 1468 733.9 62.05 <2e-16 ***
## Residuals 1561 18462 11.8
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1tukey_district <- TukeyHSD(twb_district_aov)
tukey_df <- as.data.frame(tukey_district$district)
tukey_df$comparison <- rownames(tukey_df)
# Calculate means and 95% CIs by district
district_summary <- df_district_subset %>%
group_by(district) %>%
summarise(
mean_twb = mean(twb_composite_score, na.rm = TRUE),
se = sd(twb_composite_score, na.rm = TRUE) / sqrt(n()),
n = n()
) %>%
mutate(
ci_lower = mean_twb - 1.96 * se,
ci_upper = mean_twb + 1.96 * se
)
# Plot with error bars
ggplot(district_summary, aes(x = reorder(district, -mean_twb), y = mean_twb)) +
geom_col(fill = "steelblue", alpha = 0.7) +
geom_errorbar(aes(ymin = ci_lower, ymax = ci_upper), width = 0.2) +
theme_minimal() +
labs(
title = "Teacher Well-Being by District",
x = "District",
y = "Mean TWB Composite Score"
) +
theme(axis.text.x = element_text(angle = 45, hjust = 1))
dropped whitebear from visualization due to missing data. Clifton still
seems to show greater TWB measured by the composite
# Subset the data to include only relevant gender categories
df_gender_subset <- df_combined %>%
filter(gender %in% c("Male", "Female", "Prefer not to say"))
# Run ANOVA
twb_gender_aov <- aov(twb_composite_score ~ gender, data = df_gender_subset)
summary(twb_gender_aov)## Df Sum Sq Mean Sq F value Pr(>F)
## gender 2 140 69.85 5.499 0.00417 **
## Residuals 1522 19331 12.70
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 724 observations deleted due to missingness# Tukey HSD for gender
tukey_gender <- TukeyHSD(twb_gender_aov)
# Convert to data frame and extract specific comparisons
tukey_gender_df <- as.data.frame(tukey_gender$gender)
tukey_gender_df$comparison <- rownames(tukey_gender_df)
# Filter comparisons of interest
tukey_gender_df_filtered <- tukey_gender_df %>%
filter(
grepl("Male-Female|Female-Male|Male-Prefer not to say|Prefer not to say-Male|Female-Prefer not to say|Prefer not to say-Female", comparison)
)
print(tukey_gender_df_filtered)## diff lwr upr p adj
## Male-Female -0.1454754 -0.7320466 0.44109591 0.829872021
## Prefer not to say-Female -1.1675669 -1.9946393 -0.34049453 0.002727362
## Prefer not to say-Male -1.0220916 -1.9751458 -0.06903727 0.032085760
## comparison
## Male-Female Male-Female
## Prefer not to say-Female Prefer not to say-Female
## Prefer not to say-Male Prefer not to say-Male# Visualization
library(ggplot2)
ggplot(df_gender_subset, aes(x = gender, y = twb_composite_score, fill = gender)) +
geom_boxplot(alpha = 0.7, outlier.shape = NA) +
geom_jitter(width = 0.2, alpha = 0.2) +
theme_minimal() +
labs(
title = "Teacher Well-Being by Gender (Selected Groups)",
x = "Gender",
y = "TWB Composite Score"
) +
theme(legend.position = "none")
#look at the count for responses, way more women to be expected
df_gender_subset %>%
count(gender) %>%
mutate(percent = round(100 * n / sum(n), 1))## # A tibble: 3 × 3
## gender n percent
## <fct> <int> <dbl>
## 1 Female 1706 75.9
## 2 Male 365 16.2
## 3 Prefer not to say 178 7.9peopel who select prefer not to say report lower wellbeing than female and male, but not differneces emerge between male and females
# Subset only the key gender groups and drop missing TWB values
df_gender_subset <- df_combined %>%
filter(gender %in% c("Male", "Female", "Prefer not to say") & !is.na(twb_composite_score)) %>%
droplevels()
# Run ANOVA
twb_gender_aov <- aov(twb_composite_score ~ gender, data = df_gender_subset)
summary(twb_gender_aov)## Df Sum Sq Mean Sq F value Pr(>F)
## gender 2 140 69.85 5.499 0.00417 **
## Residuals 1522 19331 12.70
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# Tukey post-hoc test
tukey_gender <- TukeyHSD(twb_gender_aov)
tukey_gender_df <- as.data.frame(tukey_gender$gender)
tukey_gender_df$comparison <- rownames(tukey_gender_df)
# Optional: Filter comparisons of interest
tukey_gender_df_filtered <- tukey_gender_df %>%
filter(
grepl("Male-Female|Female-Male|Male-Prefer not to say|Prefer not to say-Male|Female-Prefer not to say|Prefer not to say-Female", comparison)
)
print(tukey_gender_df_filtered)## diff lwr upr p adj
## Male-Female -0.1454754 -0.7320466 0.44109591 0.829872021
## Prefer not to say-Female -1.1675669 -1.9946393 -0.34049453 0.002727362
## Prefer not to say-Male -1.0220916 -1.9751458 -0.06903727 0.032085760
## comparison
## Male-Female Male-Female
## Prefer not to say-Female Prefer not to say-Female
## Prefer not to say-Male Prefer not to say-Male# Summary statistics: Mean + 95% CI for each gender
gender_summary <- df_gender_subset %>%
group_by(gender) %>%
summarise(
mean_twb = mean(twb_composite_score, na.rm = TRUE),
se = sd(twb_composite_score, na.rm = TRUE) / sqrt(n()),
n = n()
) %>%
mutate(
ci_lower = mean_twb - 1.96 * se,
ci_upper = mean_twb + 1.96 * se
)
# Visualization
ggplot(gender_summary, aes(x = reorder(gender, -mean_twb), y = mean_twb)) +
geom_col(fill = "steelblue", alpha = 0.7) +
geom_errorbar(aes(ymin = ci_lower, ymax = ci_upper), width = 0.2) +
theme_minimal() +
labs(
title = "Teacher Well-Being by Gender",
x = "Gender",
y = "Mean TWB Composite Score"
) +
theme(axis.text.x = element_text(angle = 45, hjust = 1))
df_gender_subset %>%
count(gender) %>%
mutate(percent = round(100 * n / sum(n), 1))## # A tibble: 3 × 3
## gender n percent
## <fct> <int> <dbl>
## 1 Female 1167 76.5
## 2 Male 246 16.1
## 3 Prefer not to say 112 7.3library(dplyr)
# Step 1: Inspect unique grade levels
table(df_combined$race_ethnicity)##
## American Indian/Native American or Alaska Native
## 2
## American Indian/Native American or Alaska Native,Spanish, Hispanic, or LatinX origin
## 1
## Asian
## 41
## Asian,Native Hawaiian or Other Pacific Islander
## 1
## Asian,Other
## 1
## Asian,Prefer not to say
## 1
## Asian,Spanish, Hispanic, or LatinX origin
## 3
## Black or African American
## 77
## Black or African American,American Indian/Native American or Alaska Native
## 2
## Black or African American,American Indian/Native American or Alaska Native,Spanish, Hispanic, or LatinX origin
## 1
## Black or African American,Prefer not to say
## 2
## Black or African American,Spanish, Hispanic, or LatinX origin
## 3
## Other
## 55
## Prefer not to say
## 238
## Spanish, Hispanic, or LatinX origin
## 206
## Spanish, Hispanic, or LatinX origin,Other
## 1
## White or Caucasion
## 1573
## White or Caucasion,American Indian/Native American or Alaska Native
## 4
## White or Caucasion,American Indian/Native American or Alaska Native,Spanish, Hispanic, or LatinX origin
## 1
## White or Caucasion,Asian
## 6
## White or Caucasion,Black or African American
## 4
## White or Caucasion,Black or African American,American Indian/Native American or Alaska Native,Asian
## 1
## White or Caucasion,Native Hawaiian or Other Pacific Islander
## 1
## White or Caucasion,Other
## 2
## White or Caucasion,Prefer not to say
## 6
## White or Caucasion,Spanish, Hispanic, or LatinX origin
## 20df_combined %>%
count(race_ethnicity, sort = TRUE) %>%
mutate(percent = round(100 * n / sum(n), 1)) %>%
rename(
Race_Ethnicity = race_ethnicity,
Count = n,
Percent = percent
)## # A tibble: 27 × 3
## Race_Ethnicity Count Percent
## <fct> <int> <dbl>
## 1 White or Caucasion 1573 68.2
## 2 Prefer not to say 238 10.3
## 3 Spanish, Hispanic, or LatinX origin 206 8.9
## 4 Black or African American 77 3.3
## 5 Other 55 2.4
## 6 <NA> 53 2.3
## 7 Asian 41 1.8
## 8 White or Caucasion,Spanish, Hispanic, or LatinX origin 20 0.9
## 9 White or Caucasion,Asian 6 0.3
## 10 White or Caucasion,Prefer not to say 6 0.3
## # ℹ 17 more rows# Step 1: Filter out NA race_ethnicity and run ANOVA
df_race_subset <- df_combined %>%
filter(!is.na(race_ethnicity))
twb_race_aov <- aov(twb_composite_score ~ race_ethnicity, data = df_race_subset)
summary(twb_race_aov)## Df Sum Sq Mean Sq F value Pr(>F)
## race_ethnicity 22 605 27.51 2.188 0.00119 **
## Residuals 1500 18863 12.57
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 730 observations deleted due to missingness# Step 2: Tukey post-hoc
tukey_race <- TukeyHSD(twb_race_aov)
tukey_race_df <- as.data.frame(tukey_race$race_ethnicity)
tukey_race_df$comparison <- rownames(tukey_race_df)
# Step 3: View top comparisons (sorted by p-value)
tukey_race_df %>%
arrange(`p adj`) %>%
head(10) # view the 10 most significant differences## diff
## Spanish, Hispanic, or LatinX origin-Prefer not to say 2.1115578
## White or Caucasion-Spanish, Hispanic, or LatinX origin -1.1421779
## White or Caucasion-Prefer not to say 0.9693799
## Spanish, Hispanic, or LatinX origin-Black or African American 1.5414588
## Prefer not to say-Asian -1.8530321
## Prefer not to say-Asian,Prefer not to say -9.4622758
## White or Caucasion,Prefer not to say-Asian,Prefer not to say -10.0000000
## Black or African American,American Indian/Native American or Alaska Native,Spanish, Hispanic, or LatinX origin-Asian,Prefer not to say -12.5238095
## Black or African American-Asian,Prefer not to say -8.8921769
## White or Caucasion-Asian,Prefer not to say -8.4928959
## lwr
## Spanish, Hispanic, or LatinX origin-Prefer not to say 0.7170619
## White or Caucasion-Spanish, Hispanic, or LatinX origin -2.1625374
## White or Caucasion-Prefer not to say -0.1439773
## Spanish, Hispanic, or LatinX origin-Black or African American -0.2558860
## Prefer not to say-Asian -4.2871441
## Prefer not to say-Asian,Prefer not to say -22.3497239
## White or Caucasion,Prefer not to say-Asian,Prefer not to say -24.0718780
## Black or African American,American Indian/Native American or Alaska Native,Spanish, Hispanic, or LatinX origin-Asian,Prefer not to say -30.6905259
## Black or African American-Asian,Prefer not to say -21.8294156
## White or Caucasion-Asian,Prefer not to say -21.3452433
## upr
## Spanish, Hispanic, or LatinX origin-Prefer not to say 3.5060536
## White or Caucasion-Spanish, Hispanic, or LatinX origin -0.1218183
## White or Caucasion-Prefer not to say 2.0827370
## Spanish, Hispanic, or LatinX origin-Black or African American 3.3388036
## Prefer not to say-Asian 0.5810798
## Prefer not to say-Asian,Prefer not to say 3.4251722
## White or Caucasion,Prefer not to say-Asian,Prefer not to say 4.0718780
## Black or African American,American Indian/Native American or Alaska Native,Spanish, Hispanic, or LatinX origin-Asian,Prefer not to say 5.6429069
## Black or African American-Asian,Prefer not to say 4.0450619
## White or Caucasion-Asian,Prefer not to say 4.3594514
## p adj
## Spanish, Hispanic, or LatinX origin-Prefer not to say 1.195613e-05
## White or Caucasion-Spanish, Hispanic, or LatinX origin 1.052915e-02
## White or Caucasion-Prefer not to say 1.948681e-01
## Spanish, Hispanic, or LatinX origin-Black or African American 2.188284e-01
## Prefer not to say-Asian 4.505172e-01
## Prefer not to say-Asian,Prefer not to say 5.278436e-01
## White or Caucasion,Prefer not to say-Asian,Prefer not to say 5.962382e-01
## Black or African American,American Indian/Native American or Alaska Native,Spanish, Hispanic, or LatinX origin-Asian,Prefer not to say 6.568727e-01
## Black or African American-Asian,Prefer not to say 6.626113e-01
## White or Caucasion-Asian,Prefer not to say 7.341314e-01
## comparison
## Spanish, Hispanic, or LatinX origin-Prefer not to say Spanish, Hispanic, or LatinX origin-Prefer not to say
## White or Caucasion-Spanish, Hispanic, or LatinX origin White or Caucasion-Spanish, Hispanic, or LatinX origin
## White or Caucasion-Prefer not to say White or Caucasion-Prefer not to say
## Spanish, Hispanic, or LatinX origin-Black or African American Spanish, Hispanic, or LatinX origin-Black or African American
## Prefer not to say-Asian Prefer not to say-Asian
## Prefer not to say-Asian,Prefer not to say Prefer not to say-Asian,Prefer not to say
## White or Caucasion,Prefer not to say-Asian,Prefer not to say White or Caucasion,Prefer not to say-Asian,Prefer not to say
## Black or African American,American Indian/Native American or Alaska Native,Spanish, Hispanic, or LatinX origin-Asian,Prefer not to say Black or African American,American Indian/Native American or Alaska Native,Spanish, Hispanic, or LatinX origin-Asian,Prefer not to say
## Black or African American-Asian,Prefer not to say Black or African American-Asian,Prefer not to say
## White or Caucasion-Asian,Prefer not to say White or Caucasion-Asian,Prefer not to say# Step 4: Plot means with 95% CIs
library(ggplot2)
library(dplyr)
df_race_subset %>%
group_by(race_ethnicity) %>%
summarise(
mean_twb = mean(twb_composite_score, na.rm = TRUE),
se = sd(twb_composite_score, na.rm = TRUE) / sqrt(n()),
n = n()
) %>%
mutate(
ci_lower = mean_twb - 1.96 * se,
ci_upper = mean_twb + 1.96 * se
) %>%
ggplot(aes(x = reorder(race_ethnicity, -mean_twb), y = mean_twb)) +
geom_col(fill = "steelblue", alpha = 0.7) +
geom_errorbar(aes(ymin = ci_lower, ymax = ci_upper), width = 0.2) +
theme_minimal() +
labs(
title = "Teacher Well-Being by Race/Ethnicity",
x = "Race/Ethnicity",
y = "Mean TWB Composite Score"
) +
theme(axis.text.x = element_text(angle = 45, hjust = 1))
harder to look at ethnicity since people identify many different
ways, need to adjust the groups if so likely White or Caucasion , Prefer
not to say and Spanish, Hispanic, or LatinX origin
Black or African American
library(dplyr)
library(ggplot2)
# Recode race_ethnicity into broader race_group
df_combined <- df_combined %>%
mutate(race_group = case_when(
grepl("^White or Caucasion$", race_ethnicity) ~ "White",
grepl("^White or Caucasion,", race_ethnicity) ~ "White",
grepl("Black or African American", race_ethnicity) ~ "Black",
grepl("Spanish|Hispanic|Latinx", race_ethnicity, ignore.case = TRUE) ~ "Latinx",
grepl("Asian", race_ethnicity) ~ "Asian",
grepl("American Indian|Alaska Native", race_ethnicity) ~ "Indigenous",
race_ethnicity == "Prefer not to say" ~ "Prefer not to say",
TRUE ~ "Multiracial / Other"
))
# Check the distribution after recoding
df_combined %>%
count(race_group, sort = TRUE)## # A tibble: 7 × 2
## race_group n
## <chr> <int>
## 1 White 1618
## 2 Prefer not to say 238
## 3 Latinx 211
## 4 Multiracial / Other 108
## 5 Black 85
## 6 Asian 44
## 7 Indigenous 2# Filter and drop NAs for analysis
df_race_subset <- df_combined %>%
filter(!is.na(race_group), !is.na(twb_composite_score)) %>%
droplevels()
# ANOVA
twb_racegroup_aov <- aov(twb_composite_score ~ race_group, data = df_race_subset)
summary(twb_racegroup_aov)## Df Sum Sq Mean Sq F value Pr(>F)
## race_group 6 462 77.0 6.159 2.14e-06 ***
## Residuals 1557 19467 12.5
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# Tukey HSD
tukey_racegroup <- TukeyHSD(twb_racegroup_aov)
tukey_racegroup_df <- as.data.frame(tukey_racegroup$race_group)
tukey_racegroup_df$comparison <- rownames(tukey_racegroup_df)
# View significant comparisons
tukey_racegroup_df %>%
arrange(`p adj`) %>%
head(10)## diff lwr upr
## Prefer not to say-Latinx -2.0699096 -3.19654273 -0.94327646
## White-Latinx -1.1027214 -1.92081349 -0.28462940
## Prefer not to say-Asian -2.2138846 -4.12509974 -0.30266941
## Latinx-Black 1.5485738 0.14255042 2.95459716
## White-Prefer not to say 0.9671881 0.06431972 1.87005658
## Multiracial / Other-Latinx -1.4022766 -2.74391811 -0.06063516
## Black-Asian -1.6925488 -3.78069218 0.39559465
## Multiracial / Other-Asian -1.5462516 -3.59159829 0.49909507
## White-Asian -1.2466964 -2.99389870 0.50050585
## Prefer not to say-Multiracial / Other -0.6676330 -2.06258767 0.72732175
## p adj
## Prefer not to say-Latinx 1.407607e-06
## White-Latinx 1.406277e-03
## Prefer not to say-Asian 1.144698e-02
## Latinx-Black 2.005614e-02
## White-Prefer not to say 2.661902e-02
## Multiracial / Other-Latinx 3.373211e-02
## Black-Asian 2.021238e-01
## Multiracial / Other-Asian 2.789556e-01
## White-Asian 3.491881e-01
## Prefer not to say-Multiracial / Other 7.950011e-01
## comparison
## Prefer not to say-Latinx Prefer not to say-Latinx
## White-Latinx White-Latinx
## Prefer not to say-Asian Prefer not to say-Asian
## Latinx-Black Latinx-Black
## White-Prefer not to say White-Prefer not to say
## Multiracial / Other-Latinx Multiracial / Other-Latinx
## Black-Asian Black-Asian
## Multiracial / Other-Asian Multiracial / Other-Asian
## White-Asian White-Asian
## Prefer not to say-Multiracial / Other Prefer not to say-Multiracial / Other# Plot TWB by race_group with 95% CIs
df_race_subset %>%
group_by(race_group) %>%
summarise(
mean_twb = mean(twb_composite_score),
se = sd(twb_composite_score) / sqrt(n()),
n = n()
) %>%
mutate(
ci_lower = mean_twb - 1.96 * se,
ci_upper = mean_twb + 1.96 * se
) %>%
ggplot(aes(x = reorder(race_group, -mean_twb), y = mean_twb)) +
geom_col(fill = "steelblue", alpha = 0.7) +
geom_errorbar(aes(ymin = ci_lower, ymax = ci_upper), width = 0.2) +
theme_minimal() +
labs(
title = "Teacher Well-Being by Race/Ethnicity Group",
x = "Race/Ethnicity Group",
y = "Mean TWB Composite Score"
) +
theme(axis.text.x = element_text(angle = 45, hjust = 1))
| Comparison | Difference | 95% CI | p adj | Interpretation | |
—————————————– | ———- | ————— | ——- | ———————————————————————- | |
Prefer not to say - Latinx | -2.07 | [-3.20, -0.94] |
< 0.001 | Significantly lower TWB among those who prefer not to say
vs Latinx | | White - Latinx | -1.10 | [-1.92, -0.28] |
0.001 | White participants had lower TWB than Latinx participants | |
Prefer not to say - Asian | -2.21 | [-4.13, -0.30] |
0.011 | “Prefer not to say” group had lower TWB than Asian participants
| | Latinx - Black | 1.55 | [0.14, 2.95] | 0.020 |
Latinx participants had higher TWB than Black participants | |
White - Prefer not to say | 0.97 | [0.06, 1.87] | 0.027
| White participants scored higher on TWB than “Prefer not to say” group
| | Multiracial / Other - Latinx | -1.40 | [-2.74,
-0.06] | 0.034 | Multiracial/Other had lower TWB than Latinx | |
Black - Asian | -1.69 | [-3.78, 0.40] | 0.202 | Not
statistically significant | | White - Asian | -1.25 |
[-2.99, 0.50] | 0.349 | Not statistically significant | | Prefer
not to say - Multiracial/Other | -0.67 | [-2.06, 0.73] | 0.795
| Not statistically significant |
library(dplyr)
df_combined %>%
count(role, sort = TRUE) %>%
mutate(percent = round(100 * n / sum(n), 1)) %>%
rename(
Role = role,
Count = n,
Percent = percent
)## # A tibble: 12 × 3
## Role Count Percent
## <fct> <int> <dbl>
## 1 Certificated Staff (e.g., classroom teacher, counselor, servic… 983 42.6
## 2 Certified Educator (e.g., classroom teacher, counselor, servic… 526 22.8
## 3 Professional Certified Staff 234 10.1
## 4 Classified Staff (e.g., paraprofessional, clerical, etc.) 172 7.5
## 5 Non-Certificated Staff (e.g., paraprofessional, clerical, etc.) 170 7.4
## 6 Certified Educator 64 2.8
## 7 Educational Support Professionals 49 2.1
## 8 <NA> 29 1.3
## 9 Classified Staff 27 1.2
## 10 School Site Administrator 22 1
## 11 Support Personnel 17 0.7
## 12 District Administrator 13 0.6library(dplyr)
library(ggplot2)
# Step 1: Define the roles of interest
selected_roles <- c(
"Certificated Staff (e.g., classroom teacher, counselor, service provider etc.)",
"Certified Educator (e.g., classroom teacher, counselor, service provider etc.)",
"Professional Certified Staff",
"Classified Staff (e.g., paraprofessional, clerical, etc.)",
"Non-Certificated Staff (e.g., paraprofessional, clerical, etc.)"
)
# Filter the dataset to only those roles
df_role_focus <- df_combined %>%
filter(role %in% selected_roles)
# Step 2: Run ANOVA
twb_role_focus_aov <- aov(twb_composite_score ~ role, data = df_role_focus)
summary(twb_role_focus_aov)## Df Sum Sq Mean Sq F value Pr(>F)
## role 2 1110 555.1 47.87 <2e-16 ***
## Residuals 1352 15679 11.6
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 730 observations deleted due to missingness# Step 3: Tukey HSD post-hoc test
tukey_role_focus <- TukeyHSD(twb_role_focus_aov)
tukey_role_focus_df <- as.data.frame(tukey_role_focus$role)
tukey_role_focus_df$comparison <- rownames(tukey_role_focus_df)
# View top comparisons
tukey_role_focus_df %>%
arrange(`p adj`) %>%
head(10)## diff
## Professional Certified Staff-Certificated Staff (e.g., classroom teacher, counselor, service provider etc.) -2.4122502
## Professional Certified Staff-Non-Certificated Staff (e.g., paraprofessional, clerical, etc.) -2.4898535
## Non-Certificated Staff (e.g., paraprofessional, clerical, etc.)-Certificated Staff (e.g., classroom teacher, counselor, service provider etc.) 0.0776033
## lwr
## Professional Certified Staff-Certificated Staff (e.g., classroom teacher, counselor, service provider etc.) -3.001256
## Professional Certified Staff-Non-Certificated Staff (e.g., paraprofessional, clerical, etc.) -3.320814
## Non-Certificated Staff (e.g., paraprofessional, clerical, etc.)-Certificated Staff (e.g., classroom teacher, counselor, service provider etc.) -0.611549
## upr
## Professional Certified Staff-Certificated Staff (e.g., classroom teacher, counselor, service provider etc.) -1.8232443
## Professional Certified Staff-Non-Certificated Staff (e.g., paraprofessional, clerical, etc.) -1.6588932
## Non-Certificated Staff (e.g., paraprofessional, clerical, etc.)-Certificated Staff (e.g., classroom teacher, counselor, service provider etc.) 0.7667556
## p adj
## Professional Certified Staff-Certificated Staff (e.g., classroom teacher, counselor, service provider etc.) 3.741452e-14
## Professional Certified Staff-Non-Certificated Staff (e.g., paraprofessional, clerical, etc.) 9.812262e-12
## Non-Certificated Staff (e.g., paraprofessional, clerical, etc.)-Certificated Staff (e.g., classroom teacher, counselor, service provider etc.) 9.622516e-01
## comparison
## Professional Certified Staff-Certificated Staff (e.g., classroom teacher, counselor, service provider etc.) Professional Certified Staff-Certificated Staff (e.g., classroom teacher, counselor, service provider etc.)
## Professional Certified Staff-Non-Certificated Staff (e.g., paraprofessional, clerical, etc.) Professional Certified Staff-Non-Certificated Staff (e.g., paraprofessional, clerical, etc.)
## Non-Certificated Staff (e.g., paraprofessional, clerical, etc.)-Certificated Staff (e.g., classroom teacher, counselor, service provider etc.) Non-Certificated Staff (e.g., paraprofessional, clerical, etc.)-Certificated Staff (e.g., classroom teacher, counselor, service provider etc.)# Step 4: Plot means with 95% CIs
df_role_focus %>%
group_by(role) %>%
summarise(
mean_twb = mean(twb_composite_score, na.rm = TRUE),
se = sd(twb_composite_score, na.rm = TRUE) / sqrt(n()),
n = n()
) %>%
mutate(
ci_lower = mean_twb - 1.96 * se,
ci_upper = mean_twb + 1.96 * se
) %>%
ggplot(aes(x = reorder(role, -mean_twb), y = mean_twb)) +
geom_col(fill = "darkorange", alpha = 0.7) +
geom_errorbar(aes(ymin = ci_lower, ymax = ci_upper), width = 0.2) +
theme_minimal() +
labs(
title = "Teacher Well-Being by Role (Focused Comparison)",
x = "Role",
y = "Mean TWB Composite Score"
) +
theme(axis.text.x = element_text(angle = 30, hjust = 1))
ptofessional certified staff report lower well being than certificated
staff, and non certificated staff
library(dplyr)
library(ggplot2)
# Step 1: Inspect unique grade levels
table(df_combined$grade)##
## Early Childhood Elementary School High School Middle School
## 36 1191 516 444# Step 2: Filter out NAs
df_grade_subset <- df_combined %>%
filter(!is.na(grade))
# Step 3: Run ANOVA
twb_grade_aov <- aov(twb_composite_score ~ grade, data = df_grade_subset)
summary(twb_grade_aov)## Df Sum Sq Mean Sq F value Pr(>F)
## grade 2 776 388.1 31.69 3.3e-14 ***
## Residuals 1514 18542 12.2
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 670 observations deleted due to missingness# Step 4: Tukey HSD post-hoc
tukey_grade <- TukeyHSD(twb_grade_aov)
tukey_grade_df <- as.data.frame(tukey_grade$grade)
tukey_grade_df$comparison <- rownames(tukey_grade_df)
# Step 5: View most significant comparisons
tukey_grade_df %>%
arrange(`p adj`) %>%
head(10)## diff lwr upr p adj
## High School-Elementary School -1.5755421 -2.1107573 -1.0403270 1.967815e-11
## Middle School-Elementary School -1.2952183 -1.8310423 -0.7593942 5.091151e-08
## Middle School-High School 0.2803238 -0.3672235 0.9278712 5.671012e-01
## comparison
## High School-Elementary School High School-Elementary School
## Middle School-Elementary School Middle School-Elementary School
## Middle School-High School Middle School-High School# Step 6: Plot means with 95% CIs
df_grade_subset %>%
group_by(grade) %>%
summarise(
mean_twb = mean(twb_composite_score, na.rm = TRUE),
se = sd(twb_composite_score, na.rm = TRUE) / sqrt(n()),
n = n()
) %>%
mutate(
ci_lower = mean_twb - 1.96 * se,
ci_upper = mean_twb + 1.96 * se
) %>%
ggplot(aes(x = reorder(grade, -mean_twb), y = mean_twb)) +
geom_col(fill = "steelblue", alpha = 0.8) +
geom_errorbar(aes(ymin = ci_lower, ymax = ci_upper), width = 0.2) +
theme_minimal() +
labs(
title = "Teacher Well-Being by Grade Level",
x = "Grade Level",
y = "Mean TWB Composite Score"
) +
theme(axis.text.x = element_text(angle = 30, hjust = 1))
elementary school staff report significantly higher wellbeing than
middle and high school staff. no difference between middle and high
school.
library(psych)
describe(df$twb_composite_score)## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 1564 32.54 3.57 32.74 32.69 3.35 13 42 29 -0.6 1.5 0.09library(dplyr)
library(ggplot2)
# Step 1: Inspect sample sizes
df_combined %>%
count(union_involvement) %>%
mutate(percent = round(100 * n / sum(n), 1))## # A tibble: 6 × 3
## union_involvement n percent
## <chr> <int> <dbl>
## 1 1 416 18
## 2 2 750 32.5
## 3 3 575 24.9
## 4 4 153 6.6
## 5 No 1 0
## 6 <NA> 411 17.8# Step 2: Filter out NAs and run ANOVA
df_union <- df_combined %>%
filter(!is.na(union_involvement))
twb_union_aov <- aov(twb_composite_score ~ union_involvement, data = df_union)
summary(twb_union_aov)## Df Sum Sq Mean Sq F value Pr(>F)
## union_involvement 3 77 25.65 2.023 0.109
## Residuals 1557 19741 12.68
## 334 observations deleted due to missingness# Step 3: Tukey post-hoc test
tukey_union <- TukeyHSD(twb_union_aov)
tukey_union_df <- as.data.frame(tukey_union$union_involvement)
tukey_union_df$comparison <- rownames(tukey_union_df)
# View top comparisons
tukey_union_df %>%
arrange(`p adj`) %>%
head(10)## diff lwr upr p adj comparison
## 4-3 -0.91910020 -1.8995344 0.06133404 0.07542358 4-3
## 4-1 -0.85637629 -1.8528593 0.14010675 0.12086547 4-1
## 4-2 -0.78555387 -1.7344393 0.16333158 0.14431158 4-2
## 3-2 0.13354633 -0.4347217 0.70181441 0.93069805 3-2
## 2-1 -0.07082242 -0.6663522 0.52470740 0.99007282 2-1
## 3-1 0.06272391 -0.5818872 0.70733501 0.99449898 3-1# Step 4: Plot means with 95% CIs
df_union %>%
group_by(union_involvement) %>%
summarise(
mean_twb = mean(twb_composite_score, na.rm = TRUE),
se = sd(twb_composite_score, na.rm = TRUE) / sqrt(n()),
n = n()
) %>%
mutate(
ci_lower = mean_twb - 1.96 * se,
ci_upper = mean_twb + 1.96 * se
) %>%
ggplot(aes(x = union_involvement, y = mean_twb)) +
geom_col(fill = "purple", alpha = 0.7) +
geom_errorbar(aes(ymin = ci_lower, ymax = ci_upper), width = 0.2) +
theme_minimal() +
labs(
title = "Teacher Well-Being by Union Involvement",
x = "Union Involvement (1 = None, 4 = A Lot)",
y = "Mean TWB Composite Score"
)
library(ggplot2)
library(dplyr)
library(dplyr)
library(ggplot2)
# Step 1: Create new data frame and ensure numeric type
df_union_cont <- df_combined %>%
select(union_involvement, twb_composite_score) %>%
filter(!is.na(union_involvement), !is.na(twb_composite_score)) %>%
mutate(union_involvement = as.numeric(as.character(union_involvement)))
# Step 2: Confirm variable type
str(df_union_cont)## tibble [1,561 × 2] (S3: tbl_df/tbl/data.frame)
## $ union_involvement : num [1:1561] 1 2 1 1 2 1 1 2 1 2 ...
## $ twb_composite_score: num [1:1561] 13 14.9 27.9 31 19.7 ...# Step 3: Run linear regression
union_lm <- lm(twb_composite_score ~ union_involvement, data = df_union_cont)
summary(union_lm)##
## Call:
## lm(formula = twb_composite_score ~ union_involvement, data = df_union_cont)
##
## Residuals:
## Min 1Q Median 3Q Max
## -19.6803 -2.0877 0.2429 2.3857 9.6687
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 32.7966 0.2419 135.59 <2e-16 ***
## union_involvement -0.1163 0.1030 -1.13 0.259
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.564 on 1559 degrees of freedom
## Multiple R-squared: 0.0008177, Adjusted R-squared: 0.0001768
## F-statistic: 1.276 on 1 and 1559 DF, p-value: 0.2588# Step 4: Plot relationship with regression line
ggplot(df_union_cont, aes(x = union_involvement, y = twb_composite_score)) +
geom_jitter(width = 0.1, alpha = 0.3) +
geom_smooth(method = "lm", se = TRUE, color = "blue") +
theme_minimal() +
labs(
title = "Teacher Well-Being by Union Involvement (Continuous)",
x = "Union Involvement (1 = None, 4 = A Lot)",
y = "TWB Composite Score"
)
the rating of union involvement as a continous variable is not
associated with greater wellbeing, in fact the opposite relationship is
evident but not significant.
library(dplyr)
library(knitr)
library(kableExtra)# Define demographic variables
demographic_vars <- c("gender", "race_group", "role", "district", "grade", "union_involvement")
# Create a summary table of counts and percentages
demo_summary <- df_combined %>%
select(all_of(demographic_vars)) %>%
pivot_longer(cols = everything(), names_to = "Variable", values_to = "Response") %>%
filter(!is.na(Response)) %>%
group_by(Variable, Response) %>%
summarise(Count = n(), .groups = "drop") %>%
group_by(Variable) %>%
mutate(Percent = round(100 * Count / sum(Count), 1)) %>%
arrange(Variable, desc(Count))
# Display
demo_summary %>%
kable("html", caption = "Table 1. Demographic Characteristics", align = "lrr") %>%
kable_styling(full_width = FALSE, bootstrap_options = c("striped", "hover", "condensed"))| Variable | Response | Count | Percent |
|---|---|---|---|
| district | Clifton | 1199 | 52.0 |
| district | White Bear | 702 | 30.4 |
| district | Pleasantville | 309 | 13.4 |
| district | Hopatcong | 96 | 4.2 |
| gender | Female | 1706 | 75.2 |
| gender | Male | 365 | 16.1 |
| gender | Prefer not to say | 178 | 7.8 |
| gender | Prefer to self-describe | 14 | 0.6 |
| gender | Non-binary / third gender | 6 | 0.3 |
| grade | Elementary School | 1191 | 54.5 |
| grade | High School | 516 | 23.6 |
| grade | Middle School | 444 | 20.3 |
| grade | Early Childhood | 36 | 1.6 |
| race_group | White | 1618 | 70.2 |
| race_group | Prefer not to say | 238 | 10.3 |
| race_group | Latinx | 211 | 9.2 |
| race_group | Multiracial / Other | 108 | 4.7 |
| race_group | Black | 85 | 3.7 |
| race_group | Asian | 44 | 1.9 |
| race_group | Indigenous | 2 | 0.1 |
| role | Certificated Staff (e.g., classroom teacher, counselor, service provider etc.) | 983 | 43.2 |
| role | Certified Educator (e.g., classroom teacher, counselor, service provider etc.) | 526 | 23.1 |
| role | Professional Certified Staff | 234 | 10.3 |
| role | Classified Staff (e.g., paraprofessional, clerical, etc.) | 172 | 7.6 |
| role | Non-Certificated Staff (e.g., paraprofessional, clerical, etc.) | 170 | 7.5 |
| role | Certified Educator | 64 | 2.8 |
| role | Educational Support Professionals | 49 | 2.2 |
| role | Classified Staff | 27 | 1.2 |
| role | School Site Administrator | 22 | 1.0 |
| role | Support Personnel | 17 | 0.7 |
| role | District Administrator | 13 | 0.6 |
| union_involvement | 2 | 750 | 39.6 |
| union_involvement | 3 | 575 | 30.3 |
| union_involvement | 1 | 416 | 22.0 |
| union_involvement | 4 | 153 | 8.1 |
| union_involvement | No | 1 | 0.1 |
# Load required libraries
library(dplyr)
library(tidyr)
library(knitr)
library(kableExtra)
# Specify variables of interest
continuous_vars <- c(
"twb_composite_score",
"job_stress_score",
"job_satisfaction_score",
"retention_score",
"nps_score",
"union_view_score",
"school_lmc_score",
"district_lmc_score",
"lmc_composite_score",
"years"
)
# Create descriptive statistics summary
continuous_summary <- df_combined %>%
select(all_of(continuous_vars)) %>%
pivot_longer(cols = everything(), names_to = "Variable", values_to = "Value") %>%
group_by(Variable) %>%
summarise(
N = sum(!is.na(Value)),
Mean = round(mean(Value, na.rm = TRUE), 2),
SD = round(sd(Value, na.rm = TRUE), 2),
Min = round(min(Value, na.rm = TRUE), 2),
Max = round(max(Value, na.rm = TRUE), 2),
.groups = "drop"
)
# Display the summary table
continuous_summary %>%
kable("html", caption = "Table 2. Summary Statistics for Key Outcome and Collaboration Measures", align = "lrrrrr") %>%
kable_styling(full_width = FALSE, bootstrap_options = c("striped", "hover", "condensed"))| Variable | N | Mean | SD | Min | Max |
|---|---|---|---|---|---|
| district_lmc_score | 1813 | 4.35 | 1.02 | 1 | 6 |
| job_satisfaction_score | 2304 | 7.32 | 1.89 | 1 | 10 |
| job_stress_score | 2304 | 6.58 | 2.17 | 1 | 10 |
| lmc_composite_score | 1789 | 13.37 | 2.77 | 3 | 18 |
| nps_score | 2300 | 7.05 | 2.35 | 1 | 10 |
| retention_score | 2306 | 4.04 | 0.87 | 1 | 5 |
| school_lmc_score | 1838 | 4.43 | 1.09 | 1 | 6 |
| twb_composite_score | 1564 | 32.54 | 3.57 | 13 | 42 |
| union_view_score | 1875 | 4.56 | 1.12 | 1 | 6 |
| years | 2081 | 13.78 | 8.51 | 0 | 47 |
# Function to summarize TWB by a grouping variable
twb_by_group <- function(var) {
df_combined %>%
filter(!is.na(.data[[var]]), !is.na(twb_composite_score)) %>%
group_by(.data[[var]]) %>%
summarise(
N = n(),
Mean_TWB = round(mean(twb_composite_score), 2),
SD_TWB = round(sd(twb_composite_score), 2),
.groups = "drop"
) %>%
rename(Group = 1) %>%
mutate(Variable = var)
}
# Apply to selected variables and combine
group_summary <- bind_rows(
twb_by_group("race_group"),
twb_by_group("gender"),
twb_by_group("district"),
twb_by_group("role")
)
# Display
group_summary %>%
select(Variable, Group, N, Mean_TWB, SD_TWB) %>%
kable("html", caption = "Table 3. TWB Composite Score by Key Demographics", align = "llrrr") %>%
kable_styling(full_width = FALSE, bootstrap_options = c("striped", "hover", "condensed"))| Variable | Group | N | Mean_TWB | SD_TWB |
|---|---|---|---|---|
| race_group | Asian | 37 | 33.75 | 3.17 |
| race_group | Black | 77 | 32.06 | 3.35 |
| race_group | Indigenous | 1 | 30.81 | NA |
| race_group | Latinx | 194 | 33.61 | 3.23 |
| race_group | Multiracial / Other | 88 | 32.21 | 3.30 |
| race_group | Prefer not to say | 154 | 31.54 | 3.28 |
| race_group | White | 1013 | 32.50 | 3.67 |
| gender | Female | 1167 | 32.67 | 3.46 |
| gender | Male | 246 | 32.53 | 4.18 |
| gender | Non-binary / third gender | 4 | 30.51 | 2.69 |
| gender | Prefer not to say | 112 | 31.50 | 3.12 |
| gender | Prefer to self-describe | 8 | 33.08 | 3.25 |
| district | Clifton | 1173 | 33.10 | 3.34 |
| district | Hopatcong | 90 | 30.75 | 3.88 |
| district | Pleasantville | 301 | 30.89 | 3.67 |
| role | Certificated Staff (e.g., classroom teacher, counselor, service provider etc.) | 972 | 33.06 | 3.32 |
| role | Certified Educator | 61 | 30.52 | 4.05 |
| role | Classified Staff | 25 | 31.12 | 3.69 |
| role | District Administrator | 13 | 34.18 | 2.79 |
| role | Educational Support Professionals | 48 | 31.67 | 3.33 |
| role | Non-Certificated Staff (e.g., paraprofessional, clerical, etc.) | 156 | 33.14 | 3.50 |
| role | Professional Certified Staff | 227 | 30.65 | 3.70 |
| role | School Site Administrator | 22 | 34.46 | 2.37 |
| role | Support Personnel | 17 | 31.84 | 4.38 |