Final_Project

Setting up environment

packages <- c("tidyverse", "modelsummary", "forcats", "RColorBrewer", 
              "fst", "viridis", "knitr", "rmarkdown", "ggridges", "viridis", "questionr", "flextable", "effects", "infer") # add any you need here

new_packages <- packages[!(packages %in% installed.packages()[,"Package"])]
if(length(new_packages)) install.packages(new_packages)

lapply(packages, library, character.only = TRUE)

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setwd("C:/Users/Erika/Desktop/SOC_202_YAY"
)

library(fst)

ess <- read_fst("All-ESS-Data.fst")

Filtering and recoding

Variables:

Outcome -

Household’s Total Net Income (hinctnta): https://shorturl.at/sEFG0

Household’s Total Net Income (hinctnt): https://shorturl.at/chitY

Predictors -

Gender (gndr): https://shorturl.at/dnrS7

Highest Level of Education (edulvla): https://t.ly/mYdV3

Highest Level of Education (edulvlb): https://t.ly/_dZaa

Iceland_data <- ess %>%
  filter(cntry == "IS")

Variable Cleaning

Iceland_variables <- Iceland_data %>%
  filter(cntry == "IS") %>%
  mutate(
    edulvla = ifelse(edulvla %in% c(77, 88, 99), NA, edulvla),
    edulvlb = ifelse(edulvlb %in% c(7777, 8888, 9999), NA, edulvlb),
    gndr = ifelse(gndr %in% c(9), NA, gndr),
    hinctnta = ifelse(hinctnta %in% c(77, 88, 99), NA, hinctnta),
    hinctnt = ifelse(hinctnt %in% c(77, 88, 99), NA, hinctnt),
  )

Mean, Median, Mode & Standard Deviation

library(tidyverse)

Iceland_data <- ess %>%
     filter(cntry == "IS") %>%
     select(hinctnta)

Iceland_data$y <- Iceland_data$hinctnta
table(Iceland_data$y)

## 
##   1   2   3   4   5   6   7   8   9  10  77  88  99 
## 288 249 307 347 342 349 376 326 241 247 140 182   2

Iceland_data$y[Iceland_data$y %in% 77:99] <- NA
table(Iceland_data$y)

## 
##   1   2   3   4   5   6   7   8   9  10 
## 288 249 307 347 342 349 376 326 241 247

mean_y <- mean(Iceland_data$y, na.rm = TRUE)
cat("Mean of 'y' is:", mean_y, "\n")

## Mean of 'y' is: 5.461589

median_y <- median(Iceland_data$y, na.rm = TRUE)
cat("Median of 'y' is:", median_y, "\n")

## Median of 'y' is: 6

Iceland_data %>%
     summarize(
         mean_y = mean(y, na.rm = TRUE),
         median_y = median(y, na.rm = TRUE)
     ) %>%
     print()

##     mean_y median_y
## 1 5.461589        6

mode_y <- Iceland_data %>%
    filter(!is.na(y)) %>%
   count(y) %>%
     arrange(desc(n)) %>%
     slice(1) %>%
     pull(y)
cat("\nMode of Y:", mode_y, "\n")

## 
## Mode of Y: 7

sd_y <- sd(Iceland_data$y, na.rm = TRUE)
cat("Standard Deviation of 'y':", sd_y, "\n")

## Standard Deviation of 'y': 2.712026

summary(Iceland_data)

##     hinctnta           y         
##  Min.   : 1.00   Min.   : 1.000  
##  1st Qu.: 4.00   1st Qu.: 3.000  
##  Median : 6.00   Median : 6.000  
##  Mean   :12.89   Mean   : 5.462  
##  3rd Qu.: 8.00   3rd Qu.: 8.000  
##  Max.   :99.00   Max.   :10.000  
##  NA's   :579     NA's   :903

library(data.table)

## 
## Attaching package: 'data.table'

## The following objects are masked from 'package:lubridate':
## 
##     hour, isoweek, mday, minute, month, quarter, second, wday, week,
##     yday, year

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##     transpose

Iceland_data <- ess[ess$cntry == "IS", ]
Iceland_data_table <- as.data.table(Iceland_data)

Model Summary Tables

library(modelsummary)

Iceland_data_subset <- Iceland_data %>%
     filter(cntry == "IS") %>%
     mutate(
         edulvla = ifelse(edulvla %in% c(77, 88, 99), NA, edulvla),
        edulvlb = ifelse(edulvlb %in% c(7777, 8888, 9999), NA, edulvlb),
         gndr = ifelse(gndr %in% c(77, 88, 99), NA, gndr),
         hinctnta = ifelse(hinctnta %in% c(77, 88, 99), NA, hinctnta),
         hinctnt = ifelse(hinctnt %in% c(77, 88, 99), NA, hinctnt),
     ) %>%
     select(edulvla, edulvlb, gndr, hinctnta, hinctnt)

datasummary_skim(Iceland_data_subset)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
edulvla	4	87	3.3	1.3	2.0	3.0	5.0
edulvlb	15	15	431.2	264.3	0.0	321.0	5555.0
gndr	3	0	1.5	0.7	1.0	2.0	9.0
hinctnta	11	23	5.5	2.7	1.0	6.0	10.0
hinctnt	13	88	8.4	2.2	1.0	9.0	12.0

datasummary_skim(Iceland_data_subset, output = "flextable")

## Warning: The histogram argument is only supported for (a) output types "default",
##   "html", "kableExtra", or "gt"; (b) writing to file paths with extensions
##   ".html", ".jpg", or ".png"; and (c) Rmarkdown, knitr or Quarto documents
##   compiled to PDF (via kableExtra)  or HTML (via kableExtra or gt). Use
##   `histogram=FALSE` to silence this warning.

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
edulvla	4	87	3.3	1.3	2.0	3.0	5.0
edulvlb	15	15	431.2	264.3	0.0	321.0	5555.0
gndr	3	0	1.5	0.7	1.0	2.0	9.0
hinctnta	11	23	5.5	2.7	1.0	6.0	10.0
hinctnt	13	88	8.4	2.2	1.0	9.0	12.0

Iceland_variables <- Iceland_data %>%
  filter(cntry == "IS") %>%
  mutate(
    edulvla = ifelse(edulvla %in% c(77, 88, 99), NA, edulvla),
    edulvlb = ifelse(edulvlb %in% c(7777, 8888, 9999), NA, edulvlb),
    gndr = ifelse(gndr %in% c(77, 88, 99), NA, gndr),
    hinctnta = ifelse(hinctnta %in% c(77, 88, 99), NA, hinctnta),
    hinctnt = ifelse(hinctnt %in% c(77, 88, 99), NA, hinctnt),
  ) 
summary_table <- datasummary_skim(Iceland_variables %>% select(edulvla, edulvlb, hinctnta, hinctnt)
, output = "flextable", title = "Table 1. Descriptive Statistics for Main Variables")

## Warning: The histogram argument is only supported for (a) output types "default",
##   "html", "kableExtra", or "gt"; (b) writing to file paths with extensions
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##   compiled to PDF (via kableExtra)  or HTML (via kableExtra or gt). Use
##   `histogram=FALSE` to silence this warning.

summary_table

Table 1. Descriptive Statistics for Main Variables
	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
edulvla	4	87	3.3	1.3	2.0	3.0	5.0
edulvlb	15	15	431.2	264.3	0.0	321.0	5555.0
hinctnta	11	23	5.5	2.7	1.0	6.0	10.0
hinctnt	13	88	8.4	2.2	1.0	9.0	12.0

Iceland_v2 <- Iceland_variables %>%
  rename(
    'Total_Income (round 1-4)' = hinctnt,
    'Total_Income (round 5-10)' = hinctnta,
    'Education_Level (round 1-4)' = edulvla,
    'Education_Level (round 5-10)' = edulvlb,
    'Gender' = gndr,
  )

summary_table_v2 <- datasummary_skim(Iceland_v2 %>% select("Total_Income (round 1-4)", "Total_Income (round 5-10)", "Education_Level (round 1-4)",
                                                           "Education_Level (round 5-10)", "Gender"), output = "flextable", title = "Table 1. Descriptive Statistics for Main Variables")

## Warning: The histogram argument is only supported for (a) output types "default",
##   "html", "kableExtra", or "gt"; (b) writing to file paths with extensions
##   ".html", ".jpg", or ".png"; and (c) Rmarkdown, knitr or Quarto documents
##   compiled to PDF (via kableExtra)  or HTML (via kableExtra or gt). Use
##   `histogram=FALSE` to silence this warning.

summary_table_v2

Table 1. Descriptive Statistics for Main Variables
	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
Total_Income (round 1-4)	13	88	8.4	2.2	1.0	9.0	12.0
Total_Income (round 5-10)	11	23	5.5	2.7	1.0	6.0	10.0
Education_Level (round 1-4)	4	87	3.3	1.3	2.0	3.0	5.0
Education_Level (round 5-10)	15	15	431.2	264.3	0.0	321.0	5555.0
Gender	3	0	1.5	0.7	1.0	2.0	9.0

Simulation Based Null DIstribution and T-Stat

Iceland_data <- ess %>%
  filter(cntry == "IS")

Iceland_data <- Iceland_data %>%
  filter(cntry == "IS") %>%
  mutate(
    edulvla = ifelse(edulvla %in% c(77, 88, 99), NA, edulvla),
    edulvlb = ifelse(edulvlb %in% c(7777, 8888, 9999), NA, edulvlb),
    gndr = ifelse(gndr %in% c(77, 88, 99), NA, gndr),
    hinctnta = ifelse(hinctnta %in% c(77, 88, 99), NA, hinctnta),
    hinctnt = ifelse(hinctnt %in% c(77, 88, 99), NA, hinctnt),
  )

Iceland_data$edulvla[Iceland_data$edulvla == 55] <- NA  
Iceland_data$edulvlb[Iceland_data$edulvlb == 5555] <- NA  

Iceland_data$educ.ba <- ifelse(Iceland_data$essround < 5 & Iceland_data$edulvla == 5, "BA",
                      ifelse(Iceland_data$essround >= 5 & Iceland_data$edulvlb > 600, "BA", "No BA"))

Iceland_data <- Iceland_data %>% filter(!is.na(educ.ba))

Iceland_data <- Iceland_data %>%
  mutate(
    gndr = case_when(
      gndr == 1 ~ "Male",
      gndr == 2 ~ "Female",
      gndr == 9 ~ NA_character_,
      TRUE ~ as.character(gndr)),
    
    hinctnta = case_when(
      essround >= 4 & hinctnta == 77 ~ NA_real_,
      hinctnta > 10 ~ NA_real_,  # Set values above 10 to NA
      TRUE ~ hinctnta
    ),

    # Set hinctnt to NA where conditions are met, else keep original value
    hinctnt = case_when(
      essround <= 3 & hinctnt == 77 ~ NA_real_,
      hinctnt > 10 ~ NA_real_,  # Set values above 10 to NA
      TRUE ~ hinctnt
    ),

    # Create total_income by merging hinctnta and hinctnt
    total_income = case_when(
      !is.na(hinctnta) ~ hinctnta,  # Use hinctnta if it's not NA
      !is.na(hinctnt) ~ hinctnt,    # Else use hinctnt if it's not NA
      TRUE ~ NA_real_              # Set to NA if both are NA
    )
  )

table(Iceland_data$gndr)

## 
## Female   Male 
##   1982   1890

table(Iceland_data$total_income)

## 
##   1   2   3   4   5   6   7   8   9  10 
## 286 258 314 360 362 366 408 383 371 328

test_stat <- Iceland_data %>%
  specify(explanatory = educ.ba, 
          response = total_income) %>% 
  hypothesize(null = "independence") %>%
  calculate(stat = "t")

## Warning: Removed 447 rows containing missing values.

## Warning: The statistic is based on a difference or ratio; by default, for
## difference-based statistics, the explanatory variable is subtracted in the
## order "BA" - "No BA", or divided in the order "BA" / "No BA" for ratio-based
## statistics. To specify this order yourself, supply `order = c("BA", "No BA")`
## to the calculate() function.

print(test_stat$stat)

##        t 
## 14.98089

Interpretation: This large t-statistic indicates that the sample groups are significantly different, as well as, have strong evidence to reject the null hypothesis. The value 14.1 suggests that there is a big difference in Total Income between individuals who have or do not have a BA.

null_distribution <- Iceland_data %>%
  specify(explanatory = educ.ba,
          response = total_income) %>%
  hypothesize(null = "independence") %>%
  generate(reps = 1000, type = "permute") %>% 
  calculate(stat = "t")

## Warning: Removed 447 rows containing missing values.

## Warning: The statistic is based on a difference or ratio; by default, for
## difference-based statistics, the explanatory variable is subtracted in the
## order "BA" - "No BA", or divided in the order "BA" / "No BA" for ratio-based
## statistics. To specify this order yourself, supply `order = c("BA", "No BA")`
## to the calculate() function.

p_val <- null_distribution %>% # 
  get_pvalue(obs_stat = test_stat, direction = "two-sided")

## Warning: Please be cautious in reporting a p-value of 0. This result is an
## approximation based on the number of `reps` chosen in the `generate()` step.
## See `?get_p_value()` for more information.

p_val

## # A tibble: 1 × 1
##   p_value
##     <dbl>
## 1       0

With a p-value of 0, we have strong evidence to reject the null.

null_distribution %>%
  visualize() +
  shade_p_value(obs_stat = test_stat, direction = "two-sided")

null_distribution

## Response: total_income (numeric)
## Explanatory: educ.ba (factor)
## Null Hypothesis: independence
## # A tibble: 1,000 × 2
##    replicate   stat
##        <int>  <dbl>
##  1         1 -1.26 
##  2         2 -0.626
##  3         3 -0.521
##  4         4 -1.01 
##  5         5  0.649
##  6         6 -1.45 
##  7         7 -0.707
##  8         8 -0.579
##  9         9  0.896
## 10        10  2.56 
## # ℹ 990 more rows

Interpretation: Once again we can reject the null hypothesis as the test statistic (the red line) falls outside the simulated T Null Distribution.

conf_int <- null_distribution %>%
  get_confidence_interval(level = 0.95, type = "percentile")

null_distribution %>%
  visualize() +
  shade_p_value(obs_stat = test_stat, direction = "two-sided") +
  shade_confidence_interval(endpoints = conf_int)+
  labs(title = "Figure 1. Simulation-Based Null Distribution",
       x = "Stat",
       y = "Count")

Regression Models and Interaction visual

Regression and GLM Models

Iceland_data$edulvla[Iceland_data$edulvla == 55] <- NA  
Iceland_data$edulvlb[Iceland_data$edulvlb == 5555] <- NA  

Iceland_data$educ.ba <- ifelse(Iceland_data$essround < 5 & Iceland_data$edulvla == 5, "BA",
                      ifelse(Iceland_data$essround >= 5 & Iceland_data$edulvlb > 600, "BA", "No BA"))

Iceland_data <- Iceland_data %>% filter(!is.na(educ.ba))

Here we want to separate data frame since few variables have been changed, which won’t work in the t-test and GLM later. Therefore, we created a data frame and keep a original file.

Character copy

Iceland_variables$edulvla[Iceland_variables$edulvla == 55] <- NA  
Iceland_variables$edulvlb[Iceland_variables$edulvlb == 5555] <- NA  

# Recoding to 1 for "BA" and 0 for "No BA"
Iceland_variables$educ.ba <- ifelse(Iceland_variables$essround < 5 & Iceland_data$edulvla == 5, "BA",
                      ifelse(Iceland_variables$essround >= 5 & Iceland_data$edulvlb > 600, "BA", "No BA"))

## Warning in Iceland_variables$essround < 5 & Iceland_data$edulvla == 5: longer
## object length is not a multiple of shorter object length

## Warning in Iceland_variables$essround >= 5 & Iceland_data$edulvlb > 600: longer
## object length is not a multiple of shorter object length

Iceland_variables <- Iceland_data %>% filter(!is.na(educ.ba))
table(Iceland_variables$educ.ba)

## 
##    BA No BA 
##  1332  2551

Keep one as Numeric for GLM

Iceland_data$edulvla[Iceland_data$edulvla == 55] <- NA  
Iceland_data$edulvlb[Iceland_data$edulvlb == 5555] <- NA  

# Recoding to 1 for "BA" and 0 for "No BA"
Iceland_data$educ.ba <- ifelse(Iceland_data$essround < 5 & Iceland_data$edulvla == 5, 1,
                      ifelse(Iceland_data$essround >= 5 & Iceland_data$edulvlb > 600, 1, 0))


Iceland_data <- Iceland_data %>% filter(!is.na(educ.ba))
table(Iceland_data$educ.ba)

## 
##    0    1 
## 2551 1332

Here, we ensure we have two dataframes with two different categorical variables using class function.

class(Iceland_data$educ.ba)

## [1] "numeric"

class(Iceland_variables$educ.ba)

## [1] "character"

library(modelsummary)

model1 <- glm(educ.ba ~ total_income, family = binomial, data = Iceland_data)
model2 <- glm(educ.ba ~ total_income + gndr, family = binomial, data = Iceland_data)
model3 <- glm(educ.ba ~ total_income + gndr + total_income*gndr, family = binomial, data = Iceland_data)
modelsummary(
  list(model1, model2, model3))

	(1)	(2)	(3)
(Intercept)	−1.736	−1.466	−1.490
	(0.093)	(0.097)	(0.122)
total_income	0.192	0.202	0.206
	(0.014)	(0.014)	(0.019)
gndrMale		−0.693	−0.634
		(0.075)	(0.192)
total_income × gndrMale			−0.009
			(0.029)
Num.Obs.	3436	3429	3429
AIC	4274.5	4182.5	4184.4
BIC	4286.8	4201.0	4209.0
Log.Lik.	−2135.254	−2088.271	−2088.216
RMSE	0.47	0.46	0.46

modelsummary(
  list(model1, model2, model3),
  fmt = 1,
  estimate  = c( "{estimate} ({std.error}){stars}",
                "{estimate} ({std.error}){stars}",
                "{estimate} ({std.error}){stars}"),
  statistic = NULL,
    title = 'Table 2. Model Summary and Predictors Interacting')

Table 2. Model Summary and Predictors Interacting
	(1)	(2)	(3)
(Intercept)	−1.7 (0.1)***	−1.5 (0.1)***	−1.5 (0.1)***
total_income	0.2 (0.0)***	0.2 (0.0)***	0.2 (0.0)***
gndrMale		−0.7 (0.1)***	−0.6 (0.2)***
total_income × gndrMale			0.0 (0.0)
Num.Obs.	3436	3429	3429
AIC	4274.5	4182.5	4184.4
BIC	4286.8	4201.0	4209.0
Log.Lik.	−2135.254	−2088.271	−2088.216
RMSE	0.47	0.46	0.46

  coef_omit = "Intercept"

modelsummary(
  list(model1, model2, model3),
  fmt = 1,
  estimate  = c( "{estimate} ({std.error}){stars}",
                "{estimate} ({std.error}){stars}",
                "{estimate} ({std.error}){stars}"),
  statistic = NULL,
  title = 'Table 2. Model Summary and Predictors Interacting',
  coef_omit = "Intercept")

Table 2. Model Summary and Predictors Interacting
	(1)	(2)	(3)
total_income	0.2 (0.0)***	0.2 (0.0)***	0.2 (0.0)***
gndrMale		−0.7 (0.1)***	−0.6 (0.2)***
total_income × gndrMale			0.0 (0.0)
Num.Obs.	3436	3429	3429
AIC	4274.5	4182.5	4184.4
BIC	4286.8	4201.0	4209.0
Log.Lik.	−2135.254	−2088.271	−2088.216
RMSE	0.47	0.46	0.46

Interaction Plot

interaction_plot <- effect("total_income*gndr", model3, na.rm=TRUE)
plot(interaction_plot,
     main="Figure 2. Interaction Effect of Gender in related to Total Income",
     xlab="Total Income",
     ylab="Difference in Education level")