Economic Freedom Index
AS
2025-08-21
Setup
Libraries
Minimum set of libraries
remove(list=ls())
library(readxl)
library(tidyverse)
library(labelled)
library(ggcorrplot)
library(gridExtra)
library(GGally)
library(knitr)
library(kableExtra)
require(psych)
library(GPArotation)
library(Hmisc)
require(lavaan)
require(lavaanPlot)
require(ResourceSelection)
require(semPlot)
require(tidySEM)
require(performance)
require(car)
library(semPlot)Functions
Correlation, printing, and citing
corplot <- function(d, m = "pearson", sz = 2.5, title = NULL) {
d_num <- d %>% dplyr::select(where(is.numeric))
if (ncol(d_num) < 2) return(NULL)
mycorr <- cor(d_num, use = "pairwise.complete.obs", method = m)
p.mat <- ggcorrplot::cor_pmat(d_num)
ggcorrplot(mycorr,
hc.order = TRUE,
type = "lower",
colors = c("red","white","green"),
tl.cex = 8,
tl.col = "black",
lab = TRUE,
lab_size = sz,
p.mat = p.mat,
sig.level = 0.01,
insig = "pch",
pch = 4) +
ggplot2::ggtitle(title %||% "")
}
myprint=function(x){x%>%kbl()%>%kable_classic(html_font = "Cambria")}Data
# Import Data
raw_data <- read_excel("../data/raw/economic-freedom-of-the-world-2024-master-index-data-for-researchers-iso.xlsx",
sheet = "EFW Data 2024 Report",
range = "B5:CH4790"
)## New names:
## • `data` -> `data...9`
## • `data` -> `data...11`
## • `data` -> `data...13`
## • `data` -> `data...15`
## • `data` -> `data...17`
## • `data` -> `data...35`
## • `data` -> `data...37`
## • `data` -> `data...39`
## • `data` -> `data...44`
## • `data` -> `data...46`
## • `data` -> `data...48`df <- raw_data
#names(df)
#str(df)Data Cleaning
Area 1: Size of Government
1A: Government consumption
1B: Transfers and subsidies
1C: Government investment
1D: Top marginal tax rate
i. 1Di: Top marginal income tax rate
ii. 1Dii: Top marginal income and payroll tax rates
1E: State ownership of assets
# --- Rename only Area 1 columns ---
df <- df %>%
rename(
`1A` = `Government consumption`, # score
`1A_data` = `data...9`, # underlying data
`1B` = `Transfers and subsidies`, # score
`1B_data` = `data...11`, # underlying data
`1C` = `Government investment`, # score
`1C_data` = `data...13`, # underlying data
`1D_i` = `Top marginal income tax rate`, # score
`1D_i_data` = `data...15`, # underlying data
`1D_ii` = `Top marginal income and payroll tax rate`, # score
`1D_ii_data` = `data...17`, # underlying data
`1D` = `Top marginal tax rate`, # combined top rate
`1E` = `State ownership of Assets`, # score
`Area1` = `Size of Government`, # Area 1 summary score
`Area1_rank` = `Area 1 Rank` # Area 1 rank
)
# --- Attach labels so you keep the readable names ---
var_label(df$`1A`) <- "Government consumption"
var_label(df$`1A_data`) <- "Government consumption – data"
var_label(df$`1B`) <- "Transfers and subsidies"
var_label(df$`1B_data`) <- "Transfers and subsidies – data"
var_label(df$`1C`) <- "Government investment"
var_label(df$`1C_data`) <- "Government investment – data"
var_label(df$`1D_i`) <- "Top marginal income tax rate"
var_label(df$`1D_i_data`) <- "Top marginal income tax rate – data"
var_label(df$`1D_ii`) <- "Top marginal income and payroll tax rate"
var_label(df$`1D_ii_data`) <- "Top marginal income and payroll tax rate – data"
var_label(df$`1D`) <- "Top marginal tax rate (aggregate score)"
var_label(df$`1E`) <- "State ownership of Assets"
var_label(df$Area1) <- "Area 1: Size of Government (summary score)"
var_label(df$Area1_rank) <- "Area 1 Rank"
#dplyr::glimpse(df) # see new names
#sapply(df[c("1A","1B","1C","1D","1E","Area1")], var_label) # see labelsArea 2: Legal System and Property Rights
2A–2H cover the eight sub-indicators.
2_adj, 2_wo_gen, 2_with_gen capture the gender adjustment and the two alternate summary indices.
Area2 = the official “with gender adjustment” score.
df <- df %>%
rename(
`2A` = `Judicial independence`,
`2B` = `Impartial courts`,
`2C` = `Protection of property rights`,
`2D` = `Military interference in rule of law and politics`,
`2E` = `Integrity of the legal system`,
`2F` = `Legal enforcement of contracts`,
`2G` = `Regulatory restrictions on the sale of real property`,
`2H` = `Reliability of police`,
`2_adj` = `Gender Legal Rights Adjustment`,
`2_wo_gen` = `Legal System & Property Rights -- Without Gender Adjustment`,
`2_with_gen` = `Legal System & Property Rights -- With Gender Adjustment`,
Area2_rank = `Area 2 Rank`
) %>%
mutate(
Area2 = `2_with_gen`
) %>%
relocate(Area2, .after = `2_with_gen`)
# Labels
var_label(df$`2A`) <- "Judicial independence"
var_label(df$`2B`) <- "Impartial courts"
var_label(df$`2C`) <- "Protection of property rights"
var_label(df$`2D`) <- "Military interference in rule of law and politics"
var_label(df$`2E`) <- "Integrity of the legal system"
var_label(df$`2F`) <- "Legal enforcement of contracts"
var_label(df$`2G`) <- "Regulatory restrictions on the sale of real property"
var_label(df$`2H`) <- "Reliability of police"
var_label(df$`2_adj`) <- "Gender Legal Rights Adjustment"
var_label(df$`2_wo_gen`) <- "Legal System & Property Rights (without Gender Adjustment)"
var_label(df$`2_with_gen`) <- "Legal System & Property Rights (with Gender Adjustment)"
var_label(df$Area2) <- "Area 2: Legal System & Property Rights (summary score)"
var_label(df$Area2_rank) <- "Area 2: Rank"Area 3: Sound Money
df <- df %>%
rename(
`3A` = `Money growth`,
`3A_data` = `data...35`,
`3B` = `Standard deviation of inflation`,
`3B_data` = `data...37`,
`3C` = `Inflation: Most recent year`,
`3C_data` = `data...39`,
`3D` = `Freedom to own foreign currency bank accounts`,
Area3 = `Sound Money`,
Area3_rank = `Area 3 Rank`
)
var_label(df$`3A`) <- "Money growth"
var_label(df$`3A_data`) <- "Money growth – data"
var_label(df$`3B`) <- "Standard deviation of inflation"
var_label(df$`3B_data`) <- "Standard deviation of inflation – data"
var_label(df$`3C`) <- "Inflation: Most recent year"
var_label(df$`3C_data`) <- "Inflation: Most recent year – data"
var_label(df$`3D`) <- "Freedom to own foreign currency bank accounts"
var_label(df$Area3) <- "Area 3: Sound Money (summary score)"
var_label(df$Area3_rank) <- "Area 3: Rank"Area 4: Freedom to Trade Internationally
df <- df %>%
rename(
`4A_i` = `Revenue from trade taxes (% of trade sector)`,
`4A_i_data` = `data...44`,
`4A_ii` = `Mean tariff rate`,
`4A_ii_data`= `data...46`,
`4A_iii` = `Standard deviation of tariff rates`,
`4A_iii_data`= `data...48`,
`4A` = `Tariffs`,
`4B_i` = `Non-tariff trade barriers`,
`4B_ii` = `Compliance costs of importing and exporting`,
`4B` = `Regulatory trade barriers`,
`4C` = `Black market exchange rates`,
`4D_i` = `Financial openness`,
`4D_ii` = `Capital controls`,
`4D_iii` = `Freedom of foreigners to visit`,
`4D_iv` = `Protection of foreign assets`,
`4D` = `Controls of the movement of capital and people`,
Area4 = `Freedom to trade internationally`,
Area4_rank = `Area 4 Rank`
)
var_label(df$`4A_i`) <- "Revenue from trade taxes (% of trade sector)"
var_label(df$`4A_i_data`) <- "Revenue from trade taxes – data"
var_label(df$`4A_ii`) <- "Mean tariff rate"
var_label(df$`4A_ii_data`)<- "Mean tariff rate – data"
var_label(df$`4A_iii`) <- "Standard deviation of tariff rates"
var_label(df$`4A_iii_data`)<- "Standard deviation of tariff rates – data"
var_label(df$`4A`) <- "Tariffs (aggregate score)"
var_label(df$`4B_i`) <- "Non-tariff trade barriers"
var_label(df$`4B_ii`) <- "Compliance costs of importing and exporting"
var_label(df$`4B`) <- "Regulatory trade barriers (aggregate score)"
var_label(df$`4C`) <- "Black market exchange rates"
var_label(df$`4D_i`) <- "Financial openness"
var_label(df$`4D_ii`) <- "Capital controls"
var_label(df$`4D_iii`) <- "Freedom of foreigners to visit"
var_label(df$`4D_iv`) <- "Protection of foreign assets"
var_label(df$`4D`) <- "Controls of the movement of capital and people (aggregate score)"
var_label(df$Area4) <- "Area 4: Freedom to trade internationally (summary score)"
var_label(df$Area4_rank) <- "Area 4: Rank"Area 5: Regulation
df <- df %>%
rename(
`5A_i` = `Ownership of banks`,
`5A_ii` = `Private sector credit`,
`5A_iii` = `Interest rate controls/negative real interest rates)`,
`5A` = `Credit market regulations`,
`5B_i` = `Hiring regulations and minimum wage`,
`5B_ii` = `Hiring and firing regulations`,
`5B_iii` = `Centralized collective bargaining`,
`5B_iv` = `Hours Regulations`,
`5B_v` = `Mandated cost of worker dismissal`,
`5B_vi` = `Conscription`,
`5B_vii` = `Foreign Labor`,
`5B` = `Labor market regulations`,
`5C_i` = `Regulatory Burden`,
`5C_ii` = `Bureacracy costs`,
`5C_iii` = `Impartial Public Administration`,
`5C_iv` = `Tax compliance`,
`5C` = `Business regulations`,
`5D_i` = `Market openness`,
`5D_ii` = `Business Permits`,
`5D_iii` = `Distorton of the business environment`,
`5D` = `Freedom to enter markets and compete`,
Area5 = `Regulation`,
Area5_rank = `Area 5 Rank`
)
var_label(df$`5A_i`) <- "Ownership of banks"
var_label(df$`5A_ii`) <- "Private sector credit"
var_label(df$`5A_iii`) <- "Interest rate controls / negative real interest rates"
var_label(df$`5A`) <- "Credit market regulations (aggregate score)"
var_label(df$`5B_i`) <- "Hiring regulations and minimum wage"
var_label(df$`5B_ii`) <- "Hiring and firing regulations"
var_label(df$`5B_iii`) <- "Centralized collective bargaining"
var_label(df$`5B_iv`) <- "Hours Regulations"
var_label(df$`5B_v`) <- "Mandated cost of worker dismissal"
var_label(df$`5B_vi`) <- "Conscription"
var_label(df$`5B_vii`) <- "Foreign Labor"
var_label(df$`5B`) <- "Labor market regulations (aggregate score)"
var_label(df$`5C_i`) <- "Regulatory Burden"
var_label(df$`5C_ii`) <- "Bureaucracy costs"
var_label(df$`5C_iii`) <- "Impartial Public Administration"
var_label(df$`5C_iv`) <- "Tax compliance"
var_label(df$`5C`) <- "Business regulations (aggregate score)"
var_label(df$`5D_i`) <- "Market openness"
var_label(df$`5D_ii`) <- "Business Permits"
var_label(df$`5D_iii`) <- "Distortion of the business environment"
var_label(df$`5D`) <- "Freedom to enter markets and compete (aggregate score)"
var_label(df$Area5) <- "Area 5: Regulation (summary score)"
var_label(df$Area5_rank) <- "Area 5: Rank"library(writexl)
# export
write_xlsx(x = df, path = "economic_freedom_cleaned.xlsx")Descriptive
Create scaled variables for models
str(df)## tibble [4,785 × 86] (S3: tbl_df/tbl/data.frame)
## $ Year : num [1:4785] 2022 2022 2022 2022 2022 ...
## $ ISO Code 2 : chr [1:4785] "AL" "DZ" "AO" "AR" ...
## $ ISO Code 3 : chr [1:4785] "ALB" "DZA" "AGO" "ARG" ...
## $ Countries : chr [1:4785] "Albania" "Algeria" "Angola" "Argentina" ...
## $ Economic Freedom Summary Index : num [1:4785] 7.48 4.46 4.79 4.55 7.49 7.98 7.62 5.8 6.65 7.51 ...
## $ Rank : num [1:4785] 38 161 155 159 36 9 23 128 81 34 ...
## $ Quartile : num [1:4785] 1 4 4 4 1 1 1 4 2 1 ...
## $ 1A : num [1:4785] 8.28 3.49 7.94 6.17 7.06 ...
## ..- attr(*, "label")= chr "Government consumption"
## $ 1A_data : num [1:4785] 11.8 28.1 13 19 16 ...
## ..- attr(*, "label")= chr "Government consumption – data"
## $ 1B : num [1:4785] 7.13 7.82 9.7 5.54 7.88 ...
## ..- attr(*, "label")= chr "Transfers and subsidies"
## $ 1B_data : num [1:4785] 11.02 8.51 1.59 16.88 8.27 ...
## ..- attr(*, "label")= chr "Transfers and subsidies – data"
## $ 1C : num [1:4785] 7.55 4 7.74 8.7 8.98 ...
## ..- attr(*, "label")= chr "Government investment"
## $ 1C_data : num [1:4785] 23.6 36 22.9 19.5 18.6 ...
## ..- attr(*, "label")= chr "Government investment – data"
## $ 1D_i : num [1:4785] 9 7 9 7 9 5 4 9 10 10 ...
## ..- attr(*, "label")= chr "Top marginal income tax rate"
## $ 1D_i_data : chr [1:4785] "23" "35" "25" "35" ...
## ..- attr(*, "label")= chr "Top marginal income tax rate – data"
## $ 1D_ii : num [1:4785] 7 2 7 1 7 4 3 4 10 10 ...
## ..- attr(*, "label")= chr "Top marginal income and payroll tax rate"
## $ 1D_ii_data : chr [1:4785] "34" "53" "33" "57" ...
## ..- attr(*, "label")= chr "Top marginal income and payroll tax rate – data"
## $ 1D : num [1:4785] 8 4.5 8 4 8 4.5 3.5 6.5 10 10 ...
## ..- attr(*, "label")= chr "Top marginal tax rate (aggregate score)"
## $ 1E : num [1:4785] 8.08 2.44 4.13 6.69 8.11 ...
## ..- attr(*, "label")= chr "State ownership of Assets"
## $ Area1 : num [1:4785] 7.81 4.45 7.5 6.22 8.01 ...
## ..- attr(*, "label")= chr "Area 1: Size of Government (summary score)"
## $ Area1_rank : num [1:4785] 24 162 36 111 20 117 147 159 3 41 ...
## ..- attr(*, "label")= chr "Area 1 Rank"
## $ 2A : num [1:4785] 4.61 4.01 3.81 4.84 4.56 ...
## ..- attr(*, "label")= chr "Judicial independence"
## $ 2B : num [1:4785] 4.68 3.02 2.93 4.26 4.68 ...
## ..- attr(*, "label")= chr "Impartial courts"
## $ 2C : num [1:4785] 4.42 5.06 3.39 4.79 5.45 ...
## ..- attr(*, "label")= chr "Protection of property rights"
## $ 2D : num [1:4785] 8.33 3.33 4.17 7.5 5 ...
## ..- attr(*, "label")= chr "Military interference in rule of law and politics"
## $ 2E : num [1:4785] 5.75 4.76 3.69 4.52 5.64 ...
## ..- attr(*, "label")= chr "Integrity of the legal system"
## $ 2F : num [1:4785] 3.65 2.84 1.15 3.38 4.29 ...
## ..- attr(*, "label")= chr "Legal enforcement of contracts"
## $ 2G : num [1:4785] 6.72 6.63 5.52 6.86 9.82 ...
## ..- attr(*, "label")= chr "Regulatory restrictions on the sale of real property"
## $ 2H : num [1:4785] 5.3 6.13 2.3 5.96 7.08 ...
## ..- attr(*, "label")= chr "Reliability of police"
## $ 2_adj : num [1:4785] 1 0.706 0.882 0.882 1 ...
## ..- attr(*, "label")= chr "Gender Legal Rights Adjustment"
## $ 2_wo_gen : num [1:4785] 5.43 4.47 3.37 5.26 5.81 ...
## ..- attr(*, "label")= chr "Legal System & Property Rights (without Gender Adjustment)"
## $ 2_with_gen : num [1:4785] 5.43 3.82 3.17 4.95 5.81 ...
## ..- attr(*, "label")= chr "Legal System & Property Rights (with Gender Adjustment)"
## $ Area2 : num [1:4785] 5.43 3.82 3.17 4.95 5.81 ...
## ..- attr(*, "label")= chr "Area 2: Legal System & Property Rights (summary score)"
## $ Area2_rank : num [1:4785] 66 127 145 85 56 9 10 91 68 75 ...
## ..- attr(*, "label")= chr "Area 2: Rank"
## $ 3A : num [1:4785] 9.48 8.68 7.52 0 8.54 ...
## ..- attr(*, "label")= chr "Money growth"
## $ 3A_data : num [1:4785] 2.58 6.59 12.41 53.37 7.3 ...
## ..- attr(*, "label")= chr "Money growth – data"
## $ 3B : num [1:4785] 8.23 5.51 6.01 5.18 8.79 ...
## ..- attr(*, "label")= chr "Standard deviation of inflation"
## $ 3B_data : num [1:4785] 4.42 11.23 9.97 12.05 3.01 ...
## ..- attr(*, "label")= chr "Standard deviation of inflation – data"
## $ 3C : num [1:4785] 7.31 6.29 1.46 0 6.54 ...
## ..- attr(*, "label")= chr "Inflation: Most recent year"
## $ 3C_data : num [1:4785] 6.73 9.27 21.36 71.43 8.64 ...
## ..- attr(*, "label")= chr "Inflation: Most recent year – data"
## $ 3D : num [1:4785] 10 5 5 5 10 10 10 10 0 10 ...
## ..- attr(*, "label")= chr "Freedom to own foreign currency bank accounts"
## $ Area3 : num [1:4785] 8.76 6.37 5 2.55 8.47 ...
## ..- attr(*, "label")= chr "Area 3: Sound Money (summary score)"
## $ Area3_rank : num [1:4785] 28 123 147 162 46 23 49 127 131 12 ...
## ..- attr(*, "label")= chr "Area 3: Rank"
## $ 4A_i : num [1:4785] 9.65 8.48 9.39 4.21 9.56 ...
## ..- attr(*, "label")= chr "Revenue from trade taxes (% of trade sector)"
## $ 4A_i_data : num [1:4785] 0.53 2.28 0.91 8.68 0.66 ...
## ..- attr(*, "label")= chr "Revenue from trade taxes – data"
## $ 4A_ii : num [1:4785] 9.28 6.22 7.8 7.34 8.74 9.52 8.98 8.36 3.5 9.1 ...
## ..- attr(*, "label")= chr "Mean tariff rate"
## $ 4A_ii_data : num [1:4785] 3.6 18.9 11 13.3 6.3 2.4 5.1 8.2 32.5 4.5 ...
## ..- attr(*, "label")= chr "Mean tariff rate – data"
## $ 4A_iii : num [1:4785] 8.08 5.84 3.71 5.85 8.21 ...
## ..- attr(*, "label")= chr "Standard deviation of tariff rates"
## $ 4A_iii_data : num [1:4785] 4.79 10.39 15.73 10.37 4.47 ...
## ..- attr(*, "label")= chr "Standard deviation of tariff rates – data"
## $ 4A : num [1:4785] 9 6.85 6.97 5.8 8.84 ...
## ..- attr(*, "label")= chr "Tariffs (aggregate score)"
## $ 4B_i : num [1:4785] 8.4 2.92 3.6 4.23 4.09 ...
## ..- attr(*, "label")= chr "Non-tariff trade barriers"
## $ 4B_ii : num [1:4785] 9.405 0.479 2.515 5.65 9.315 ...
## ..- attr(*, "label")= chr "Compliance costs of importing and exporting"
## $ 4B : num [1:4785] 8.9 1.7 3.06 4.94 6.71 ...
## ..- attr(*, "label")= chr "Regulatory trade barriers (aggregate score)"
## $ 4C : num [1:4785] 10 2.17 0 2.17 10 ...
## ..- attr(*, "label")= chr "Black market exchange rates"
## $ 4D_i : num [1:4785] 4.02 1.46 2.5 2.66 7.94 ...
## ..- attr(*, "label")= chr "Financial openness"
## $ 4D_ii : num [1:4785] 4.615 0.769 1.538 0 5.385 ...
## ..- attr(*, "label")= chr "Capital controls"
## $ 4D_iii : num [1:4785] 9.27 0.75 0 8.83 8.73 0.11 9.16 2.59 10 7.11 ...
## ..- attr(*, "label")= chr "Freedom of foreigners to visit"
## $ 4D_iv : num [1:4785] 6.9 4.33 3.38 4.37 5.05 ...
## ..- attr(*, "label")= chr "Protection of foreign assets"
## $ 4D : num [1:4785] 6.2 1.83 1.85 3.97 6.78 ...
## ..- attr(*, "label")= chr "Controls of the movement of capital and people (aggregate score)"
## $ Area4 : num [1:4785] 8.53 3.14 2.97 4.22 8.08 ...
## ..- attr(*, "label")= chr "Area 4: Freedom to trade internationally (summary score)"
## $ Area4_rank : num [1:4785] 34 161 164 155 56 52 26 85 145 45 ...
## ..- attr(*, "label")= chr "Area 4: Rank"
## $ 5A_i : num [1:4785] 10 0 5 5 10 10 8 5 10 10 ...
## ..- attr(*, "label")= chr "Ownership of banks"
## $ 5A_ii : num [1:4785] 7.59 6 10 6.07 9.06 ...
## ..- attr(*, "label")= chr "Private sector credit"
## $ 5A_iii : num [1:4785] 9 5 9 0 10 10 10 5 10 10 ...
## ..- attr(*, "label")= chr "Interest rate controls / negative real interest rates"
## $ 5A : num [1:4785] 8.86 3.67 8 3.69 9.69 ...
## ..- attr(*, "label")= chr "Credit market regulations (aggregate score)"
## $ 5B_i : num [1:4785] 6.53 4.03 6.25 3.88 5.83 ...
## ..- attr(*, "label")= chr "Hiring regulations and minimum wage"
## $ 5B_ii : num [1:4785] 5.65 5.82 4.57 1.66 7.13 ...
## ..- attr(*, "label")= chr "Hiring and firing regulations"
## $ 5B_iii : num [1:4785] 5.58 6.52 6.97 3.19 7.25 ...
## ..- attr(*, "label")= chr "Centralized collective bargaining"
## $ 5B_iv : num [1:4785] 8 6 4 10 10 10 6 6 8 8 ...
## ..- attr(*, "label")= chr "Hours Regulations"
## $ 5B_v : num [1:4785] 6.3 7.76 6.63 2.52 9.25 ...
## ..- attr(*, "label")= chr "Mandated cost of worker dismissal"
## $ 5B_vi : num [1:4785] 10 3 0 10 0 10 3 1 10 10 ...
## ..- attr(*, "label")= chr "Conscription"
## $ 5B_vii : num [1:4785] 7.76 3.23 3.56 7.09 6.02 ...
## ..- attr(*, "label")= chr "Foreign Labor"
## $ 5B : num [1:4785] 7.12 5.19 4.57 5.48 6.5 ...
## ..- attr(*, "label")= chr "Labor market regulations (aggregate score)"
## $ 5C_i : num [1:4785] 5.65 4.22 2.94 2.71 5.17 ...
## ..- attr(*, "label")= chr "Regulatory Burden"
## $ 5C_ii : num [1:4785] 6.22 3.78 5.33 5.11 4.67 ...
## ..- attr(*, "label")= chr "Bureaucracy costs"
## $ 5C_iii : num [1:4785] 6.06 2.61 4.86 7.55 6.41 ...
## ..- attr(*, "label")= chr "Impartial Public Administration"
## $ 5C_iv : num [1:4785] 3.59 4.76 4.64 4.5 6.02 ...
## ..- attr(*, "label")= chr "Tax compliance"
## $ 5C : num [1:4785] 5.38 3.84 4.44 4.97 5.57 ...
## ..- attr(*, "label")= chr "Business regulations (aggregate score)"
## $ 5D_i : num [1:4785] 6.81 4.64 3.43 6.14 5.59 ...
## ..- attr(*, "label")= chr "Market openness"
## $ 5D_ii : num [1:4785] 5.62 8.77 7.92 5.73 9.3 ...
## ..- attr(*, "label")= chr "Business Permits"
## $ 5D_iii : num [1:4785] 6.25 2.58 1.25 3.38 5 ...
## ..- attr(*, "label")= chr "Distortion of the business environment"
## $ 5D : num [1:4785] 6.23 5.33 4.2 5.08 6.63 ...
## ..- attr(*, "label")= chr "Freedom to enter markets and compete (aggregate score)"
## $ Area5 : num [1:4785] 6.9 4.51 5.3 4.8 7.1 ...
## ..- attr(*, "label")= chr "Area 5: Regulation (summary score)"
## $ Area5_rank : num [1:4785] 55 156 140 148 45 6 40 107 30 21 ...
## ..- attr(*, "label")= chr "Area 5: Rank"
## $ World Bank Region : chr [1:4785] "Europe & Central Asia" "Middle East & North Africa" "Sub-Saharan Africa" "Latin America & the Caribbean" ...
## $ World Bank Current Income Classification, 1990-Present: chr [1:4785] "UM" "LM" "LM" "UM" ...# Compute scaling factor
scaling_factor <- (1 + df$`2_adj`) / 2
# Create new scaled variables and assign descriptive names
df$`2A_scaled` <- df$`2A` / scaling_factor
label(df$`2A_scaled`) <- "Judicial independence*"
df$`2B_scaled` <- df$`2B` / scaling_factor
label(df$`2B_scaled`) <- "Impartial courts*"
df$`2C_scaled` <- df$`2C` / scaling_factor
label(df$`2C_scaled`) <- "Protection of property rights*"
df$`2D_scaled` <- df$`2D` / scaling_factor
label(df$`2D_scaled`) <- "Military interference in rule of law and politics*"
df$`2E_scaled` <- df$`2E` / scaling_factor
label(df$`2E_scaled`) <- "Integrity of the legal system *"
df$`2F_scaled` <- df$`2F` / scaling_factor
label(df$`2F_scaled`) <- "Legal enforcement of contracts*"
df$`2G_scaled` <- df$`2G` / scaling_factor
label(df$`2G_scaled`) <- "Regulatory restrictions on property*"
df$`2H_scaled` <- df$`2H` / scaling_factor
label(df$`2H_scaled`) <- "Reliability of police*"Descriptive prior to normalizing (year 2022 only)
df_2022 <- df %>%
filter(Year == 2022) %>%
select(
Year, Countries, `Economic Freedom Summary Index`, Rank,
# Area 1
`1A`, `1B`, `1C`, `1D_i`, `1D_ii`, `1D`, `1E`, Area1, Area1_rank,
# Area 2
`2A`, `2B`, `2C`, `2D`, `2E`, `2F`, `2G`, `2H`, `2_adj`, `2_wo_gen`, `2_with_gen`, Area2, Area2_rank,
# Scaled variables from Area 2
`2A_scaled`, `2B_scaled`, `2C_scaled`, `2D_scaled`, `2E_scaled`, `2F_scaled`, `2G_scaled`, `2H_scaled`,
# Area 3
`3A`, `3B`, `3C`, `3D`, Area3, Area3_rank,
# Area 4
`4A_i`, `4A_ii`, `4A_iii`, `4A`, `4B_i`, `4B_ii`, `4B`, `4C`,
`4D_i`, `4D_ii`, `4D_iii`, `4D_iv`, `4D`, Area4, Area4_rank,
# Area 5
`5A_i`, `5A_ii`, `5A_iii`, `5A`,
`5B_i`, `5B_ii`, `5B_iii`, `5B_iv`, `5B_v`, `5B_vi`, `5B_vii`, `5B`,
`5C_i`, `5C_ii`, `5C_iii`, `5C_iv`, `5C`,
`5D_i`, `5D_ii`, `5D_iii`, `5D`,
Area5, Area5_rank
)
# myprint(describe(mydata))Clean Summary Stats Table
str(df_2022 )## tibble [165 × 78] (S3: tbl_df/tbl/data.frame)
## $ Year : num [1:165] 2022 2022 2022 2022 2022 ...
## $ Countries : chr [1:165] "Albania" "Algeria" "Angola" "Argentina" ...
## $ Economic Freedom Summary Index: num [1:165] 7.48 4.46 4.79 4.55 7.49 7.98 7.62 5.8 6.65 7.51 ...
## $ Rank : num [1:165] 38 161 155 159 36 9 23 128 81 34 ...
## $ 1A : num [1:165] 8.28 3.49 7.94 6.17 7.06 ...
## ..- attr(*, "label")= chr "Government consumption"
## $ 1B : num [1:165] 7.13 7.82 9.7 5.54 7.88 ...
## ..- attr(*, "label")= chr "Transfers and subsidies"
## $ 1C : num [1:165] 7.55 4 7.74 8.7 8.98 ...
## ..- attr(*, "label")= chr "Government investment"
## $ 1D_i : num [1:165] 9 7 9 7 9 5 4 9 10 10 ...
## ..- attr(*, "label")= chr "Top marginal income tax rate"
## $ 1D_ii : num [1:165] 7 2 7 1 7 4 3 4 10 10 ...
## ..- attr(*, "label")= chr "Top marginal income and payroll tax rate"
## $ 1D : num [1:165] 8 4.5 8 4 8 4.5 3.5 6.5 10 10 ...
## ..- attr(*, "label")= chr "Top marginal tax rate (aggregate score)"
## $ 1E : num [1:165] 8.08 2.44 4.13 6.69 8.11 ...
## ..- attr(*, "label")= chr "State ownership of Assets"
## $ Area1 : num [1:165] 7.81 4.45 7.5 6.22 8.01 ...
## ..- attr(*, "label")= chr "Area 1: Size of Government (summary score)"
## $ Area1_rank : num [1:165] 24 162 36 111 20 117 147 159 3 41 ...
## ..- attr(*, "label")= chr "Area 1 Rank"
## $ 2A : num [1:165] 4.61 4.01 3.81 4.84 4.56 ...
## ..- attr(*, "label")= chr "Judicial independence"
## $ 2B : num [1:165] 4.68 3.02 2.93 4.26 4.68 ...
## ..- attr(*, "label")= chr "Impartial courts"
## $ 2C : num [1:165] 4.42 5.06 3.39 4.79 5.45 ...
## ..- attr(*, "label")= chr "Protection of property rights"
## $ 2D : num [1:165] 8.33 3.33 4.17 7.5 5 ...
## ..- attr(*, "label")= chr "Military interference in rule of law and politics"
## $ 2E : num [1:165] 5.75 4.76 3.69 4.52 5.64 ...
## ..- attr(*, "label")= chr "Integrity of the legal system"
## $ 2F : num [1:165] 3.65 2.84 1.15 3.38 4.29 ...
## ..- attr(*, "label")= chr "Legal enforcement of contracts"
## $ 2G : num [1:165] 6.72 6.63 5.52 6.86 9.82 ...
## ..- attr(*, "label")= chr "Regulatory restrictions on the sale of real property"
## $ 2H : num [1:165] 5.3 6.13 2.3 5.96 7.08 ...
## ..- attr(*, "label")= chr "Reliability of police"
## $ 2_adj : num [1:165] 1 0.706 0.882 0.882 1 ...
## ..- attr(*, "label")= chr "Gender Legal Rights Adjustment"
## $ 2_wo_gen : num [1:165] 5.43 4.47 3.37 5.26 5.81 ...
## ..- attr(*, "label")= chr "Legal System & Property Rights (without Gender Adjustment)"
## $ 2_with_gen : num [1:165] 5.43 3.82 3.17 4.95 5.81 ...
## ..- attr(*, "label")= chr "Legal System & Property Rights (with Gender Adjustment)"
## $ Area2 : num [1:165] 5.43 3.82 3.17 4.95 5.81 ...
## ..- attr(*, "label")= chr "Area 2: Legal System & Property Rights (summary score)"
## $ Area2_rank : num [1:165] 66 127 145 85 56 9 10 91 68 75 ...
## ..- attr(*, "label")= chr "Area 2: Rank"
## $ 2A_scaled : 'labelled' num [1:165] 4.61 4.71 4.04 5.15 4.56 ...
## ..- attr(*, "label")= chr "Judicial independence*"
## $ 2B_scaled : 'labelled' num [1:165] 4.68 3.54 3.11 4.52 4.68 ...
## ..- attr(*, "label")= chr "Impartial courts*"
## $ 2C_scaled : 'labelled' num [1:165] 4.42 5.94 3.6 5.09 5.45 ...
## ..- attr(*, "label")= chr "Protection of property rights*"
## $ 2D_scaled : 'labelled' num [1:165] 8.33 3.91 4.43 7.97 5 ...
## ..- attr(*, "label")= chr "Military interference in rule of law and politics*"
## $ 2E_scaled : 'labelled' num [1:165] 5.75 5.58 3.93 4.81 5.64 ...
## ..- attr(*, "label")= chr "Integrity of the legal system *"
## $ 2F_scaled : 'labelled' num [1:165] 3.65 3.33 1.22 3.59 4.29 ...
## ..- attr(*, "label")= chr "Legal enforcement of contracts*"
## $ 2G_scaled : 'labelled' num [1:165] 6.72 7.77 5.87 7.29 9.82 ...
## ..- attr(*, "label")= chr "Regulatory restrictions on property*"
## $ 2H_scaled : 'labelled' num [1:165] 5.3 7.19 2.45 6.33 7.08 ...
## ..- attr(*, "label")= chr "Reliability of police*"
## $ 3A : num [1:165] 9.48 8.68 7.52 0 8.54 ...
## ..- attr(*, "label")= chr "Money growth"
## $ 3B : num [1:165] 8.23 5.51 6.01 5.18 8.79 ...
## ..- attr(*, "label")= chr "Standard deviation of inflation"
## $ 3C : num [1:165] 7.31 6.29 1.46 0 6.54 ...
## ..- attr(*, "label")= chr "Inflation: Most recent year"
## $ 3D : num [1:165] 10 5 5 5 10 10 10 10 0 10 ...
## ..- attr(*, "label")= chr "Freedom to own foreign currency bank accounts"
## $ Area3 : num [1:165] 8.76 6.37 5 2.55 8.47 ...
## ..- attr(*, "label")= chr "Area 3: Sound Money (summary score)"
## $ Area3_rank : num [1:165] 28 123 147 162 46 23 49 127 131 12 ...
## ..- attr(*, "label")= chr "Area 3: Rank"
## $ 4A_i : num [1:165] 9.65 8.48 9.39 4.21 9.56 ...
## ..- attr(*, "label")= chr "Revenue from trade taxes (% of trade sector)"
## $ 4A_ii : num [1:165] 9.28 6.22 7.8 7.34 8.74 9.52 8.98 8.36 3.5 9.1 ...
## ..- attr(*, "label")= chr "Mean tariff rate"
## $ 4A_iii : num [1:165] 8.08 5.84 3.71 5.85 8.21 ...
## ..- attr(*, "label")= chr "Standard deviation of tariff rates"
## $ 4A : num [1:165] 9 6.85 6.97 5.8 8.84 ...
## ..- attr(*, "label")= chr "Tariffs (aggregate score)"
## $ 4B_i : num [1:165] 8.4 2.92 3.6 4.23 4.09 ...
## ..- attr(*, "label")= chr "Non-tariff trade barriers"
## $ 4B_ii : num [1:165] 9.405 0.479 2.515 5.65 9.315 ...
## ..- attr(*, "label")= chr "Compliance costs of importing and exporting"
## $ 4B : num [1:165] 8.9 1.7 3.06 4.94 6.71 ...
## ..- attr(*, "label")= chr "Regulatory trade barriers (aggregate score)"
## $ 4C : num [1:165] 10 2.17 0 2.17 10 ...
## ..- attr(*, "label")= chr "Black market exchange rates"
## $ 4D_i : num [1:165] 4.02 1.46 2.5 2.66 7.94 ...
## ..- attr(*, "label")= chr "Financial openness"
## $ 4D_ii : num [1:165] 4.615 0.769 1.538 0 5.385 ...
## ..- attr(*, "label")= chr "Capital controls"
## $ 4D_iii : num [1:165] 9.27 0.75 0 8.83 8.73 0.11 9.16 2.59 10 7.11 ...
## ..- attr(*, "label")= chr "Freedom of foreigners to visit"
## $ 4D_iv : num [1:165] 6.9 4.33 3.38 4.37 5.05 ...
## ..- attr(*, "label")= chr "Protection of foreign assets"
## $ 4D : num [1:165] 6.2 1.83 1.85 3.97 6.78 ...
## ..- attr(*, "label")= chr "Controls of the movement of capital and people (aggregate score)"
## $ Area4 : num [1:165] 8.53 3.14 2.97 4.22 8.08 ...
## ..- attr(*, "label")= chr "Area 4: Freedom to trade internationally (summary score)"
## $ Area4_rank : num [1:165] 34 161 164 155 56 52 26 85 145 45 ...
## ..- attr(*, "label")= chr "Area 4: Rank"
## $ 5A_i : num [1:165] 10 0 5 5 10 10 8 5 10 10 ...
## ..- attr(*, "label")= chr "Ownership of banks"
## $ 5A_ii : num [1:165] 7.59 6 10 6.07 9.06 ...
## ..- attr(*, "label")= chr "Private sector credit"
## $ 5A_iii : num [1:165] 9 5 9 0 10 10 10 5 10 10 ...
## ..- attr(*, "label")= chr "Interest rate controls / negative real interest rates"
## $ 5A : num [1:165] 8.86 3.67 8 3.69 9.69 ...
## ..- attr(*, "label")= chr "Credit market regulations (aggregate score)"
## $ 5B_i : num [1:165] 6.53 4.03 6.25 3.88 5.83 ...
## ..- attr(*, "label")= chr "Hiring regulations and minimum wage"
## $ 5B_ii : num [1:165] 5.65 5.82 4.57 1.66 7.13 ...
## ..- attr(*, "label")= chr "Hiring and firing regulations"
## $ 5B_iii : num [1:165] 5.58 6.52 6.97 3.19 7.25 ...
## ..- attr(*, "label")= chr "Centralized collective bargaining"
## $ 5B_iv : num [1:165] 8 6 4 10 10 10 6 6 8 8 ...
## ..- attr(*, "label")= chr "Hours Regulations"
## $ 5B_v : num [1:165] 6.3 7.76 6.63 2.52 9.25 ...
## ..- attr(*, "label")= chr "Mandated cost of worker dismissal"
## $ 5B_vi : num [1:165] 10 3 0 10 0 10 3 1 10 10 ...
## ..- attr(*, "label")= chr "Conscription"
## $ 5B_vii : num [1:165] 7.76 3.23 3.56 7.09 6.02 ...
## ..- attr(*, "label")= chr "Foreign Labor"
## $ 5B : num [1:165] 7.12 5.19 4.57 5.48 6.5 ...
## ..- attr(*, "label")= chr "Labor market regulations (aggregate score)"
## $ 5C_i : num [1:165] 5.65 4.22 2.94 2.71 5.17 ...
## ..- attr(*, "label")= chr "Regulatory Burden"
## $ 5C_ii : num [1:165] 6.22 3.78 5.33 5.11 4.67 ...
## ..- attr(*, "label")= chr "Bureaucracy costs"
## $ 5C_iii : num [1:165] 6.06 2.61 4.86 7.55 6.41 ...
## ..- attr(*, "label")= chr "Impartial Public Administration"
## $ 5C_iv : num [1:165] 3.59 4.76 4.64 4.5 6.02 ...
## ..- attr(*, "label")= chr "Tax compliance"
## $ 5C : num [1:165] 5.38 3.84 4.44 4.97 5.57 ...
## ..- attr(*, "label")= chr "Business regulations (aggregate score)"
## $ 5D_i : num [1:165] 6.81 4.64 3.43 6.14 5.59 ...
## ..- attr(*, "label")= chr "Market openness"
## $ 5D_ii : num [1:165] 5.62 8.77 7.92 5.73 9.3 ...
## ..- attr(*, "label")= chr "Business Permits"
## $ 5D_iii : num [1:165] 6.25 2.58 1.25 3.38 5 ...
## ..- attr(*, "label")= chr "Distortion of the business environment"
## $ 5D : num [1:165] 6.23 5.33 4.2 5.08 6.63 ...
## ..- attr(*, "label")= chr "Freedom to enter markets and compete (aggregate score)"
## $ Area5 : num [1:165] 6.9 4.51 5.3 4.8 7.1 ...
## ..- attr(*, "label")= chr "Area 5: Regulation (summary score)"
## $ Area5_rank : num [1:165] 55 156 140 148 45 6 40 107 30 21 ...
## ..- attr(*, "label")= chr "Area 5: Rank"# Step 1: Extract variable labels (fallback to variable name if missing)
# --- Create clean variable labels for df_2022 ---
lab_vec <- vapply(
names(df_2022),
function(n) {
lb <- attr(df_2022[[n]], "label", exact = TRUE)
if (is.null(lb) || is.na(lb) || lb == "") {
return(n)
}
# Remove redundant repetition of variable name inside the label
lb_clean <- sub(paste0("^", n, "\\s*[:\\-]?\\s*", collapse = ""), "", lb)
# Output as "varname: cleaned label"
paste0(n, ": ", lb_clean)
},
character(1)
)
# Step 2: Run describe() only on numeric columns
desc <- psych::describe(select(df_2022, where(is.numeric)), fast = FALSE)
# Step 3: Apply labels as rownames
rownames(desc) <- lab_vec[rownames(desc)]
# Step 4: Create final summary data.frame
desc_df <- desc %>%
as.data.frame() %>%
tibble::rownames_to_column("Variable") %>%
select(Variable, n, mean, sd, min, max) %>%
rename(
N = n,
Mean = mean,
SD = sd,
Min = min,
Max = max
)
# Step 5: Render as nicely formatted table
kable(
desc_df,
digits = 2,
col.names = c("Variable", "N", "Mean", "SD", "Min", "Max"),
align = "lccccc",
caption = "Summary Statistics with Labels (Including Scaled Variables)"
) %>%
kable_styling(full_width = FALSE, position = "center", font_size = 12)| Variable | N | Mean | SD | Min | Max |
|---|---|---|---|---|---|
| Year | 165 | 2022.00 | 0.00 | 2022.00 | 2022.00 |
| Economic Freedom Summary Index | 165 | 6.53 | 1.05 | 3.02 | 8.58 |
| Rank | 165 | 82.78 | 47.80 | 1.00 | 165.00 |
| 1A: Government consumption | 165 | 5.47 | 2.46 | 0.00 | 10.00 |
| 1B: Transfers and subsidies | 156 | 7.53 | 2.05 | 1.82 | 10.00 |
| 1C: Government investment | 161 | 7.12 | 3.28 | 0.00 | 10.00 |
| 1D_i: Top marginal income tax rate | 165 | 7.47 | 2.19 | 2.00 | 10.00 |
| 1D_ii: Top marginal income and payroll tax rate | 162 | 5.48 | 2.63 | 0.00 | 10.00 |
| 1D: Top marginal tax rate (aggregate score) | 165 | 6.50 | 2.23 | 1.00 | 10.00 |
| 1E: State ownership of Assets | 162 | 6.66 | 1.58 | 2.44 | 9.52 |
| Area1: Area 1: Size of Government (summary score) | 165 | 6.64 | 1.12 | 3.62 | 9.06 |
| Area1_rank: Area 1 Rank | 165 | 83.00 | 47.78 | 1.00 | 165.00 |
| 2A: Judicial independence | 165 | 5.51 | 1.45 | 2.45 | 8.64 |
| 2B: Impartial courts | 165 | 4.66 | 1.89 | 0.83 | 8.84 |
| 2C: Protection of property rights | 165 | 5.44 | 2.16 | 0.00 | 9.67 |
| 2D: Military interference in rule of law and politics | 138 | 6.29 | 2.66 | 0.00 | 10.00 |
| 2E: Integrity of the legal system | 164 | 5.83 | 1.85 | 1.70 | 9.80 |
| 2F: Legal enforcement of contracts | 165 | 3.97 | 1.98 | 0.00 | 8.73 |
| 2G: Regulatory restrictions on the sale of real property | 163 | 7.59 | 1.52 | 2.67 | 9.98 |
| 2H: Reliability of police | 165 | 5.21 | 2.42 | 0.00 | 9.77 |
| 2_adj: Gender Legal Rights Adjustment | 165 | 0.87 | 0.17 | 0.29 | 1.00 |
| 2_wo_gen: Legal System & Property Rights (without Gender Adjustment) | 165 | 5.53 | 1.66 | 1.98 | 9.10 |
| 2_with_gen: Legal System & Property Rights (with Gender Adjustment) | 165 | 5.23 | 1.79 | 1.63 | 9.10 |
| Area2: Area 2: Legal System & Property Rights (summary score) | 165 | 5.23 | 1.79 | 1.63 | 9.10 |
| Area2_rank: Area 2: Rank | 165 | 83.00 | 47.78 | 1.00 | 165.00 |
| 2A_scaled: Judicial independence* | 165 | 5.89 | 1.42 | 2.45 | 8.64 |
| 2B_scaled: Impartial courts* | 165 | 4.95 | 1.88 | 1.00 | 8.84 |
| 2C_scaled: Protection of property rights* | 165 | 5.78 | 2.15 | 0.00 | 9.93 |
| 2D_scaled: Military interference in rule of law and politics* | 138 | 6.66 | 2.65 | 0.00 | 11.33 |
| 2E_scaled: Integrity of the legal system * | 164 | 6.21 | 1.81 | 1.70 | 9.80 |
| 2F_scaled: Legal enforcement of contracts* | 165 | 4.22 | 2.00 | 0.00 | 8.73 |
| 2G_scaled: Regulatory restrictions on property* | 163 | 8.16 | 1.75 | 3.02 | 13.81 |
| 2H_scaled: Reliability of police* | 165 | 5.55 | 2.59 | 0.00 | 12.13 |
| 3A: Money growth | 163 | 8.24 | 1.61 | 0.00 | 9.98 |
| 3B: Standard deviation of inflation | 165 | 7.65 | 2.52 | 0.00 | 9.74 |
| 3C: Inflation: Most recent year | 165 | 5.88 | 2.61 | 0.00 | 9.46 |
| 3D: Freedom to own foreign currency bank accounts | 165 | 7.15 | 3.95 | 0.00 | 10.00 |
| Area3: Area 3: Sound Money (summary score) | 165 | 7.23 | 1.71 | 0.74 | 9.55 |
| Area3_rank: Area 3: Rank | 165 | 82.99 | 47.77 | 1.00 | 165.00 |
| 4A_i: Revenue from trade taxes (% of trade sector) | 156 | 8.63 | 1.47 | 3.33 | 10.00 |
| 4A_ii: Mean tariff rate | 164 | 8.26 | 1.02 | 3.50 | 10.00 |
| 4A_iii: Standard deviation of tariff rates | 165 | 6.06 | 2.13 | 0.00 | 10.00 |
| 4A: Tariffs (aggregate score) | 165 | 7.62 | 1.18 | 3.92 | 10.00 |
| 4B_i: Non-tariff trade barriers | 165 | 5.75 | 1.80 | 0.00 | 9.18 |
| 4B_ii: Compliance costs of importing and exporting | 165 | 6.46 | 3.01 | 0.00 | 9.98 |
| 4B: Regulatory trade barriers (aggregate score) | 165 | 6.11 | 2.11 | 1.69 | 9.41 |
| 4C: Black market exchange rates | 165 | 9.22 | 2.47 | 0.00 | 10.00 |
| 4D_i: Financial openness | 165 | 5.84 | 3.02 | 0.00 | 10.00 |
| 4D_ii: Capital controls | 164 | 3.52 | 2.76 | 0.00 | 10.00 |
| 4D_iii: Freedom of foreigners to visit | 165 | 7.10 | 3.38 | 0.00 | 10.00 |
| 4D_iv: Protection of foreign assets | 165 | 5.73 | 2.10 | 0.00 | 9.27 |
| 4D: Controls of the movement of capital and people (aggregate score) | 165 | 5.55 | 2.15 | 0.69 | 9.40 |
| Area4: Area 4: Freedom to trade internationally (summary score) | 165 | 7.12 | 1.49 | 2.48 | 9.66 |
| Area4_rank: Area 4: Rank | 165 | 83.00 | 47.78 | 1.00 | 165.00 |
| 5A_i: Ownership of banks | 151 | 7.59 | 2.78 | 0.00 | 10.00 |
| 5A_ii: Private sector credit | 162 | 7.39 | 2.53 | 0.00 | 10.00 |
| 5A_iii: Interest rate controls / negative real interest rates | 163 | 8.35 | 2.27 | 0.00 | 10.00 |
| 5A: Credit market regulations (aggregate score) | 164 | 7.74 | 1.63 | 0.00 | 10.00 |
| 5B_i: Hiring regulations and minimum wage | 165 | 5.81 | 1.80 | 1.25 | 9.45 |
| 5B_ii: Hiring and firing regulations | 165 | 5.64 | 1.97 | 0.00 | 10.00 |
| 5B_iii: Centralized collective bargaining | 141 | 6.48 | 1.22 | 1.61 | 8.67 |
| 5B_iv: Hours Regulations | 165 | 7.84 | 1.94 | 2.00 | 10.00 |
| 5B_v: Mandated cost of worker dismissal | 162 | 6.49 | 2.83 | 0.00 | 10.00 |
| 5B_vi: Conscription | 165 | 6.61 | 4.20 | 0.00 | 10.00 |
| 5B_vii: Foreign Labor | 165 | 5.02 | 1.49 | 0.00 | 8.14 |
| 5B: Labor market regulations (aggregate score) | 165 | 6.25 | 1.22 | 2.67 | 9.14 |
| 5C_i: Regulatory Burden | 158 | 4.15 | 1.22 | 1.14 | 7.44 |
| 5C_ii: Bureaucracy costs | 165 | 5.04 | 2.22 | 0.00 | 9.56 |
| 5C_iii: Impartial Public Administration | 162 | 5.62 | 2.48 | 0.34 | 9.91 |
| 5C_iv: Tax compliance | 165 | 5.90 | 1.92 | 0.00 | 9.87 |
| 5C: Business regulations (aggregate score) | 165 | 5.17 | 1.55 | 0.60 | 9.05 |
| 5D_i: Market openness | 165 | 6.07 | 1.80 | 1.24 | 10.00 |
| 5D_ii: Business Permits | 161 | 8.39 | 1.14 | 4.98 | 10.00 |
| 5D_iii: Distortion of the business environment | 165 | 5.20 | 2.29 | 0.00 | 10.00 |
| 5D: Freedom to enter markets and compete (aggregate score) | 165 | 6.52 | 1.44 | 2.59 | 9.86 |
| Area5: Area 5: Regulation (summary score) | 165 | 6.41 | 1.13 | 2.54 | 8.86 |
| Area5_rank: Area 5: Rank | 165 | 83.00 | 47.78 | 1.00 | 165.00 |
Correlation plots by Area
# ---- Helper that ignores missing vars gracefully ----
sel_vars <- function(df_2022, vars) dplyr::select(df, dplyr::any_of(vars))
# ============
# GROUPS by Area (matches your current columns)
# ============
groups <- list(
A1 = c("1A","1B","1C","1D_i","1D_ii","1D","1E","Area1"),
A2 = c("2A","2B","2C","2D","2E","2F","2G","2H","2_adj","2_wo_gen","2_with_gen","Area2"),
A2_scaled = c("2A_scaled","2B_scaled","2C_scaled","2D_scaled", "2E_scaled","2F_scaled","2G_scaled","2H_scaled", "Area2"),
A3 = c("3A","3B","3C","3D","Area3"),
A4 = c("4A_i","4A_ii","4A_iii","4A","4B_i","4B_ii","4B","4C","4D_i","4D_ii","4D_iii","4D_iv","4D","Area4"),
A5 = c("5A_i","5A_ii","5A_iii","5A",
"5B_i","5B_ii","5B_iii","5B_iv","5B_v","5B_vi","5B_vii","5B",
"5C_i","5C_ii","5C_iii","5C_iv","5C",
"5D_i","5D_ii","5D_iii","5D","Area5")
)
# Optional: keep rank columns for reference or plotting separately
ranks <- c("Area1_rank","Area2_rank","Area3_rank","Area4_rank","Area5_rank")
# ============
# EXAMPLE: build a 2x3 grid of correlation plots by Area
# (skips a plot if not enough numeric columns)
# ============
plots <- list(
corplot(sel_vars(df_2002, groups$A1), title = "Area 1 (1A–1E + Area1)"),
corplot(sel_vars(df_2002, groups$A2), title = "Area 2 (2A–2H + adj & summaries)"),
corplot(sel_vars(df_2002, groups$A2_scaled), title = "Area 2 (scaled variables)"),
corplot(sel_vars(df_2002, groups$A3), title = "Area 3 (3A–3D + Area3)"),
corplot(sel_vars(df_2002, groups$A4), title = "Area 4 (4A–4D + Area4)"),
corplot(sel_vars(df_2002, groups$A5), title = "Area 5 (5A–5D + Area5)")
)
# Drop NULLs (in case a group had <2 numeric vars)
plots <- Filter(Negate(is.null), plots)
# Arrange (2 columns looks small)
# if (length(plots) > 0) gridExtra::grid.arrange(grobs = plots, ncol = 1)
# Print each correlation plot separately
for (i in seq_along(plots)) {
print(plots[[i]])
}
all_vars <- unique(unlist(groups))
plot_all <- corplot(sel_vars(df_2002, all_vars), sz = 2, title = "All Areas: indicators + Area summaries")
if (!is.null(plot_all)) print(plot_all)
KDE Pairs Plot 1
KDE Pairs of data - not evaluted for speeding computations
Normalize
Z-scores to adjust for magnitudes
# 1) drop overall index/ranks and Area summaries/ranks
df_2022_clean <- df_2022 %>%
select(
-`Economic Freedom Summary Index`,
-Rank,
-matches("^Area[1-5]$"),
-matches("^Area[1-5]_rank$")
)
# 2) standardize all numeric columns except Year (Countries is chr, so untouched)
num_cols <- df_2022_clean %>%
select(where(is.numeric)) %>%
names() %>%
setdiff("Year")
df_2022_std <- df_2022_clean %>%
mutate(across(all_of(num_cols), ~ as.numeric(scale(.))))mydata_std has Year, Countries, all other numeric
columns z-scored, labels preserved
Descriptive of Standardized Data
# 1. Rename variables to make them lavaan-safe (prepend "X")
df_2022_std <- df_2022_std %>%
dplyr::rename_with(.fn = ~ paste0("X", .x), .cols = matches("^[0-9]"))
# names(mydata_std)[1:20] # check: now you have X1A, X1B, X1C, X1D_i, ...
# Step 2: Run describe() only on numeric columns
desc_std <- psych::describe(select(df_2022_std, where(is.numeric)), fast = FALSE)
# Step 4: Create final summary data.frame
desc_std_df <- desc_std %>%
as.data.frame() %>%
tibble::rownames_to_column("Variable") %>%
select(Variable, n, mean, sd, min, max) %>%
rename(
N = n,
Mean = mean,
SD = sd,
Min = min,
Max = max
)
# Note: labels are lost after renaming variables to lavaan-safe names
# Step 5: Render as nicely formatted table
kable(
desc_std_df,
digits = 2,
col.names = c("Variable", "N", "Mean", "SD", "Min", "Max"),
align = "lccccc",
caption = "Summary Statistics with Labels (Including Scaled Variables)"
) %>%
kable_styling(full_width = FALSE, position = "center", font_size = 12)| Variable | N | Mean | SD | Min | Max |
|---|---|---|---|---|---|
| Year | 165 | 2022 | 0 | 2022.00 | 2022.00 |
| X1A | 165 | 0 | 1 | -2.23 | 1.84 |
| X1B | 156 | 0 | 1 | -2.78 | 1.20 |
| X1C | 161 | 0 | 1 | -2.17 | 0.88 |
| X1D_i | 165 | 0 | 1 | -2.49 | 1.15 |
| X1D_ii | 162 | 0 | 1 | -2.08 | 1.72 |
| X1D | 165 | 0 | 1 | -2.47 | 1.57 |
| X1E | 162 | 0 | 1 | -2.68 | 1.81 |
| X2A | 165 | 0 | 1 | -2.12 | 2.16 |
| X2B | 165 | 0 | 1 | -2.03 | 2.22 |
| X2C | 165 | 0 | 1 | -2.52 | 1.96 |
| X2D | 138 | 0 | 1 | -2.37 | 1.39 |
| X2E | 164 | 0 | 1 | -2.23 | 2.15 |
| X2F | 165 | 0 | 1 | -2.00 | 2.40 |
| X2G | 163 | 0 | 1 | -3.24 | 1.57 |
| X2H | 165 | 0 | 1 | -2.15 | 1.89 |
| X2_adj | 165 | 0 | 1 | -3.45 | 0.77 |
| X2_wo_gen | 165 | 0 | 1 | -2.13 | 2.15 |
| X2_with_gen | 165 | 0 | 1 | -2.01 | 2.16 |
| X2A_scaled | 165 | 0 | 1 | -2.43 | 1.94 |
| X2B_scaled | 165 | 0 | 1 | -2.10 | 2.08 |
| X2C_scaled | 165 | 0 | 1 | -2.68 | 1.93 |
| X2D_scaled | 138 | 0 | 1 | -2.51 | 1.76 |
| X2E_scaled | 164 | 0 | 1 | -2.49 | 1.99 |
| X2F_scaled | 165 | 0 | 1 | -2.11 | 2.26 |
| X2G_scaled | 163 | 0 | 1 | -2.93 | 3.22 |
| X2H_scaled | 165 | 0 | 1 | -2.14 | 2.54 |
| X3A | 163 | 0 | 1 | -5.11 | 1.08 |
| X3B | 165 | 0 | 1 | -3.04 | 0.83 |
| X3C | 165 | 0 | 1 | -2.25 | 1.37 |
| X3D | 165 | 0 | 1 | -1.81 | 0.72 |
| X4A_i | 156 | 0 | 1 | -3.61 | 0.93 |
| X4A_ii | 164 | 0 | 1 | -4.68 | 1.71 |
| X4A_iii | 165 | 0 | 1 | -2.85 | 1.85 |
| X4A | 165 | 0 | 1 | -3.15 | 2.02 |
| X4B_i | 165 | 0 | 1 | -3.19 | 1.90 |
| X4B_ii | 165 | 0 | 1 | -2.14 | 1.17 |
| X4B | 165 | 0 | 1 | -2.09 | 1.57 |
| X4C | 165 | 0 | 1 | -3.73 | 0.32 |
| X4D_i | 165 | 0 | 1 | -1.94 | 1.38 |
| X4D_ii | 164 | 0 | 1 | -1.28 | 2.35 |
| X4D_iii | 165 | 0 | 1 | -2.10 | 0.86 |
| X4D_iv | 165 | 0 | 1 | -2.73 | 1.69 |
| X4D | 165 | 0 | 1 | -2.27 | 1.79 |
| X5A_i | 151 | 0 | 1 | -2.73 | 0.87 |
| X5A_ii | 162 | 0 | 1 | -2.92 | 1.03 |
| X5A_iii | 163 | 0 | 1 | -3.68 | 0.73 |
| X5A | 164 | 0 | 1 | -4.75 | 1.38 |
| X5B_i | 165 | 0 | 1 | -2.54 | 2.02 |
| X5B_ii | 165 | 0 | 1 | -2.87 | 2.21 |
| X5B_iii | 141 | 0 | 1 | -3.99 | 1.80 |
| X5B_iv | 165 | 0 | 1 | -3.01 | 1.11 |
| X5B_v | 162 | 0 | 1 | -2.29 | 1.24 |
| X5B_vi | 165 | 0 | 1 | -1.57 | 0.81 |
| X5B_vii | 165 | 0 | 1 | -3.36 | 2.09 |
| X5B | 165 | 0 | 1 | -2.93 | 2.36 |
| X5C_i | 158 | 0 | 1 | -2.46 | 2.69 |
| X5C_ii | 165 | 0 | 1 | -2.27 | 2.04 |
| X5C_iii | 162 | 0 | 1 | -2.13 | 1.73 |
| X5C_iv | 165 | 0 | 1 | -3.07 | 2.07 |
| X5C | 165 | 0 | 1 | -2.95 | 2.51 |
| X5D_i | 165 | 0 | 1 | -2.69 | 2.19 |
| X5D_ii | 161 | 0 | 1 | -2.99 | 1.41 |
| X5D_iii | 165 | 0 | 1 | -2.27 | 2.10 |
| X5D | 165 | 0 | 1 | -2.73 | 2.33 |
# export
write_xlsx(x = df_2022_std,
path = "economic_freedom_cleaned_standardised.xlsx")Models
CFA
Once the data has been normalized (see previous section), we build the models to test the assumption of equal weighting at three levels:
Across the five Areas (Area 1–Area 5),
Across the subcategories within each Area, and
Across the individual indicators within each subcategory.
Equal/Current Model
equal_mod <- '
Economic_Freedom =~ Area1 + Area2 + Area3 + Area4 + Area5
Area1 =~ X1A + X1B + X1C + X1D + X1E
Area2 =~ X2A_scaled + X2B_scaled + X2C_scaled + X2D_scaled + X2E_scaled + X2F_scaled + X2G_scaled + X2H_scaled
Area3 =~ X3A + X3B + X3C + X3D
Area4 =~ X4A + X4B + X4C + X4D
Area5 =~ X5A + X5B + X5C + X5D
'
?cfa## Help on topic 'cfa' was found in the following packages:
##
## Package Library
## sem /Library/Frameworks/R.framework/Versions/4.5-arm64/Resources/library
## lavaan /Library/Frameworks/R.framework/Versions/4.5-arm64/Resources/library
##
##
## Using the first match ...fit_equal_mod <- cfa(model = equal_mod,
data = df_2022_std,
estimator = "MLR",
std.lv = TRUE,
missing = "fiml"
)
summary(object = fit_equal_mod,
standardized = TRUE,
fit.measures = TRUE
)## lavaan 0.6-19 ended normally after 111 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 80
##
## Number of observations 165
## Number of missing patterns 13
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 1061.792 945.712
## Degrees of freedom 270 270
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.123
## Yuan-Bentler correction (Mplus variant)
##
## Model Test Baseline Model:
##
## Test statistic 3120.950 2735.681
## Degrees of freedom 300 300
## P-value 0.000 0.000
## Scaling correction factor 1.141
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.719 0.723
## Tucker-Lewis Index (TLI) 0.688 0.692
##
## Robust Comparative Fit Index (CFI) 0.727
## Robust Tucker-Lewis Index (TLI) 0.697
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -4741.476 -4741.476
## Scaling correction factor 1.228
## for the MLR correction
## Loglikelihood unrestricted model (H1) -4210.580 -4210.580
## Scaling correction factor 1.147
## for the MLR correction
##
## Akaike (AIC) 9642.951 9642.951
## Bayesian (BIC) 9891.427 9891.427
## Sample-size adjusted Bayesian (SABIC) 9638.147 9638.147
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.133 0.123
## 90 Percent confidence interval - lower 0.125 0.115
## 90 Percent confidence interval - upper 0.142 0.131
## P-value H_0: RMSEA <= 0.050 0.000 0.000
## P-value H_0: RMSEA >= 0.080 1.000 1.000
##
## Robust RMSEA 0.131
## 90 Percent confidence interval - lower 0.122
## 90 Percent confidence interval - upper 0.141
## P-value H_0: Robust RMSEA <= 0.050 0.000
## P-value H_0: Robust RMSEA >= 0.080 1.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.121 0.121
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Economic_Freedom =~
## Area1 -1.290 0.432 -2.987 0.003 -0.790 -0.790
## Area2 2.264 0.390 5.801 0.000 0.915 0.915
## Area3 0.479 0.127 3.768 0.000 0.432 0.432
## Area4 2.075 0.386 5.377 0.000 0.901 0.901
## Area5 9.627 14.891 0.646 0.518 0.995 0.995
## Area1 =~
## X1A 0.307 0.075 4.082 0.000 0.502 0.503
## X1B 0.446 0.150 2.978 0.003 0.728 0.732
## X1C -0.281 0.071 -3.949 0.000 -0.459 -0.461
## X1D 0.217 0.102 2.125 0.034 0.354 0.355
## X1E -0.259 0.067 -3.857 0.000 -0.423 -0.425
## Area2 =~
## X2A_scaled 0.348 0.056 6.192 0.000 0.861 0.863
## X2B_scaled 0.385 0.055 6.997 0.000 0.953 0.955
## X2C_scaled 0.359 0.050 7.146 0.000 0.887 0.890
## X2D_scaled 0.291 0.043 6.711 0.000 0.720 0.735
## X2E_scaled 0.351 0.051 6.893 0.000 0.869 0.873
## X2F_scaled 0.320 0.045 7.079 0.000 0.793 0.795
## X2G_scaled 0.076 0.037 2.041 0.041 0.187 0.188
## X2H_scaled 0.310 0.049 6.277 0.000 0.766 0.769
## Area3 =~
## X3A 0.639 0.151 4.225 0.000 0.709 0.712
## X3B 0.457 0.108 4.217 0.000 0.507 0.509
## X3C 0.736 0.070 10.451 0.000 0.816 0.818
## X3D 0.108 0.080 1.352 0.176 0.120 0.120
## Area4 =~
## X4A 0.212 0.048 4.387 0.000 0.488 0.490
## X4B 0.374 0.062 6.064 0.000 0.862 0.865
## X4C 0.170 0.048 3.534 0.000 0.392 0.393
## X4D 0.360 0.053 6.811 0.000 0.828 0.831
## Area5 =~
## X5A 0.043 0.067 0.644 0.520 0.419 0.420
## X5B 0.054 0.082 0.658 0.511 0.521 0.523
## X5C 0.095 0.146 0.651 0.515 0.917 0.920
## X5D 0.083 0.127 0.653 0.514 0.801 0.803
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .X1A 0.000 0.078 0.000 1.000 0.000 0.000
## .X1B 0.016 0.078 0.207 0.836 0.016 0.016
## .X1C -0.005 0.079 -0.060 0.952 -0.005 -0.005
## .X1D 0.000 0.078 0.000 1.000 0.000 0.000
## .X1E 0.001 0.078 0.008 0.994 0.001 0.001
## .X2A_scaled -0.000 0.078 -0.000 1.000 -0.000 -0.000
## .X2B_scaled -0.000 0.078 -0.000 1.000 -0.000 -0.000
## .X2C_scaled -0.000 0.078 -0.000 1.000 -0.000 -0.000
## .X2D_scaled -0.061 0.080 -0.756 0.450 -0.061 -0.062
## .X2E_scaled -0.003 0.078 -0.035 0.972 -0.003 -0.003
## .X2F_scaled -0.000 0.078 -0.000 1.000 -0.000 -0.000
## .X2G_scaled -0.002 0.078 -0.028 0.978 -0.002 -0.002
## .X2H_scaled 0.000 0.078 0.000 1.000 0.000 0.000
## .X3A 0.004 0.077 0.047 0.963 0.004 0.004
## .X3B -0.000 0.078 -0.000 1.000 -0.000 -0.000
## .X3C 0.000 0.078 0.000 1.000 0.000 0.000
## .X3D -0.000 0.078 -0.000 1.000 -0.000 -0.000
## .X4A -0.000 0.078 -0.000 1.000 -0.000 -0.000
## .X4B 0.000 0.078 0.000 1.000 0.000 0.000
## .X4C -0.000 0.078 -0.000 1.000 -0.000 -0.000
## .X4D 0.000 0.078 0.000 1.000 0.000 0.000
## .X5A -0.005 0.078 -0.063 0.950 -0.005 -0.005
## .X5B 0.000 0.078 0.000 1.000 0.000 0.000
## .X5C -0.000 0.078 -0.000 1.000 -0.000 -0.000
## .X5D -0.000 0.078 -0.000 1.000 -0.000 -0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .X1A 0.742 0.123 6.048 0.000 0.742 0.747
## .X1B 0.460 0.145 3.172 0.002 0.460 0.465
## .X1C 0.782 0.093 8.411 0.000 0.782 0.788
## .X1D 0.869 0.087 9.948 0.000 0.869 0.874
## .X1E 0.813 0.099 8.255 0.000 0.813 0.819
## .X2A_scaled 0.253 0.036 6.971 0.000 0.253 0.254
## .X2B_scaled 0.087 0.019 4.508 0.000 0.087 0.087
## .X2C_scaled 0.207 0.037 5.571 0.000 0.207 0.208
## .X2D_scaled 0.442 0.053 8.293 0.000 0.442 0.461
## .X2E_scaled 0.236 0.032 7.474 0.000 0.236 0.238
## .X2F_scaled 0.365 0.048 7.669 0.000 0.365 0.368
## .X2G_scaled 0.959 0.133 7.224 0.000 0.959 0.965
## .X2H_scaled 0.407 0.056 7.204 0.000 0.407 0.409
## .X3A 0.488 0.139 3.500 0.000 0.488 0.493
## .X3B 0.737 0.148 4.978 0.000 0.737 0.741
## .X3C 0.328 0.097 3.390 0.001 0.328 0.330
## .X3D 0.980 0.091 10.752 0.000 0.980 0.985
## .X4A 0.755 0.103 7.360 0.000 0.755 0.760
## .X4B 0.251 0.050 4.983 0.000 0.251 0.252
## .X4C 0.841 0.178 4.717 0.000 0.841 0.846
## .X4D 0.308 0.054 5.745 0.000 0.308 0.309
## .X5A 0.821 0.133 6.193 0.000 0.821 0.824
## .X5B 0.722 0.080 9.079 0.000 0.722 0.727
## .X5C 0.152 0.030 5.072 0.000 0.152 0.153
## .X5D 0.352 0.054 6.480 0.000 0.352 0.355
## Economic_Fredm 1.000 1.000 1.000
## .Area1 1.000 0.375 0.375
## .Area2 1.000 0.163 0.163
## .Area3 1.000 0.813 0.813
## .Area4 1.000 0.189 0.189
## .Area5 1.000 0.011 0.011# --- (Optional) factor scores for Areas and EFI ---
scores_equal_mod <- lavPredict(fit_equal_mod) # matrix with Area1..Area5 and EFI scores
head(scores_equal_mod)## Economic_Freedom Area1 Area2 Area3 Area4 Area5
## [1,] 0.1693968 -0.06153098 -0.5728420 0.6688394 1.4848666 1.620732
## [2,] -1.1016796 1.21285791 -1.5696241 -0.1092653 -3.9504531 -10.627482
## [3,] -1.2658848 2.04237700 -3.0676169 -1.4452406 -3.7176650 -11.938752
## [4,] -0.5892202 -0.29831512 -0.8889231 -3.3572114 -1.8926603 -5.682556
## [5,] 0.1745439 -0.07445816 -0.4113683 0.3299082 0.8714919 1.786236
## [6,] 1.5077831 -2.07860552 4.2653192 0.7415639 2.3430630 14.621932# --- (Optional) path diagram ---
lavaanPlot(model = fit_equal_mod, coefs = TRUE, covs = FALSE,
graph_options = list(rankdir = "LR"),
edge_options = list(color = "grey40"))Free Model
- All individual indicators within each subcategory.
mod_free_mod <- '
Economic_Freedom =~ Area1 + Area2 + Area3 + Area4 + Area5
Area1 =~ X1A + X1B + X1C + X1D_i + X1D_ii + X1E
Area2 =~ X2A_scaled + X2B_scaled + X2C_scaled + X2D_scaled + X2E_scaled + X2F_scaled + X2G_scaled + X2H_scaled
Area3 =~ X3A + X3B + X3C + X3D
Area4 =~ X4A_i + X4A_ii + X4A_iii +
X4B_i + X4B_ii +
X4C +
X4D_i + X4D_ii + X4D_iii + X4D_iv
Area5 =~ X5A_i + X5A_ii + X5A_iii +
X5B_i + X5B_ii + X5B_iii + X5B_iv + X5B_v + X5B_vi + X5B_vii +
X5C_i + X5C_ii + X5C_iii + X5C_iv +
X5D_i + X5D_ii + X5D_iii
'
fit_free_mod <- cfa(mod_free_mod,
data = df_2022_std,
estimator = "MLR",
std.lv = TRUE,
missing = "fiml"
)
summary(object = fit_free_mod,
standardized = TRUE,
fit.measures = TRUE
)## lavaan 0.6-19 ended normally after 125 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 140
##
## Number of observations 165
## Number of missing patterns 31
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 3029.053 2863.543
## Degrees of freedom 940 940
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.058
## Yuan-Bentler correction (Mplus variant)
##
## Model Test Baseline Model:
##
## Test statistic 6008.987 5603.398
## Degrees of freedom 990 990
## P-value 0.000 0.000
## Scaling correction factor 1.072
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.584 0.583
## Tucker-Lewis Index (TLI) 0.562 0.561
##
## Robust Comparative Fit Index (CFI) 0.589
## Robust Tucker-Lewis Index (TLI) 0.567
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -8849.971 -8849.971
## Scaling correction factor 1.204
## for the MLR correction
## Loglikelihood unrestricted model (H1) -7335.445 -7335.445
## Scaling correction factor 1.077
## for the MLR correction
##
## Akaike (AIC) 17979.942 17979.942
## Bayesian (BIC) 18414.774 18414.774
## Sample-size adjusted Bayesian (SABIC) 17971.534 17971.534
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.116 0.111
## 90 Percent confidence interval - lower 0.111 0.107
## 90 Percent confidence interval - upper 0.121 0.116
## P-value H_0: RMSEA <= 0.050 0.000 0.000
## P-value H_0: RMSEA >= 0.080 1.000 1.000
##
## Robust RMSEA 0.115
## 90 Percent confidence interval - lower 0.110
## 90 Percent confidence interval - upper 0.121
## P-value H_0: Robust RMSEA <= 0.050 0.000
## P-value H_0: Robust RMSEA >= 0.080 1.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.117 0.117
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Economic_Freedom =~
## Area1 -1.058 0.292 -3.623 0.000 -0.727 -0.727
## Area2 1.849 0.278 6.655 0.000 0.880 0.880
## Area3 0.470 0.127 3.689 0.000 0.425 0.425
## Area4 2.488 0.540 4.611 0.000 0.928 0.928
## Area5 5.182 2.654 1.952 0.051 0.982 0.982
## Area1 =~
## X1A 0.299 0.068 4.418 0.000 0.436 0.437
## X1B 0.523 0.101 5.186 0.000 0.761 0.766
## X1C -0.316 0.064 -4.937 0.000 -0.460 -0.461
## X1D_i 0.324 0.120 2.705 0.007 0.472 0.474
## X1D_ii 0.302 0.125 2.414 0.016 0.440 0.442
## X1E -0.305 0.070 -4.357 0.000 -0.445 -0.446
## Area2 =~
## X2A_scaled 0.410 0.053 7.698 0.000 0.861 0.864
## X2B_scaled 0.453 0.050 9.138 0.000 0.953 0.956
## X2C_scaled 0.424 0.044 9.719 0.000 0.891 0.894
## X2D_scaled 0.341 0.042 8.177 0.000 0.717 0.731
## X2E_scaled 0.411 0.049 8.436 0.000 0.865 0.869
## X2F_scaled 0.378 0.041 9.149 0.000 0.794 0.796
## X2G_scaled 0.089 0.042 2.135 0.033 0.188 0.189
## X2H_scaled 0.364 0.046 7.853 0.000 0.764 0.767
## Area3 =~
## X3A 0.643 0.152 4.245 0.000 0.711 0.714
## X3B 0.460 0.109 4.226 0.000 0.508 0.510
## X3C 0.735 0.069 10.636 0.000 0.813 0.815
## X3D 0.112 0.081 1.389 0.165 0.124 0.124
## Area4 =~
## X4A_i 0.211 0.051 4.145 0.000 0.566 0.568
## X4A_ii 0.244 0.057 4.289 0.000 0.653 0.656
## X4A_iii 0.061 0.033 1.835 0.066 0.164 0.165
## X4B_i 0.304 0.061 4.983 0.000 0.814 0.817
## X4B_ii 0.256 0.047 5.483 0.000 0.686 0.688
## X4C 0.138 0.041 3.377 0.001 0.371 0.372
## X4D_i 0.331 0.065 5.118 0.000 0.887 0.890
## X4D_ii 0.189 0.050 3.793 0.000 0.507 0.509
## X4D_iii 0.145 0.038 3.796 0.000 0.388 0.389
## X4D_iv 0.328 0.057 5.709 0.000 0.879 0.882
## Area5 =~
## X5A_i 0.070 0.038 1.850 0.064 0.370 0.370
## X5A_ii 0.037 0.022 1.680 0.093 0.197 0.197
## X5A_iii 0.033 0.023 1.418 0.156 0.174 0.175
## X5B_i 0.078 0.045 1.728 0.084 0.410 0.411
## X5B_ii 0.100 0.056 1.791 0.073 0.527 0.528
## X5B_iii 0.029 0.025 1.172 0.241 0.155 0.155
## X5B_iv 0.016 0.018 0.872 0.383 0.082 0.083
## X5B_v 0.066 0.037 1.769 0.077 0.348 0.349
## X5B_vi 0.024 0.019 1.241 0.215 0.125 0.125
## X5B_vii 0.118 0.062 1.908 0.056 0.625 0.627
## X5C_i 0.076 0.039 1.977 0.048 0.402 0.402
## X5C_ii 0.152 0.073 2.102 0.036 0.805 0.807
## X5C_iii 0.135 0.063 2.142 0.032 0.714 0.718
## X5C_iv 0.132 0.066 2.001 0.045 0.695 0.697
## X5D_i 0.161 0.082 1.968 0.049 0.848 0.851
## X5D_ii 0.041 0.027 1.480 0.139 0.214 0.215
## X5D_iii 0.146 0.077 1.888 0.059 0.770 0.772
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .X1A 0.000 0.078 0.000 1.000 0.000 0.000
## .X1B 0.017 0.078 0.219 0.827 0.017 0.017
## .X1C -0.006 0.079 -0.072 0.942 -0.006 -0.006
## .X1D_i 0.000 0.078 0.000 1.000 0.000 0.000
## .X1D_ii 0.007 0.079 0.087 0.931 0.007 0.007
## .X1E -0.002 0.079 -0.026 0.979 -0.002 -0.002
## .X2A_scaled -0.000 0.078 -0.000 1.000 -0.000 -0.000
## .X2B_scaled -0.000 0.078 -0.000 1.000 -0.000 -0.000
## .X2C_scaled -0.000 0.078 -0.000 1.000 -0.000 -0.000
## .X2D_scaled -0.063 0.081 -0.784 0.433 -0.063 -0.064
## .X2E_scaled -0.003 0.078 -0.038 0.970 -0.003 -0.003
## .X2F_scaled -0.000 0.078 -0.000 1.000 -0.000 -0.000
## .X2G_scaled -0.002 0.078 -0.028 0.978 -0.002 -0.002
## .X2H_scaled -0.000 0.078 -0.000 1.000 -0.000 -0.000
## .X3A 0.004 0.077 0.048 0.961 0.004 0.004
## .X3B -0.000 0.078 -0.000 1.000 -0.000 -0.000
## .X3C -0.000 0.078 -0.000 1.000 -0.000 -0.000
## .X3D -0.000 0.078 -0.000 1.000 -0.000 -0.000
## .X4A_i -0.024 0.081 -0.291 0.771 -0.024 -0.024
## .X4A_ii -0.001 0.078 -0.016 0.987 -0.001 -0.001
## .X4A_iii -0.000 0.078 -0.000 1.000 -0.000 -0.000
## .X4B_i -0.000 0.078 -0.000 1.000 -0.000 -0.000
## .X4B_ii -0.000 0.078 -0.000 1.000 -0.000 -0.000
## .X4C -0.000 0.078 -0.000 1.000 -0.000 -0.000
## .X4D_i -0.000 0.078 -0.000 1.000 -0.000 -0.000
## .X4D_ii 0.003 0.078 0.038 0.969 0.003 0.003
## .X4D_iii -0.000 0.078 -0.000 1.000 -0.000 -0.000
## .X4D_iv -0.000 0.078 -0.000 1.000 -0.000 -0.000
## .X5A_i -0.028 0.084 -0.334 0.739 -0.028 -0.028
## .X5A_ii -0.005 0.079 -0.058 0.954 -0.005 -0.005
## .X5A_iii -0.003 0.079 -0.044 0.965 -0.003 -0.003
## .X5B_i -0.000 0.078 -0.000 1.000 -0.000 -0.000
## .X5B_ii -0.000 0.078 -0.000 1.000 -0.000 -0.000
## .X5B_iii -0.020 0.081 -0.252 0.801 -0.020 -0.020
## .X5B_iv -0.000 0.078 -0.000 1.000 -0.000 -0.000
## .X5B_v -0.007 0.079 -0.095 0.924 -0.007 -0.008
## .X5B_vi -0.000 0.078 -0.000 1.000 -0.000 -0.000
## .X5B_vii -0.000 0.078 -0.000 1.000 -0.000 -0.000
## .X5C_i -0.020 0.079 -0.248 0.804 -0.020 -0.020
## .X5C_ii -0.000 0.078 -0.000 1.000 -0.000 -0.000
## .X5C_iii 0.003 0.078 0.036 0.971 0.003 0.003
## .X5C_iv -0.000 0.078 -0.000 1.000 -0.000 -0.000
## .X5D_i -0.000 0.078 -0.000 1.000 -0.000 -0.000
## .X5D_ii -0.009 0.079 -0.108 0.914 -0.009 -0.009
## .X5D_iii -0.000 0.078 -0.000 1.000 -0.000 -0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .X1A 0.804 0.129 6.239 0.000 0.804 0.809
## .X1B 0.408 0.105 3.890 0.000 0.408 0.413
## .X1C 0.781 0.089 8.758 0.000 0.781 0.787
## .X1D_i 0.771 0.108 7.162 0.000 0.771 0.776
## .X1D_ii 0.800 0.101 7.948 0.000 0.800 0.805
## .X1E 0.794 0.096 8.273 0.000 0.794 0.801
## .X2A_scaled 0.252 0.036 6.963 0.000 0.252 0.254
## .X2B_scaled 0.086 0.020 4.352 0.000 0.086 0.087
## .X2C_scaled 0.200 0.038 5.306 0.000 0.200 0.201
## .X2D_scaled 0.448 0.054 8.282 0.000 0.448 0.465
## .X2E_scaled 0.243 0.032 7.592 0.000 0.243 0.245
## .X2F_scaled 0.364 0.048 7.609 0.000 0.364 0.366
## .X2G_scaled 0.959 0.132 7.238 0.000 0.959 0.964
## .X2H_scaled 0.410 0.057 7.161 0.000 0.410 0.412
## .X3A 0.485 0.138 3.525 0.000 0.485 0.490
## .X3B 0.735 0.148 4.954 0.000 0.735 0.740
## .X3C 0.334 0.094 3.550 0.000 0.334 0.336
## .X3D 0.979 0.091 10.704 0.000 0.979 0.985
## .X4A_i 0.674 0.120 5.638 0.000 0.674 0.678
## .X4A_ii 0.565 0.117 4.815 0.000 0.565 0.569
## .X4A_iii 0.967 0.154 6.293 0.000 0.967 0.973
## .X4B_i 0.331 0.058 5.715 0.000 0.331 0.333
## .X4B_ii 0.524 0.069 7.574 0.000 0.524 0.527
## .X4C 0.856 0.185 4.624 0.000 0.856 0.861
## .X4D_i 0.207 0.041 5.006 0.000 0.207 0.208
## .X4D_ii 0.737 0.103 7.119 0.000 0.737 0.741
## .X4D_iii 0.843 0.084 10.013 0.000 0.843 0.849
## .X4D_iv 0.221 0.040 5.464 0.000 0.221 0.222
## .X5A_i 0.860 0.092 9.359 0.000 0.860 0.863
## .X5A_ii 0.956 0.138 6.922 0.000 0.956 0.961
## .X5A_iii 0.964 0.153 6.313 0.000 0.964 0.969
## .X5B_i 0.826 0.086 9.597 0.000 0.826 0.831
## .X5B_ii 0.716 0.081 8.856 0.000 0.716 0.721
## .X5B_iii 0.970 0.180 5.402 0.000 0.970 0.976
## .X5B_iv 0.987 0.107 9.255 0.000 0.987 0.993
## .X5B_v 0.877 0.089 9.839 0.000 0.877 0.879
## .X5B_vi 0.978 0.056 17.487 0.000 0.978 0.984
## .X5B_vii 0.603 0.083 7.227 0.000 0.603 0.607
## .X5C_i 0.837 0.091 9.161 0.000 0.837 0.838
## .X5C_ii 0.347 0.041 8.400 0.000 0.347 0.349
## .X5C_iii 0.478 0.069 6.886 0.000 0.478 0.484
## .X5C_iv 0.511 0.067 7.599 0.000 0.511 0.514
## .X5D_i 0.275 0.042 6.468 0.000 0.275 0.276
## .X5D_ii 0.950 0.127 7.493 0.000 0.950 0.954
## .X5D_iii 0.401 0.068 5.860 0.000 0.401 0.404
## Economic_Fredm 1.000 1.000 1.000
## .Area1 1.000 0.472 0.472
## .Area2 1.000 0.226 0.226
## .Area3 1.000 0.819 0.819
## .Area4 1.000 0.139 0.139
## .Area5 1.000 0.036 0.036# --- (Optional) factor scores for Areas and EFI ---
scores_free_mod <- lavPredict(fit_free_mod) # matrix with Area1..Area5 and EFI scores
head(scores_free_mod)## Economic_Freedom Area1 Area2 Area3 Area4 Area5
## [1,] 0.3142640 -0.0285082 -0.5016252 0.6867110 1.2853752 1.8469396
## [2,] -1.1293803 0.8222416 -1.2781262 -0.1126493 -3.8907686 -5.9546947
## [3,] -1.2837399 1.8067887 -2.6025663 -1.4339128 -3.5706036 -6.4708314
## [4,] -0.6547537 -0.6176454 -0.7422474 -3.3720247 -2.6824339 -3.1704754
## [5,] 0.1035932 0.1123482 -0.4098862 0.3209719 0.4793034 0.6856501
## [6,] 1.4546878 -1.7654570 3.6350048 0.7300353 3.0872796 7.6868876# --- (Optional) path diagram ---
lavaanPlot(model = fit_free_mod, coefs = TRUE, covs = FALSE,
graph_options = list(rankdir = "LR"),
edge_options = list(color = "grey40"))Free vs Equal Model
Ideally, we would like to check/show that the equal model of EFI is significantly worse than free model.
#summary(fit_free_mod, standardized = TRUE, fit.measures = TRUE)
#summary(fit_equal_mod, standardized = TRUE, fit.measures = TRUE)
anova(fit_equal_mod, fit_free_mod)## Warning: lavaan->lavTestLRT():
## some models are based on a different set of observed variables##
## Scaled Chi-Squared Difference Test (method = "satorra.bentler.2001")
##
## lavaan->lavTestLRT():
## lavaan NOTE: The "Chisq" column contains standard test statistics, not the
## robust test that should be reported per model. A robust difference test is
## a function of two standard (not robust) statistics.
## Df AIC BIC Chisq Chisq diff Df diff Pr(>Chisq)
## fit_equal_mod 270 9643 9891.4 1061.8
## fit_free_mod 940 17980 18414.8 3029.1 1907 670 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1library(lavaan)
library(dplyr)
library(semPlot)
# --- Model definitions ------------------------------------------------------
mod_5areas <- '
Economic_Freedom =~ Area1 + Area2 + Area3 + Area4 + Area5
Area1 =~ X1A + X1B + X1C + X1D_i + X1D_ii + X1E
Area2 =~ X2A_scaled + X2B_scaled + X2C_scaled + X2D_scaled +
X2E_scaled + X2F_scaled + X2G_scaled + X2H_scaled
Area3 =~ X3A + X3B + X3C + X3D
Area4 =~ X4A_i + X4A_ii + X4A_iii +
X4B_i + X4B_ii + X4C +
X4D_i + X4D_ii + X4D_iii + X4D_iv
Area5 =~ X5A_i + X5A_ii + X5A_iii +
X5B_i + X5B_ii + X5B_iii + X5B_iv + X5B_v + X5B_vi + X5B_vii +
X5C_i + X5C_ii + X5C_iii + X5C_iv +
X5D_i + X5D_ii + X5D_iii
'
mod_4areas <- '
Economic_Freedom =~ Area1 + Area2 + Area3 + Area45
Area1 =~ X1A + X1B + X1C + X1D_i + X1D_ii + X1E
Area2 =~ X2A_scaled + X2B_scaled + X2C_scaled + X2D_scaled +
X2E_scaled + X2F_scaled + X2G_scaled + X2H_scaled
Area3 =~ X3A + X3B + X3C + X3D
Area45 =~ X4A_i + X4A_ii + X4A_iii +
X4B_i + X4B_ii + X4C +
X4D_i + X4D_ii + X4D_iii + X4D_iv +
X5A_i + X5A_ii + X5A_iii +
X5B_i + X5B_ii + X5B_iii + X5B_iv + X5B_v + X5B_vi + X5B_vii +
X5C_i + X5C_ii + X5C_iii + X5C_iv +
X5D_i + X5D_ii + X5D_iii
'
mod_6areas <- '
Economic_Freedom =~ Area1 + Area2a + Area2b + Area3 + Area4 + Area5
Area1 =~ X1A + X1B + X1C + X1D_i + X1D_ii + X1E
Area2a =~ X2A_scaled + X2B_scaled + X2C_scaled + X2D_scaled
Area2b =~ X2E_scaled + X2F_scaled + X2G_scaled + X2H_scaled
Area3 =~ X3A + X3B + X3C + X3D
Area4 =~ X4A_i + X4A_ii + X4A_iii +
X4B_i + X4B_ii + X4C +
X4D_i + X4D_ii + X4D_iii + X4D_iv
Area5 =~ X5A_i + X5A_ii + X5A_iii +
X5B_i + X5B_ii + X5B_iii + X5B_iv + X5B_v + X5B_vi + X5B_vii +
X5C_i + X5C_ii + X5C_iii + X5C_iv +
X5D_i + X5D_ii + X5D_iii
'
# --- Fit models --------------------------------------------------------------
fit_5 <- cfa(mod_5areas, data = df_2022_std , std.lv = TRUE, estimator = "MLR")
fit_4 <- cfa(mod_4areas, data = df_2022_std , std.lv = TRUE, estimator = "MLR")
fit_6 <- cfa(mod_6areas, data = df_2022_std , std.lv = TRUE, estimator = "MLR")
# --- Summaries (optional, comment out if too long) ---------------------------
summary(fit_5, fit.measures = TRUE, standardized = TRUE)## lavaan 0.6-19 ended normally after 172 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 95
##
## Used Total
## Number of observations 108 165
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 2602.082 2593.232
## Degrees of freedom 940 940
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.003
## Yuan-Bentler correction (Mplus variant)
##
## Model Test Baseline Model:
##
## Test statistic 4845.188 4758.297
## Degrees of freedom 990 990
## P-value 0.000 0.000
## Scaling correction factor 1.018
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.569 0.561
## Tucker-Lewis Index (TLI) 0.546 0.538
##
## Robust Comparative Fit Index (CFI) 0.568
## Robust Tucker-Lewis Index (TLI) 0.545
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -5460.590 -5460.590
## Scaling correction factor 1.343
## for the MLR correction
## Loglikelihood unrestricted model (H1) -4159.549 -4159.549
## Scaling correction factor 1.035
## for the MLR correction
##
## Akaike (AIC) 11111.180 11111.180
## Bayesian (BIC) 11365.983 11365.983
## Sample-size adjusted Bayesian (SABIC) 11065.811 11065.811
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.128 0.128
## 90 Percent confidence interval - lower 0.122 0.122
## 90 Percent confidence interval - upper 0.134 0.133
## P-value H_0: RMSEA <= 0.050 0.000 0.000
## P-value H_0: RMSEA >= 0.080 1.000 1.000
##
## Robust RMSEA 0.128
## 90 Percent confidence interval - lower 0.122
## 90 Percent confidence interval - upper 0.134
## P-value H_0: Robust RMSEA <= 0.050 0.000
## P-value H_0: Robust RMSEA >= 0.080 1.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.127 0.127
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Economic_Freedom =~
## Area1 -0.873 0.216 -4.049 0.000 -0.658 -0.658
## Area2 1.498 0.250 5.983 0.000 0.832 0.832
## Area3 0.630 0.166 3.801 0.000 0.533 0.533
## Area4 3.273 1.132 2.891 0.004 0.956 0.956
## Area5 10.825 35.994 0.301 0.764 0.996 0.996
## Area1 =~
## X1A 0.439 0.063 7.007 0.000 0.583 0.629
## X1B 0.671 0.102 6.597 0.000 0.890 0.849
## X1C -0.256 0.057 -4.531 0.000 -0.340 -0.432
## X1D_i 0.380 0.113 3.355 0.001 0.504 0.490
## X1D_ii 0.343 0.112 3.053 0.002 0.456 0.458
## X1E -0.238 0.062 -3.856 0.000 -0.316 -0.346
## Area2 =~
## X2A_scaled 0.505 0.063 8.068 0.000 0.910 0.909
## X2B_scaled 0.516 0.056 9.248 0.000 0.929 0.967
## X2C_scaled 0.454 0.048 9.378 0.000 0.818 0.912
## X2D_scaled 0.365 0.049 7.515 0.000 0.657 0.701
## X2E_scaled 0.431 0.058 7.473 0.000 0.776 0.866
## X2F_scaled 0.436 0.051 8.602 0.000 0.786 0.828
## X2G_scaled 0.105 0.051 2.068 0.039 0.189 0.217
## X2H_scaled 0.408 0.055 7.469 0.000 0.735 0.795
## Area3 =~
## X3A 0.493 0.170 2.903 0.004 0.583 0.633
## X3B 0.482 0.108 4.477 0.000 0.570 0.703
## X3C 0.655 0.092 7.109 0.000 0.774 0.830
## X3D 0.196 0.077 2.534 0.011 0.232 0.258
## Area4 =~
## X4A_i 0.151 0.050 3.003 0.003 0.516 0.595
## X4A_ii 0.192 0.070 2.732 0.006 0.657 0.719
## X4A_iii 0.075 0.040 1.878 0.060 0.256 0.249
## X4B_i 0.222 0.070 3.170 0.002 0.761 0.873
## X4B_ii 0.198 0.068 2.933 0.003 0.678 0.732
## X4C 0.143 0.059 2.432 0.015 0.488 0.495
## X4D_i 0.256 0.085 3.016 0.003 0.878 0.900
## X4D_ii 0.174 0.064 2.718 0.007 0.594 0.620
## X4D_iii 0.080 0.040 1.997 0.046 0.275 0.319
## X4D_iv 0.240 0.069 3.470 0.001 0.820 0.903
## Area5 =~
## X5A_i 0.033 0.109 0.303 0.762 0.360 0.377
## X5A_ii 0.022 0.074 0.302 0.762 0.244 0.298
## X5A_iii 0.012 0.039 0.301 0.763 0.127 0.137
## X5B_i 0.041 0.136 0.300 0.764 0.444 0.473
## X5B_ii 0.054 0.182 0.300 0.764 0.592 0.569
## X5B_iii 0.014 0.049 0.291 0.771 0.154 0.144
## X5B_iv 0.005 0.018 0.278 0.781 0.053 0.053
## X5B_v 0.039 0.127 0.304 0.761 0.422 0.398
## X5B_vi 0.007 0.024 0.294 0.769 0.077 0.078
## X5B_vii 0.045 0.153 0.294 0.769 0.491 0.555
## X5C_i 0.034 0.111 0.309 0.757 0.374 0.370
## X5C_ii 0.059 0.193 0.307 0.759 0.642 0.763
## X5C_iii 0.056 0.179 0.311 0.756 0.604 0.641
## X5C_iv 0.055 0.179 0.305 0.761 0.594 0.653
## X5D_i 0.075 0.251 0.298 0.766 0.815 0.854
## X5D_ii 0.014 0.046 0.300 0.764 0.149 0.151
## X5D_iii 0.078 0.263 0.298 0.766 0.851 0.877
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .X1A 0.521 0.103 5.050 0.000 0.521 0.605
## .X1B 0.306 0.107 2.861 0.004 0.306 0.278
## .X1C 0.505 0.084 5.976 0.000 0.505 0.813
## .X1D_i 0.805 0.119 6.796 0.000 0.805 0.760
## .X1D_ii 0.782 0.097 8.100 0.000 0.782 0.790
## .X1E 0.732 0.120 6.079 0.000 0.732 0.880
## .X2A_scaled 0.173 0.028 6.120 0.000 0.173 0.173
## .X2B_scaled 0.060 0.017 3.616 0.000 0.060 0.065
## .X2C_scaled 0.135 0.028 4.814 0.000 0.135 0.168
## .X2D_scaled 0.447 0.061 7.284 0.000 0.447 0.509
## .X2E_scaled 0.201 0.030 6.583 0.000 0.201 0.250
## .X2F_scaled 0.284 0.046 6.144 0.000 0.284 0.315
## .X2G_scaled 0.724 0.120 6.041 0.000 0.724 0.953
## .X2H_scaled 0.316 0.061 5.197 0.000 0.316 0.369
## .X3A 0.508 0.170 2.995 0.003 0.508 0.600
## .X3B 0.332 0.098 3.378 0.001 0.332 0.506
## .X3C 0.271 0.101 2.698 0.007 0.271 0.312
## .X3D 0.755 0.124 6.082 0.000 0.755 0.933
## .X4A_i 0.486 0.123 3.943 0.000 0.486 0.646
## .X4A_ii 0.403 0.074 5.409 0.000 0.403 0.483
## .X4A_iii 0.989 0.198 4.991 0.000 0.989 0.938
## .X4B_i 0.181 0.028 6.408 0.000 0.181 0.238
## .X4B_ii 0.398 0.062 6.387 0.000 0.398 0.464
## .X4C 0.734 0.177 4.150 0.000 0.734 0.755
## .X4D_i 0.180 0.042 4.324 0.000 0.180 0.189
## .X4D_ii 0.567 0.099 5.726 0.000 0.567 0.616
## .X4D_iii 0.666 0.108 6.155 0.000 0.666 0.898
## .X4D_iv 0.152 0.035 4.275 0.000 0.152 0.184
## .X5A_i 0.780 0.104 7.469 0.000 0.780 0.858
## .X5A_ii 0.611 0.127 4.799 0.000 0.611 0.911
## .X5A_iii 0.852 0.181 4.699 0.000 0.852 0.981
## .X5B_i 0.683 0.091 7.542 0.000 0.683 0.776
## .X5B_ii 0.733 0.089 8.219 0.000 0.733 0.676
## .X5B_iii 1.112 0.223 4.992 0.000 1.112 0.979
## .X5B_iv 0.985 0.120 8.209 0.000 0.985 0.997
## .X5B_v 0.945 0.111 8.474 0.000 0.945 0.842
## .X5B_vi 0.973 0.069 14.089 0.000 0.973 0.994
## .X5B_vii 0.540 0.080 6.721 0.000 0.540 0.692
## .X5C_i 0.883 0.125 7.072 0.000 0.883 0.863
## .X5C_ii 0.297 0.054 5.510 0.000 0.297 0.418
## .X5C_iii 0.523 0.094 5.543 0.000 0.523 0.589
## .X5C_iv 0.475 0.078 6.109 0.000 0.475 0.574
## .X5D_i 0.246 0.044 5.572 0.000 0.246 0.270
## .X5D_ii 0.954 0.143 6.686 0.000 0.954 0.977
## .X5D_iii 0.216 0.049 4.426 0.000 0.216 0.230
## Economic_Fredm 1.000 1.000 1.000
## .Area1 1.000 0.567 0.567
## .Area2 1.000 0.308 0.308
## .Area3 1.000 0.716 0.716
## .Area4 1.000 0.085 0.085
## .Area5 1.000 0.008 0.008summary(fit_4, fit.measures = TRUE, standardized = TRUE)## lavaan 0.6-19 ended normally after 86 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 94
##
## Used Total
## Number of observations 108 165
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 2608.019 2592.893
## Degrees of freedom 941 941
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.006
## Yuan-Bentler correction (Mplus variant)
##
## Model Test Baseline Model:
##
## Test statistic 4845.188 4758.297
## Degrees of freedom 990 990
## P-value 0.000 0.000
## Scaling correction factor 1.018
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.568 0.562
## Tucker-Lewis Index (TLI) 0.545 0.539
##
## Robust Comparative Fit Index (CFI) 0.567
## Robust Tucker-Lewis Index (TLI) 0.544
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -5463.558 -5463.558
## Scaling correction factor 1.322
## for the MLR correction
## Loglikelihood unrestricted model (H1) -4159.549 -4159.549
## Scaling correction factor 1.035
## for the MLR correction
##
## Akaike (AIC) 11115.117 11115.117
## Bayesian (BIC) 11367.237 11367.237
## Sample-size adjusted Bayesian (SABIC) 11070.225 11070.225
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.128 0.127
## 90 Percent confidence interval - lower 0.122 0.122
## 90 Percent confidence interval - upper 0.134 0.133
## P-value H_0: RMSEA <= 0.050 0.000 0.000
## P-value H_0: RMSEA >= 0.080 1.000 1.000
##
## Robust RMSEA 0.128
## 90 Percent confidence interval - lower 0.122
## 90 Percent confidence interval - upper 0.134
## P-value H_0: Robust RMSEA <= 0.050 0.000
## P-value H_0: Robust RMSEA >= 0.080 1.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.128 0.128
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Economic_Freedom =~
## Area1 -1.096 0.301 -3.645 0.000 -0.739 -0.739
## Area2 2.263 0.726 3.118 0.002 0.915 0.915
## Area3 0.584 0.163 3.582 0.000 0.505 0.505
## Area45 1.886 0.510 3.697 0.000 0.883 0.883
## Area1 =~
## X1A 0.415 0.058 7.105 0.000 0.616 0.664
## X1B 0.586 0.115 5.096 0.000 0.870 0.830
## X1C -0.230 0.057 -4.030 0.000 -0.341 -0.432
## X1D_i 0.345 0.109 3.178 0.001 0.512 0.498
## X1D_ii 0.294 0.114 2.567 0.010 0.436 0.438
## X1E -0.200 0.064 -3.103 0.002 -0.297 -0.326
## Area2 =~
## X2A_scaled 0.367 0.098 3.743 0.000 0.909 0.909
## X2B_scaled 0.375 0.097 3.866 0.000 0.928 0.966
## X2C_scaled 0.330 0.088 3.733 0.000 0.817 0.912
## X2D_scaled 0.267 0.071 3.756 0.000 0.661 0.705
## X2E_scaled 0.314 0.083 3.780 0.000 0.778 0.869
## X2F_scaled 0.317 0.081 3.907 0.000 0.785 0.827
## X2G_scaled 0.076 0.042 1.807 0.071 0.188 0.215
## X2H_scaled 0.297 0.081 3.656 0.000 0.735 0.795
## Area3 =~
## X3A 0.502 0.170 2.945 0.003 0.581 0.631
## X3B 0.478 0.111 4.305 0.000 0.554 0.683
## X3C 0.689 0.094 7.327 0.000 0.798 0.856
## X3D 0.190 0.079 2.389 0.017 0.220 0.244
## Area45 =~
## X4A_i 0.234 0.071 3.273 0.001 0.499 0.575
## X4A_ii 0.297 0.070 4.214 0.000 0.633 0.693
## X4A_iii 0.114 0.052 2.183 0.029 0.243 0.237
## X4B_i 0.353 0.079 4.485 0.000 0.753 0.863
## X4B_ii 0.313 0.067 4.655 0.000 0.667 0.721
## X4C 0.226 0.069 3.271 0.001 0.483 0.489
## X4D_i 0.403 0.086 4.692 0.000 0.859 0.882
## X4D_ii 0.269 0.065 4.154 0.000 0.575 0.599
## X4D_iii 0.119 0.053 2.242 0.025 0.254 0.295
## X4D_iv 0.390 0.089 4.373 0.000 0.833 0.917
## X5A_i 0.176 0.060 2.916 0.004 0.375 0.393
## X5A_ii 0.113 0.049 2.302 0.021 0.241 0.294
## X5A_iii 0.064 0.053 1.209 0.227 0.137 0.146
## X5B_i 0.199 0.060 3.339 0.001 0.425 0.453
## X5B_ii 0.269 0.071 3.759 0.000 0.573 0.551
## X5B_iii 0.078 0.055 1.420 0.156 0.166 0.155
## X5B_iv 0.012 0.043 0.280 0.779 0.026 0.026
## X5B_v 0.189 0.057 3.348 0.001 0.404 0.382
## X5B_vi 0.047 0.047 0.985 0.325 0.099 0.100
## X5B_vii 0.237 0.067 3.536 0.000 0.505 0.572
## X5C_i 0.163 0.053 3.071 0.002 0.348 0.344
## X5C_ii 0.300 0.067 4.508 0.000 0.641 0.761
## X5C_iii 0.274 0.055 4.950 0.000 0.585 0.620
## X5C_iv 0.277 0.072 3.844 0.000 0.591 0.650
## X5D_i 0.372 0.087 4.283 0.000 0.795 0.833
## X5D_ii 0.058 0.047 1.231 0.218 0.124 0.125
## X5D_iii 0.398 0.093 4.289 0.000 0.849 0.875
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .X1A 0.481 0.106 4.557 0.000 0.481 0.559
## .X1B 0.341 0.100 3.418 0.001 0.341 0.311
## .X1C 0.504 0.085 5.937 0.000 0.504 0.813
## .X1D_i 0.797 0.118 6.768 0.000 0.797 0.752
## .X1D_ii 0.800 0.099 8.107 0.000 0.800 0.808
## .X1E 0.743 0.122 6.097 0.000 0.743 0.894
## .X2A_scaled 0.174 0.028 6.194 0.000 0.174 0.174
## .X2B_scaled 0.062 0.016 3.754 0.000 0.062 0.067
## .X2C_scaled 0.135 0.028 4.812 0.000 0.135 0.168
## .X2D_scaled 0.441 0.062 7.112 0.000 0.441 0.502
## .X2E_scaled 0.197 0.030 6.483 0.000 0.197 0.246
## .X2F_scaled 0.285 0.046 6.188 0.000 0.285 0.316
## .X2G_scaled 0.724 0.120 6.037 0.000 0.724 0.954
## .X2H_scaled 0.316 0.061 5.217 0.000 0.316 0.369
## .X3A 0.510 0.170 3.002 0.003 0.510 0.602
## .X3B 0.351 0.105 3.339 0.001 0.351 0.533
## .X3C 0.233 0.112 2.077 0.038 0.233 0.268
## .X3D 0.760 0.124 6.138 0.000 0.760 0.940
## .X4A_i 0.503 0.121 4.148 0.000 0.503 0.669
## .X4A_ii 0.434 0.073 5.921 0.000 0.434 0.520
## .X4A_iii 0.995 0.197 5.038 0.000 0.995 0.944
## .X4B_i 0.194 0.028 6.881 0.000 0.194 0.255
## .X4B_ii 0.412 0.063 6.593 0.000 0.412 0.481
## .X4C 0.740 0.179 4.128 0.000 0.740 0.761
## .X4D_i 0.212 0.040 5.272 0.000 0.212 0.223
## .X4D_ii 0.590 0.100 5.881 0.000 0.590 0.641
## .X4D_iii 0.677 0.111 6.122 0.000 0.677 0.913
## .X4D_iv 0.130 0.028 4.717 0.000 0.130 0.158
## .X5A_i 0.769 0.100 7.665 0.000 0.769 0.845
## .X5A_ii 0.612 0.129 4.744 0.000 0.612 0.913
## .X5A_iii 0.850 0.180 4.722 0.000 0.850 0.979
## .X5B_i 0.700 0.089 7.867 0.000 0.700 0.795
## .X5B_ii 0.756 0.086 8.803 0.000 0.756 0.697
## .X5B_iii 1.109 0.222 4.986 0.000 1.109 0.976
## .X5B_iv 0.987 0.121 8.154 0.000 0.987 0.999
## .X5B_v 0.959 0.108 8.877 0.000 0.959 0.854
## .X5B_vi 0.969 0.070 13.773 0.000 0.969 0.990
## .X5B_vii 0.526 0.076 6.955 0.000 0.526 0.673
## .X5C_i 0.902 0.127 7.104 0.000 0.902 0.882
## .X5C_ii 0.298 0.050 5.907 0.000 0.298 0.420
## .X5C_iii 0.546 0.085 6.461 0.000 0.546 0.615
## .X5C_iv 0.479 0.076 6.283 0.000 0.479 0.578
## .X5D_i 0.278 0.036 7.802 0.000 0.278 0.306
## .X5D_ii 0.961 0.143 6.730 0.000 0.961 0.984
## .X5D_iii 0.220 0.037 5.964 0.000 0.220 0.234
## Economic_Fredm 1.000 1.000 1.000
## .Area1 1.000 0.454 0.454
## .Area2 1.000 0.163 0.163
## .Area3 1.000 0.745 0.745
## .Area45 1.000 0.220 0.220summary(fit_6, fit.measures = TRUE, standardized = TRUE)## lavaan 0.6-19 ended normally after 107 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 96
##
## Used Total
## Number of observations 108 165
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 2656.602 2655.209
## Degrees of freedom 939 939
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.001
## Yuan-Bentler correction (Mplus variant)
##
## Model Test Baseline Model:
##
## Test statistic 4845.188 4758.297
## Degrees of freedom 990 990
## P-value 0.000 0.000
## Scaling correction factor 1.018
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.554 0.545
## Tucker-Lewis Index (TLI) 0.530 0.520
##
## Robust Comparative Fit Index (CFI) 0.552
## Robust Tucker-Lewis Index (TLI) 0.528
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -5487.850 -5487.850
## Scaling correction factor 1.367
## for the MLR correction
## Loglikelihood unrestricted model (H1) -4159.549 -4159.549
## Scaling correction factor 1.035
## for the MLR correction
##
## Akaike (AIC) 11167.699 11167.699
## Bayesian (BIC) 11425.184 11425.184
## Sample-size adjusted Bayesian (SABIC) 11121.852 11121.852
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.130 0.130
## 90 Percent confidence interval - lower 0.124 0.124
## 90 Percent confidence interval - upper 0.136 0.136
## P-value H_0: RMSEA <= 0.050 0.000 0.000
## P-value H_0: RMSEA >= 0.080 1.000 1.000
##
## Robust RMSEA 0.130
## 90 Percent confidence interval - lower 0.124
## 90 Percent confidence interval - upper 0.136
## P-value H_0: Robust RMSEA <= 0.050 0.000
## P-value H_0: Robust RMSEA >= 0.080 1.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.131 0.131
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Economic_Freedom =~
## Area1 -1.028 0.260 -3.952 0.000 -0.717 -0.717
## Area2a 3.967 2.413 1.644 0.100 0.970 0.970
## Area2b 3.072 1.346 2.282 0.022 0.951 0.951
## Area3 0.549 0.138 3.969 0.000 0.481 0.481
## Area4 1.504 0.403 3.726 0.000 0.833 0.833
## Area5 2.130 0.860 2.476 0.013 0.905 0.905
## Area1 =~
## X1A 0.437 0.053 8.224 0.000 0.627 0.676
## X1B 0.604 0.109 5.544 0.000 0.867 0.827
## X1C -0.233 0.056 -4.126 0.000 -0.334 -0.424
## X1D_i 0.361 0.108 3.343 0.001 0.517 0.502
## X1D_ii 0.303 0.114 2.664 0.008 0.435 0.437
## X1E -0.194 0.064 -3.040 0.002 -0.278 -0.305
## Area2a =~
## X2A_scaled 0.221 0.124 1.774 0.076 0.903 0.903
## X2B_scaled 0.228 0.129 1.766 0.077 0.933 0.971
## X2C_scaled 0.201 0.112 1.788 0.074 0.822 0.917
## X2D_scaled 0.159 0.087 1.821 0.069 0.650 0.694
## Area2b =~
## X2E_scaled 0.236 0.082 2.879 0.004 0.763 0.852
## X2F_scaled 0.256 0.106 2.415 0.016 0.829 0.873
## X2G_scaled 0.076 0.049 1.567 0.117 0.247 0.283
## X2H_scaled 0.240 0.096 2.498 0.012 0.777 0.839
## Area3 =~
## X3A 0.512 0.173 2.952 0.003 0.584 0.634
## X3B 0.479 0.113 4.224 0.000 0.546 0.673
## X3C 0.707 0.090 7.868 0.000 0.806 0.864
## X3D 0.189 0.080 2.368 0.018 0.215 0.239
## Area4 =~
## X4A_i 0.287 0.071 4.054 0.000 0.519 0.599
## X4A_ii 0.374 0.082 4.578 0.000 0.675 0.739
## X4A_iii 0.141 0.061 2.302 0.021 0.255 0.248
## X4B_i 0.418 0.079 5.279 0.000 0.755 0.866
## X4B_ii 0.377 0.078 4.851 0.000 0.681 0.736
## X4C 0.267 0.084 3.164 0.002 0.482 0.489
## X4D_i 0.497 0.095 5.243 0.000 0.898 0.921
## X4D_ii 0.344 0.074 4.651 0.000 0.622 0.648
## X4D_iii 0.165 0.062 2.656 0.008 0.298 0.346
## X4D_iv 0.438 0.079 5.561 0.000 0.791 0.871
## Area5 =~
## X5A_i 0.141 0.064 2.184 0.029 0.331 0.347
## X5A_ii 0.099 0.050 1.998 0.046 0.233 0.284
## X5A_iii 0.044 0.050 0.865 0.387 0.103 0.110
## X5B_i 0.205 0.079 2.587 0.010 0.483 0.514
## X5B_ii 0.261 0.102 2.567 0.010 0.615 0.591
## X5B_iii 0.064 0.055 1.174 0.240 0.152 0.142
## X5B_iv 0.040 0.042 0.941 0.347 0.094 0.094
## X5B_v 0.188 0.075 2.495 0.013 0.442 0.417
## X5B_vi 0.017 0.044 0.376 0.707 0.039 0.039
## X5B_vii 0.195 0.091 2.129 0.033 0.458 0.518
## X5C_i 0.189 0.062 3.058 0.002 0.444 0.439
## X5C_ii 0.269 0.085 3.184 0.001 0.634 0.753
## X5C_iii 0.258 0.075 3.444 0.001 0.608 0.645
## X5C_iv 0.261 0.082 3.191 0.001 0.615 0.675
## X5D_i 0.346 0.134 2.581 0.010 0.814 0.853
## X5D_ii 0.086 0.047 1.843 0.065 0.202 0.205
## X5D_iii 0.349 0.136 2.560 0.010 0.820 0.846
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .X1A 0.467 0.102 4.602 0.000 0.467 0.543
## .X1B 0.347 0.102 3.400 0.001 0.347 0.316
## .X1C 0.509 0.086 5.895 0.000 0.509 0.820
## .X1D_i 0.792 0.117 6.784 0.000 0.792 0.748
## .X1D_ii 0.800 0.100 8.021 0.000 0.800 0.809
## .X1E 0.754 0.122 6.159 0.000 0.754 0.907
## .X2A_scaled 0.184 0.030 6.083 0.000 0.184 0.184
## .X2B_scaled 0.052 0.021 2.443 0.015 0.052 0.057
## .X2C_scaled 0.128 0.032 4.042 0.000 0.128 0.159
## .X2D_scaled 0.456 0.064 7.093 0.000 0.456 0.519
## .X2E_scaled 0.220 0.055 3.997 0.000 0.220 0.274
## .X2F_scaled 0.215 0.048 4.490 0.000 0.215 0.239
## .X2G_scaled 0.699 0.115 6.061 0.000 0.699 0.920
## .X2H_scaled 0.253 0.051 4.927 0.000 0.253 0.295
## .X3A 0.507 0.170 2.985 0.003 0.507 0.598
## .X3B 0.359 0.106 3.378 0.001 0.359 0.546
## .X3C 0.221 0.115 1.923 0.054 0.221 0.253
## .X3D 0.762 0.122 6.225 0.000 0.762 0.943
## .X4A_i 0.483 0.130 3.725 0.000 0.483 0.642
## .X4A_ii 0.378 0.067 5.639 0.000 0.378 0.453
## .X4A_iii 0.989 0.199 4.974 0.000 0.989 0.939
## .X4B_i 0.190 0.036 5.332 0.000 0.190 0.250
## .X4B_ii 0.394 0.063 6.271 0.000 0.394 0.459
## .X4C 0.740 0.181 4.085 0.000 0.740 0.761
## .X4D_i 0.143 0.038 3.817 0.000 0.143 0.151
## .X4D_ii 0.533 0.093 5.759 0.000 0.533 0.580
## .X4D_iii 0.653 0.107 6.125 0.000 0.653 0.880
## .X4D_iv 0.198 0.039 5.102 0.000 0.198 0.241
## .X5A_i 0.800 0.111 7.232 0.000 0.800 0.880
## .X5A_ii 0.616 0.129 4.792 0.000 0.616 0.919
## .X5A_iii 0.858 0.186 4.613 0.000 0.858 0.988
## .X5B_i 0.648 0.092 7.074 0.000 0.648 0.735
## .X5B_ii 0.706 0.096 7.385 0.000 0.706 0.651
## .X5B_iii 1.113 0.224 4.967 0.000 1.113 0.980
## .X5B_iv 0.979 0.118 8.316 0.000 0.979 0.991
## .X5B_v 0.927 0.117 7.932 0.000 0.927 0.826
## .X5B_vi 0.978 0.068 14.318 0.000 0.978 0.998
## .X5B_vii 0.571 0.086 6.671 0.000 0.571 0.732
## .X5C_i 0.826 0.115 7.163 0.000 0.826 0.807
## .X5C_ii 0.307 0.057 5.361 0.000 0.307 0.433
## .X5C_iii 0.519 0.096 5.387 0.000 0.519 0.584
## .X5C_iv 0.450 0.078 5.804 0.000 0.450 0.544
## .X5D_i 0.247 0.066 3.771 0.000 0.247 0.272
## .X5D_ii 0.936 0.141 6.644 0.000 0.936 0.958
## .X5D_iii 0.268 0.076 3.504 0.000 0.268 0.284
## Economic_Fredm 1.000 1.000 1.000
## .Area1 1.000 0.486 0.486
## .Area2a 1.000 0.060 0.060
## .Area2b 1.000 0.096 0.096
## .Area3 1.000 0.769 0.769
## .Area4 1.000 0.307 0.307
## .Area5 1.000 0.181 0.181# --- Compare key fit indices side by side ------------------------------------
fits <- list(Four_Areas = fit_4, Five_Areas = fit_5, Six_Areas = fit_6)
fit_table <- sapply(fits, function(f) fitMeasures(f,
c("cfi","tli","rmsea","srmr","aic","bic")))
print(round(fit_table, 3))## Four_Areas Five_Areas Six_Areas
## cfi 0.568 0.569 0.554
## tli 0.545 0.546 0.530
## rmsea 0.128 0.128 0.130
## srmr 0.128 0.127 0.131
## aic 11115.117 11111.180 11167.699
## bic 11367.237 11365.983 11425.184# --- Optional visualization --------------------------------------------------
semPaths(fit_4, "std", layout="tree",
residuals=FALSE, nCharNodes=0,
edge.label.cex=0.7, sizeMan=4, sizeLat=6,
title=TRUE)
semPaths(fit_5, "std", layout="tree",
residuals=FALSE, nCharNodes=0,
edge.label.cex=0.7, sizeMan=4, sizeLat=6,
title=TRUE)
semPaths(fit_6, "std", layout="tree",
residuals=FALSE, nCharNodes=0,
edge.label.cex=0.7, sizeMan=4, sizeLat=6,
title=TRUE)
anova(fit_5, fit_4, fit_6 )## Warning: lavaan->lavTestLRT():
## Some restricted models fit better than less restricted models; either
## these models are not nested, or the less restricted model failed to reach
## a global optimum.Smallest difference = -54.5193445436962.##
## Scaled Chi-Squared Difference Test (method = "satorra.bentler.2001")
##
## lavaan->lavTestLRT():
## lavaan NOTE: The "Chisq" column contains standard test statistics, not the
## robust test that should be reported per model. A robust difference test is
## a function of two standard (not robust) statistics.
## Df AIC BIC Chisq Chisq diff Df diff Pr(>Chisq)
## fit_6 939 11168 11425 2656.6
## fit_5 940 11111 11366 2602.1 -14.6731 1 1.0000
## fit_4 941 11115 11367 2608.0 1.8091 1 0.1786EFA
set.seed(42) # reproducibility
# --- 1) Collect indicators ---------------------------------------------------
efa_cols <- c(
"X1A","X1B","X1C","X1D_i","X1D_ii","X1E",
"X2A_scaled","X2B_scaled","X2C_scaled","X2D_scaled",
"X2E_scaled","X2F_scaled","X2G_scaled","X2H_scaled",
"X3A","X3B","X3C","X3D",
"X4A_i","X4A_ii","X4A_iii","X4B_i","X4B_ii","X4C",
"X4D_i","X4D_ii","X4D_iii","X4D_iv",
"X5A_i","X5A_ii","X5A_iii",
"X5B_i","X5B_ii","X5B_iii","X5B_iv","X5B_v","X5B_vi","X5B_vii",
"X5C_i","X5C_ii","X5C_iii","X5C_iv",
"X5D_i","X5D_ii","X5D_iii"
)
efa_vars <- df_2022_std %>%
select(any_of(efa_cols)) %>%
select(where(is.numeric))
# --- 2) Pretty labels --------------------------------------------------------
pretty_names <- function(df, vars) {
sapply(vars, function(v) {
lb <- attr(df[[v]], "label", exact=TRUE)
if (is.null(lb) || is.na(lb) || lb=="") v else lb
}, USE.NAMES=FALSE)
}
var_labels <- pretty_names(df_2022_std, colnames(efa_vars))
# --- 3) Factorability checks -------------------------------------------------
cat("KMO:\n"); print(KMO(efa_vars))## KMO:## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = efa_vars)
## Overall MSA = 0.84
## MSA for each item =
## X1A X1B X1C X1D_i X1D_ii X1E X2A_scaled
## 0.84 0.88 0.80 0.67 0.59 0.82 0.88
## X2B_scaled X2C_scaled X2D_scaled X2E_scaled X2F_scaled X2G_scaled X2H_scaled
## 0.89 0.91 0.89 0.88 0.94 0.54 0.90
## X3A X3B X3C X3D X4A_i X4A_ii X4A_iii
## 0.70 0.68 0.71 0.87 0.83 0.84 0.47
## X4B_i X4B_ii X4C X4D_i X4D_ii X4D_iii X4D_iv
## 0.92 0.91 0.80 0.92 0.77 0.83 0.93
## X5A_i X5A_ii X5A_iii X5B_i X5B_ii X5B_iii X5B_iv
## 0.70 0.78 0.59 0.68 0.72 0.76 0.38
## X5B_v X5B_vi X5B_vii X5C_i X5C_ii X5C_iii X5C_iv
## 0.56 0.42 0.88 0.82 0.93 0.91 0.94
## X5D_i X5D_ii X5D_iii
## 0.92 0.66 0.90R <- cor(efa_vars, use="pairwise.complete.obs")
cat("\nBartlett:\n")##
## Bartlett:print(cortest.bartlett(R, n=nrow(efa_vars)))## $chisq
## [1] 5631.827
##
## $p.value
## [1] 0
##
## $df
## [1] 990# --- 4) EFA (5 factors, ML, oblimin) ----------------------------------------
efa_result <- fa(efa_vars, nfactors=5, fm="ml", rotate="oblimin", use="pairwise")
print(efa_result$loadings, cutoff=.30)##
## Loadings:
## ML2 ML5 ML3 ML1 ML4
## X1A -0.562 -0.301 0.500
## X1B -0.419 0.492
## X1C
## X1D_i -0.415 0.442
## X1D_ii 0.591
## X1E 0.659
## X2A_scaled 0.904
## X2B_scaled 0.898
## X2C_scaled 0.685
## X2D_scaled 0.640
## X2E_scaled 0.890
## X2F_scaled 0.601
## X2G_scaled
## X2H_scaled 0.705
## X3A 0.309
## X3B 0.517
## X3C 0.375
## X3D 0.670
## X4A_i 0.733
## X4A_ii 0.695
## X4A_iii 0.396
## X4B_i 0.640
## X4B_ii 0.414
## X4C 0.302
## X4D_i 0.630
## X4D_ii 0.486
## X4D_iii
## X4D_iv 0.308 0.416 0.459
## X5A_i 0.337
## X5A_ii
## X5A_iii 0.320
## X5B_i 0.458
## X5B_ii 0.981
## X5B_iii 0.477
## X5B_iv
## X5B_v 0.914
## X5B_vi
## X5B_vii 0.355 0.429
## X5C_i 0.474 0.603
## X5C_ii 0.527
## X5C_iii 0.616 -0.318
## X5C_iv 0.457 0.305
## X5D_i 0.387 0.426
## X5D_ii 0.411
## X5D_iii 0.621
##
## ML2 ML5 ML3 ML1 ML4
## SS loadings 6.775 4.321 3.000 2.294 2.552
## Proportion Var 0.151 0.096 0.067 0.051 0.057
## Cumulative Var 0.151 0.247 0.313 0.364 0.421# --- 5) Clean loading table --------------------------------------------------
load_tbl <- as.data.frame(unclass(efa_result$loadings))
load_tbl <- tibble::rownames_to_column(load_tbl, "var")
colnames(load_tbl) <- c("var", paste0("F", seq_len(ncol(load_tbl)-1)))
load_tbl$label <- var_labels[match(load_tbl$var, colnames(efa_vars))]
Fcols <- paste0("F", 1:5)
load_tbl$primary <- apply(load_tbl[,Fcols], 1, function(x) paste0("F", which.max(abs(x))))
load_tbl$loading <- apply(load_tbl[,Fcols], 1, function(x) x[which.max(abs(x))])
cat("\n=== Primary loadings (|λ| ≥ .30) ===\n")##
## === Primary loadings (|λ| ≥ .30) ===print(
load_tbl %>%
filter(abs(loading) >= .30) %>%
arrange(primary, desc(abs(loading))) %>%
select(var, label, primary, loading),
digits=3, row.names=FALSE
)## var label primary loading
## X2A_scaled X2A_scaled F1 0.904
## X2B_scaled X2B_scaled F1 0.898
## X2E_scaled X2E_scaled F1 0.890
## X2H_scaled X2H_scaled F1 0.705
## X2C_scaled X2C_scaled F1 0.685
## X2D_scaled X2D_scaled F1 0.640
## X5C_iii X5C_iii F1 0.616
## X2F_scaled X2F_scaled F1 0.601
## X1A X1A F1 -0.562
## X5C_ii X5C_ii F1 0.527
## X5C_iv X5C_iv F1 0.457
## X3C X3C F1 0.375
## X4A_i X4A_i F2 0.733
## X4A_ii X4A_ii F2 0.695
## X3D X3D F2 0.670
## X4B_i X4B_i F2 0.640
## X4D_i X4D_i F2 0.630
## X4D_ii X4D_ii F2 0.486
## X4B_ii X4B_ii F2 0.414
## X4A_iii X4A_iii F2 0.396
## X1E X1E F3 0.659
## X5D_iii X5D_iii F3 0.621
## X3B X3B F3 0.517
## X4D_iv X4D_iv F3 0.459
## X5B_vii X5B_vii F3 0.429
## X5D_i X5D_i F3 0.426
## X5A_i X5A_i F3 0.337
## X5A_iii X5A_iii F3 0.320
## X4C X4C F3 0.302
## X5B_ii X5B_ii F4 0.981
## X5B_v X5B_v F4 0.914
## X5C_i X5C_i F5 0.603
## X1D_ii X1D_ii F5 0.591
## X1B X1B F5 0.492
## X5B_iii X5B_iii F5 0.477
## X5B_i X5B_i F5 0.458
## X1D_i X1D_i F5 0.442
## X5D_ii X5D_ii F5 0.411
## X3A X3A F5 0.309# --- 6) Heatmap --------------------------------------------------------------
long_load <- load_tbl %>%
select(var, label, all_of(Fcols)) %>%
pivot_longer(all_of(Fcols), names_to="Factor", values_to="Loading")
item_order <- load_tbl %>%
arrange(primary, desc(abs(loading))) %>%
pull(label)
long_load$label <- factor(long_load$label, levels=rev(unique(item_order)))
ggplot(long_load, aes(x=Factor, y=label, fill=Loading)) +
geom_tile() +
scale_fill_gradient2(limits=c(-1,1)) +
labs(x=NULL, y=NULL, title="EFA Loadings Heatmap (ML, oblimin)") +
theme_minimal(base_size=11) +
theme(panel.grid=element_blank(),
axis.text.y=element_text(size=8))
# --- 7) Factor scores --------------------------------------------------------
scores <- factor.scores(efa_vars, efa_result, method="tenBerge")$scores
head(scores)## ML2 ML5 ML3 ML1 ML4
## [1,] -0.4542841 0.6792904 0.9024044 -0.09729673 -0.04579784
## [2,] -0.3892151 -1.1134279 -1.9015050 0.24645906 0.15825061
## [3,] -1.1995054 -0.8113216 -1.2940769 -0.47999342 0.10047567
## [4,] -0.0824798 -0.8221474 -0.4936583 -1.76199196 -2.37812532
## [5,] -0.3626357 0.4010869 0.1318660 0.67520264 0.65293589
## [6,] 1.7443159 0.7466526 0.5367044 0.83908722 -0.37068569fa.diagram(efa_result, main = "EFA (5 Factors)")
Citations
citation("lavaan")## To cite lavaan in publications use:
##
## Yves Rosseel (2012). lavaan: An R Package for Structural Equation
## Modeling. Journal of Statistical Software, 48(2), 1-36.
## https://doi.org/10.18637/jss.v048.i02
##
## A BibTeX entry for LaTeX users is
##
## @Article{,
## title = {{lavaan}: An {R} Package for Structural Equation Modeling},
## author = {Yves Rosseel},
## journal = {Journal of Statistical Software},
## year = {2012},
## volume = {48},
## number = {2},
## pages = {1--36},
## doi = {10.18637/jss.v048.i02},
## }