Homework 4
Melanie Fidel Rodriguez
2024-03-18
# List of packages
packages <- c("tidyverse", "infer", "fst", "modelsummary", "effects", "survey", "interactions") # add any you need here
# Install packages if they aren't installed already
new_packages <- packages[!(packages %in% installed.packages()[,"Package"])]
if(length(new_packages)) install.packages(new_packages)
# Load the packages
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## [26] "methods" "base"Homework 4 (5%): due by next lecture on March 19th
Instructions: Start a new R markdown for the homework and call it “Yourlastname_Firstname_Homework_4”.
Copy everything below from Task 1 to Task 5. Keep the task prompt and questions, and provide your code and answer underneath.
Remember: you need all the steps for your code to work, including loading your data – otherwise it will not knit.
To generate a new code box, click on the +C sign above. Underneath your code, provide your answer to the task question.
When you are done, click on “Knit” above, then “Knit to Html”. Wait for everything to compile. If you get an error like “Execution halted”, it means there are issues with your code you must fix. When all issues are fixed, it will prompt a new window. Then click on “Publish” in the top right, and then Rpubs (the first option) and follow the instructions to create your Rpubs account and get your Rpubs link for your document (i.e., html link as I provide for the tutorial).
Note: Make sure to provide both your markdown file and R pubs link. If you do not submit both, you will be penalized 2 pts. out of the 5 pts. total.
Task 1
Graph the histogram distribution using the populist scale (as we did in the tutorial) for the country of Sweden. What do you note?
sweden_data <- read.fst("sweden_data.fst")# Setting values greater than 10 to NA
sweden_data$trstplt <- ifelse(sweden_data$trstplt > 10, NA, sweden_data$trstplt)
sweden_data$trstprl <- ifelse(sweden_data$trstprl > 10, NA, sweden_data$trstprl)
sweden_data$trstprt <- ifelse(sweden_data$trstprt > 10, NA, sweden_data$trstprt)
# Creating and rescaling the trust variable
sweden_data$trust <- scales::rescale(sweden_data$trstplt + sweden_data$trstprl + sweden_data$trstprt, na.rm = TRUE, to = c(0, 100))
# Here's how you would "flip it" because populist is conceived by N + I as 'anti-trust'
# As Schafer explains there are some issues with that conceptualization, but N + I is also widely applied
sweden_data$populist <- scales::rescale(sweden_data$trust, na.rm = TRUE, to=c(100,0))ggplot(sweden_data, aes(x = populist)) +
geom_histogram(bins = 30, fill = "pink", color = "black") +
theme_minimal() +
labs(title = "Distribution of Populist Scale for Sweden",
x = "Populist Scale",
y = "Count")## Warning: Removed 2503 rows containing non-finite values (`stat_bin()`).
The histrogram distribution appears to be slightly right-skewed, indicating that there are more observations with lower levels of populism, with fewer observations having higher levels of populism. The mode also appears to be below 50.
Task 2
Run a linear regression with populist attitudes as the outcome, educational attainment (recoded as a binary “BA or more” and “No BA”), and using the Swedish data. Print the intercept and coefficients only and interpret. Then do a tidy model table displaying the p-value (with digits = 3) and interpret.
sweden_data <- sweden_data %>%
mutate(
educ.ba = case_when(
essround < 5 & edulvla == 5 ~ "BA or more",
essround >= 5 & edulvlb > 600 ~ "BA or more",
TRUE ~ "No BA"
),
edulvla = ifelse(edulvla %in% c(77, 88, 99), NA_integer_, edulvla),
edulvlb = ifelse(edulvlb %in% c(5555, 7777, 8888), NA_integer_, edulvlb),
educ.ba = factor(educ.ba, levels = c("No BA", "BA or more"))
)sweden_pop_model <- lm(populist ~ educ.ba, data = sweden_data)coefficients_sweden <- coef(sweden_pop_model)
print(coefficients_sweden)## (Intercept) educ.baBA or more
## 51.358680 -7.868121broom::tidy## Registered S3 methods overwritten by 'broom':
## method from
## tidy.glht jtools
## tidy.summary.glht jtools## function (x, ...)
## {
## UseMethod("tidy")
## }
## <bytecode: 0x000002c714f95510>
## <environment: namespace:generics>tidy(sweden_pop_model)## # A tibble: 2 × 5
## term estimate std.error statistic p.value
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept) 51.4 0.181 283. 0
## 2 educ.baBA or more -7.87 0.350 -22.5 2.58e-110tidy(sweden_pop_model) |>
knitr::kable(digits = 3)| term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|
| (Intercept) | 51.359 | 0.181 | 283.363 | 0 |
| educ.baBA or more | -7.868 | 0.350 | -22.494 | 0 |
summary(sweden_pop_model)##
## Call:
## lm(formula = populist ~ educ.ba, data = sweden_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -51.359 -14.692 -1.359 11.975 56.509
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 51.3587 0.1812 283.36 <2e-16 ***
## educ.baBA or more -7.8681 0.3498 -22.49 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 19.43 on 15711 degrees of freedom
## (2503 observations deleted due to missingness)
## Multiple R-squared: 0.0312, Adjusted R-squared: 0.03114
## F-statistic: 506 on 1 and 15711 DF, p-value: < 2.2e-16The intercept of 51.4 suggests that when the level of education (educ.ba) is zero, the estimated populist scale is 51.4.
A coefficient of -7.9 suggests that individuals with a “BA or more” education level have an estimated decrease of 7.9 in their populist scale compared to those with lower education levels.
The p-values are very small (less than 0.001), suggesting strong evidence against the null hypothesis. In other words, both the intercept and coefficient for “educ.baBA or more” are statistically significant.
Task 3
Now using the Italian dataset and the authoritarian values scale (as we did in the tutorial), graph the average by survey year. Interpret.
italy_data <- read.fst("italy_data.fst")
italy_data <- italy_data %>%
mutate(behave = ipbhprp,
secure = impsafe,
safety = ipstrgv,
tradition = imptrad,
rules = ipfrule) %>%
mutate(across(c("behave", "secure", "safety", "tradition", "rules"),
~ na_if(.x, 7) %>% na_if(8) %>% na_if(9))) %>%
mutate(across(c("behave", "secure", "safety", "tradition", "rules"), ~ 7 - .x ))
italy_data$auth <- scales::rescale(italy_data$behave +
italy_data$secure +
italy_data$safety +
italy_data$tradition +
italy_data$rules, to=c(0,100), na.rm=TRUE)
italy_data <- italy_data %>% filter(!is.na(auth))
table(italy_data$secure)##
## 1 2 3 4 5 6
## 54 139 626 1856 2876 2881table(italy_data$auth)##
## 0 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84
## 7 4 4 9 13 20 27 57 113 155 163 323 367 596 647 789 823 897 992 733
## 88 92 96 100
## 632 465 299 297italy_data$year <- NA
replacements <- c(2002, 2004, 2006, 2008, 2010, 2012, 2014, 2016, 2018, 2020)
for(i in 1:10){
italy_data$year[italy_data$essround == i] <- replacements[i]
}
auth_avg <- italy_data %>%
group_by(year) %>%
summarize(auth_avg = mean(auth, na.rm = TRUE))
plot_auth <- ggplot(auth_avg, aes(x = year, y = auth_avg)) +
geom_point(aes(color = auth_avg), alpha = 1.0) +
geom_line(aes(group = 1), color = "purple", linetype = "dashed") +
labs(title = "Authoritarian Scale Average by Year (Italy)",
x = "Survey Year",
y = "Authoritarian Scale Average") +
theme_minimal() +
theme(legend.position = "none") +
scale_y_continuous(limits = c(0, 100))
print(plot_auth)
The graph demonstrates that from 2012 to 2020, the authoritarian scale
has remained quite stable, with no major increase or decrease. However,
in 2016 there appears to be a slight decrease that remains steady until
2020.
Task 4
Now run a linear regression model, using the modelsummary package, with authoritarian values as the outcome, and generations as the predictor/potential explanatory variable, and using the Italian data again. Rename the coefficients using the coef_rename function. Interpret the coefficients, whether they are statistically significant, and the adjusted R-squared.
model_data <- italy_data %>%
mutate(
# Recoding age, setting 999 to NA
age = ifelse(agea == 999, NA, agea),
# Recoding cohort variable, setting years before 1930 and after 2000 to NA
cohort = ifelse(yrbrn < 1930 | yrbrn > 2000, NA, yrbrn),
# Recoding generational cohorts based on year of birth
gen = case_when(
yrbrn %in% 1900:1945 ~ "1",
yrbrn %in% 1946:1964 ~ "2",
yrbrn %in% 1965:1979 ~ "3",
yrbrn %in% 1980:1996 ~ "4",
TRUE ~ as.character(cohort) # Keeping other values as character if they do not fit the ranges
),
# Converting cohort to a factor with labels
gen = factor(gen,
levels = c("1", "2", "3", "4"),
labels = c("Interwar", "Baby Boomers", "Gen X", "Millennials"))
)
table(model_data$gen)##
## Interwar Baby Boomers Gen X Millennials
## 1026 2580 2214 1811model1 <- lm(auth ~ gen, data = model_data)models <- list(
"model 1" = lm(auth ~ gen, data = model_data))
modelsummary(models, fmt = 1,
estimate = c("{estimate} ({std.error}){stars}"),
statistic = NULL,
coef_rename = c("genBaby Boomers" = "Baby Boomers", "genGen X" = "Gen X", "genMillennials" = "Millennials"),
title = 'Table 2. Regression models for authoritarian attitudes')| model 1 | |
|---|---|
| (Intercept) | 75.3 (0.5)*** |
| Baby Boomers | −1.1 (0.6)* |
| Gen X | −2.1 (0.6)*** |
| Millennials | −3.6 (0.6)*** |
| Num.Obs. | 7631 |
| R2 | 0.006 |
| R2 Adj. | 0.006 |
| AIC | 62934.0 |
| BIC | 62968.7 |
| Log.Lik. | −31462.009 |
| RMSE | 14.94 |
Since the coefficient is negative, it implies that Baby Boomers, on average, have lower authoritarian values of the outcome variable than the interwar generation. Similarly, the coefficient of -2.1 for Gen X suggests that being part of the Gen X generation is associated with a decrease of 2.1 units in authoritarian values than the interwar generation. For Millennials, the coefficient of -3.6 suggests that being a Millennial is associated with a decrease of 3.6 units in the outcome variable compared to those in the interwar generation.
The adjusted R-squared value of 0.006 represents how the ‘gen’ variable only explains around 0.6% of the variance of Italian authoritarian value scale. However, the limited scope of the model suggests that there are factors that influence authoritarian values beyond generational differences that should be considered.
Task 5
Now visualize, using the modelplot() function from the modelsummary package, coefficient estimates and 95% confidence intervals for the following three models:
Model 1 = populist attitudes scale as the outcome; left/right as the single predictor (omitting moderates as we did in the tutorial), and using data for Greece.
Model 2 = populist attitudes scale as the outcome; gender as the single predictor, and using data for Greece.
Model 3 = populist attitudes scale as the outcome; generations as the single predictor (using the four generational category recode we did in the tutorial), and using data for Greece. Interpret.
greece_data <- read.fst("greece_data.fst")greece_data$trstplt <- ifelse(greece_data$trstplt > 10, NA, greece_data$trstplt)
greece_data$trstprl <- ifelse(greece_data$trstprl > 10, NA, greece_data$trstprl)
greece_data$trstprt <- ifelse(greece_data$trstprt > 10, NA, greece_data$trstprt)
greece_data$trust <- scales::rescale(greece_data$trstplt + greece_data$trstprl + greece_data$trstprt, na.rm = TRUE, to = c(0, 100))
greece_data$populist <- scales::rescale(greece_data$trust, na.rm = TRUE, to=c(100,0))model_data <- greece_data %>%
mutate(
# Recoding gender
gndr = case_when(
gndr == 1 ~ "Male",
gndr == 2 ~ "Female",
gndr == 9 ~ NA_character_,
TRUE ~ as.character(gndr)
),
lrscale = case_when(
lrscale %in% 0:4 ~ "Left", # This time: Values 0 to 3 in 'lrscale' are categorized as "Left"
lrscale %in% 6:10 ~ "Right", # This time: Values 6 to 10 in 'lrscale' are categorized as "Right"
lrscale %in% c(77, 88, 99) ~ NA_character_, # Values 77, 88, 99 in 'lrscale' are set as NA
TRUE ~ NA_character_ # Any other values not explicitly matched above
),
# Recoding cohort variable, setting years before 1930 and after 2000 to NA
cohort = ifelse(yrbrn < 1930 | yrbrn > 2000, NA, yrbrn),
# Recoding generational cohorts based on year of birth
gen = case_when(
yrbrn %in% 1900:1945 ~ "1",
yrbrn %in% 1946:1964 ~ "2",
yrbrn %in% 1965:1979 ~ "3",
yrbrn %in% 1980:1996 ~ "4",
TRUE ~ as.character(cohort) # Keeping other values as character if they do not fit the ranges
),
# Converting cohort to a factor with labels
gen = factor(gen,
levels = c("1", "2", "3", "4"),
labels = c("Interwar", "Baby Boomers", "Gen X", "Millennials"))
)
table(model_data$gen)##
## Interwar Baby Boomers Gen X Millennials
## 2978 3484 3498 2330model1 <- lm(populist ~ lrscale, data = model_data)
model2 <- lm(populist ~ gndr, data = model_data)
model3 <- lm(populist ~ gen, data = model_data)models <- list(
"Model 1" = lm(populist ~ lrscale, data = model_data),
"Model 2" = lm(populist ~ gndr, data = model_data),
"Model 3" = lm(populist ~ gen, data = model_data))
modelsummary(models, fmt = 1,
estimate = c("{estimate} ({std.error}){stars}",
"{estimate} ({std.error}){stars}",
"{estimate} ({std.error}){stars}"),
statistic = NULL,
coef_rename = c("lrscale" = "Right", "gndrMale" = "Male", "genBaby Boomers" = "Baby Boomers", "genGen X" = "Gen X", "genMillennials" = "Millennials"),
title = 'Table 3. Regression models for populist attitudes')| Model 1 | Model 2 | Model 3 | |
|---|---|---|---|
| (Intercept) | 72.0 (0.5)*** | 70.0 (0.3)*** | 65.8 (0.5)*** |
| lrscaleRight | −8.8 (0.6)*** | ||
| Male | −1.0 (0.5)* | ||
| Baby Boomers | 3.5 (0.7)*** | ||
| Gen X | 5.6 (0.7)*** | ||
| Millennials | 5.8 (0.7)*** | ||
| Num.Obs. | 4936 | 9823 | 9562 |
| R2 | 0.037 | 0.000 | 0.009 |
| R2 Adj. | 0.036 | 0.000 | 0.009 |
| AIC | 44723.8 | 88873.2 | 86473.9 |
| BIC | 44743.3 | 88894.8 | 86509.7 |
| Log.Lik. | −22358.894 | −44433.590 | −43231.944 |
| RMSE | 22.44 | 22.30 | 22.25 |
modelplot(models, coef_omit = 'Interc')
Regarding gender, the coefficient of -1.0 reveals that, on average, men in Greece score 1.0 points lower on the populist scale compared to women. This suggests that women tend to show stronger populist attitudes than men in Greece. Regarding generational differences, Baby Boomers coefficient of 3.5 indicates that Baby Boomers in Greece score 3.5 points higher on the populist scale than the Interwar generation. This implies that Baby Boomers generally exhibit stronger populist attitudes compared to the Interwar generation. Similarly, the Gen X coefficient of 5.6 suggests that Gen X individuals in Greece have populist scale scores 5.6 points higher than the Interwar generation. This implies that Gen X tends to express stronger populist attitudes compared to the Interwar generation. Lastly, the Millennials coefficient, the highest among the generations at 5.8, indicates that Millennials in Greece have populist scale scores 5.8 points higher than the Interwar generation. This suggests that Millennials tend to show the strongest populist attitudes among the generations studied in Greece.
The adjusted R-squared value of 0.009 that our ‘gen’ variable explains about 0.9% of why people in Greece hold certain authoritarian beliefs with just one predictor in the model. Even though this result is statistically significant, it means the model only captures a small part of what shapes authoritarian attitudes, disregarding other factors beyond just generation.