# List of packages
packages <- c("tidyverse", "infer", "fst", "modelsummary", "effects", "survey", "MASS", "aod", "interactions", "kableExtra", "flextable", "scales") # 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
lapply(packages, library, character.only = TRUE)
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##Task 1 Use data for Germany and the variable coding for model3 and model4 from the tutorial (i.e., both for the cleaning & recode, as well as the linear model formulas). Do a modelsummary table displaying both model outputs. Interpret the coefficients for the MLR without the interaction (i.e., the first displayed model), and interpret model fit metrics for both models.

germany_data <- read_fst("germany_data.fst")
df <- germany_data
# Preparing weighted data set
df$weight <- df$dweight * df$pweight
survey_design <- svydesign(ids = ~1, data = df, weights = ~weight)
df <- df %>%
  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))) %>%
  # Apply the reverse coding
  mutate(across(c("behave", "secure", "safety", "tradition", "rules"), ~ 7 - .x ))

# Now you can calculate 'schwartzauth' after the NA recoding
df$auth <- scales::rescale(df$behave + 
                      df$secure + 
                      df$safety + 
                      df$tradition + 
                      df$rules, to=c(0,100), na.rm=TRUE)


df <- df %>% filter(!is.na(auth))
# Adding some covariates of interest (left/moderate/right)
df <- df %>%
  mutate(
    polID = case_when(
      lrscale %in% 0:3 ~ "Left",                    
      lrscale %in% 7:10 ~ "Right",                     
      lrscale %in% 4:6 ~ "Moderate",                  
      lrscale %in% c(77, 88, 99) ~ NA_character_      
    ),
   religious = case_when(
      rlgdgr %in% c(77, 88, 99) ~ NA_real_,
      TRUE ~ rlgdgr
    )
  )
# Recoding the variable
df <- df %>%
  mutate(
    cohort = ifelse(yrbrn < 1930 | yrbrn > 2000, NA, yrbrn),
    # Recoding generational cohorts based on the year of birth (yrbrn).
    # The year of birth is categorized into different generational cohorts.
    # Interwar (1900-1945), Baby Boomers (1946-1964), Gen X (1965-1979), Millennials (1980-1996).
    # The 'TRUE' line is a catch-all that keeps the original year of birth for those not in these ranges.
    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(yrbrn)  
    ),
    
    gen = factor(gen,
                 levels = c("1", "2", "3", "4"),
                 labels = c("Interwar", "Baby Boomers", "Gen X", "Millennials"))
  )
table(df$gen)
## 
##     Interwar Baby Boomers        Gen X  Millennials 
##         5360         8583         5601         4652
# Inputting into the models
model3 <- lm(auth ~ polID + religious, data = df, weights = weight)
model4 <- lm(auth ~ polID + religious + polID*religious, data = df, weights = weight)
# let’s run our models 
model3 <- lm(auth ~ polID + religious, data = df, weights = weight)
model4 <- lm(auth ~ polID + religious + polID*religious, data = df, weights = weight)

# Using the modelsummary function to generate our table.
modelsummary(
  list(model3, model4),

  fmt = 1,
  estimate  = c( "{estimate} ({std.error}){stars}", 
                  "{estimate} ({std.error}){stars}"),
  statistic = NULL)
 (1)   (2)
(Intercept) 55.3 (0.3)*** 56.4 (0.3)***
polIDModerate 4.6 (0.3)*** 3.4 (0.4)***
polIDRight 7.7 (0.4)*** 4.2 (0.7)***
religious 0.9 (0.0)*** 0.6 (0.1)***
polIDModerate × religious 0.3 (0.1)***
polIDRight × religious 0.8 (0.1)***
Num.Obs. 23373 23373
R2 0.048 0.050
R2 Adj. 0.048 0.050
AIC 200594.1 200558.6
BIC 200634.4 200615.0
Log.Lik. −100292.049 −100272.298
RMSE 17.27 17.24

Interpretation:

polIDModerate (4.6): This coefficient indicates that, when comparing individuals with the same religiousness (i.e., “holding constant”), the average outcome for individuals identifying as politically moderate is 4.6 units higher than the reference category (in our case, identifying ideologically as on the ‘left’). The “baseline group” refers to the omitted category, which is understood as part of the intercept.

polIDRight (7.7): This coefficient indicates that, when individuals of the same religiousness are compared, those who identify as politically right are expected to be 7.7 units higher on the authoritarian values scale than the reference category (i.e., those who identify ideologically as on the ‘left’).

religious (0.9): A coefficient of 0.9 for the’religious’ predictor indicates that for every one-unit increase in religiousness, there is an associated expected average increase of 0.9 units on the authoritarian values scale, assuming that we are comparing people with the same ideological categorization.

All three coefficients have triple asterisks, indicating a p value less than 0.001. This means a less than 0.1% chance that the observed outcome is due to randomness in our sample. This, under the most common assumptions, provides evidence to reject the null hypothesis.

For model3 (without interaction terms):

R-squared (0.048): The model’s predictors account for 4.8% of the variation in the authoritarian values scale. In other words, this model represents a small fraction of the diversity in authoritarian values.

Adjusted R-squared (0.048): An adjusted R-squared of 0.048 indicates that, after accounting for the number of predictors, the explanatory power remains comparable to the R-squared, indicating that the model is not excessively complex for the amount of data.

For model4 (with interaction terms):

R-squared (0.050): The addition of interaction variables provides a marginal increase in explaining the variance in authoritarian values since it has a slightly greater R-squared value than model 3

Adjusted R-squared (0.050): Although R-squared has slightly increased, the adjusted R-squared is still the same as model 3, suggesting that the inclusion of interaction terms has little effect on the model’s ability to explain data when taking into account the cost of adding more predictors.

##Task 2 Now generate the model4 interaction plot that we did in the tutorial, but again using the German data instead of the French. Interpret.

# Displaying the interaction plot
interaction_plot <- effect("polID*religious", model4, na.rm=TRUE)

plot(interaction_plot,
     main="Interaction effect",
     xlab="Religiousness",
     ylab="Authoritarian attitudes scale")

interaction_plot
## 
##  polID*religious effect
##           religious
## polID             0        2        5        8       10
##   Left     56.40706 57.56775 59.30879 61.04983 62.21053
##   Moderate 59.85063 61.66176 64.37844 67.09513 68.90626
##   Right    60.60237 63.35032 67.47224 71.59416 74.34211

Interpretation: All the interaction plots show an upward trend and overall positive relationship between religiousness and authoritarian attitudes across all political ideology groups. This implies that, independent of political ideology, the score on the authoritarian attitudes scale rises with increasing religiosity.

Compared to the Left group, the Moderate and Right groups seem more pronounced. This implies that the rise in authoritarian attitudes about religiousness is more noticeable for people who identify as Right or Moderate than for people who identify as Left.

The fact that these lines’ slopes are not parallel to one another suggests that a person’s political affiliation and authoritarian score have an interaction impact.

##Task 3 Use data for the Netherlands and the variable coding for model5 and model6 from the tutorial (i.e., both for the cleaning & recode, as well as the linear model formulas). Do a modelsummary table displaying both model outputs. Interpret the coefficients for the MLR without the interaction (i.e., the first displayed model), and interpret model fit metrics for both models.

#Loading data for Netherlands
netherlands_data <- read_fst("netherlands_data.fst")
df <- netherlands_data
#Authoritarian scale created
df <- df %>%
  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))) %>%
  # Apply the reverse coding
  mutate(across(c("behave", "secure", "safety", "tradition", "rules"), ~ 7 - .x ))

# Now you can calculate 'schwartzauth' after the NA recoding
df$auth <- scales::rescale(df$behave + 
                      df$secure + 
                      df$safety + 
                      df$tradition + 
                      df$rules, to=c(0,100), na.rm=TRUE)


df <- df %>% filter(!is.na(auth))
df <- df %>%
  mutate(
    cohort = ifelse(yrbrn < 1930 | yrbrn > 2000, NA, yrbrn),
    # Recoding generational cohorts based on the year of birth (yrbrn).
    # The year of birth is categorized into different generational cohorts.
    # Interwar (1900-1945), Baby Boomers (1946-1964), Gen X (1965-1979), Millennials (1980-1996).
    # The 'TRUE' line is a catch-all that keeps the original year of birth for those not in these ranges.
    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(yrbrn)  
    ),
    # After recoding, the gen variable is converted into a factor with labels for clearer interpretation.
    # Factors are used in R to handle categorical variables.
    gen = factor(gen,
                 levels = c("1", "2", "3", "4"),
                 labels = c("Interwar", "Baby Boomers", "Gen X", "Millennials"))
  )
table(df$gen)
## 
##     Interwar Baby Boomers        Gen X  Millennials 
##         3771         6147         4548         2730
# produce a table of left and right 
df <- df %>%
  mutate(ID = case_when(
    lrscale >= 0 & lrscale <= 4 ~ "Left",
    lrscale >= 6 & lrscale <= 10 ~ "Right",
    lrscale > 10 ~ NA_character_,  # Set values above 10 as NA
    TRUE ~ NA_character_  # Ensure value 5 and any other unexpected values are set as NA
  ))

# check
table(df$ID)
## 
##  Left Right 
##  5449  7010
# produce a table of no and yes 
df <- df %>%
  mutate(religion = case_when(
    rlgblg == 2 ~ "No",
    rlgblg == 1 ~ "Yes",
    rlgblg %in% c(7, 8, 9) ~ NA_character_,
    TRUE ~ as.character(rlgblg)
  ))

# check
table(df$religion)
## 
##    No   Yes 
## 10913  6750
#Run models
model5 <- lm(auth ~ religion + ID + gen, data = df, weights = weight)
model6 <- lm(auth ~ religion + ID + gen + religion*gen, data = df, weights = weight)
## Using the modelsummary function to generate our table.
modelsummary(
  list(model5, model6),
  fmt = 1,
  estimate  = c( "{estimate} ({std.error}){stars}",
                "{estimate} ({std.error}){stars}"),
  statistic = NULL,
  coef_omit = "Intercept")
 (1)   (2)
religionYes 8.2 (0.9)*** 7.5 (2.1)***
IDRight 3.4 (0.9)*** 3.4 (0.9)***
genBaby Boomers −5.8 (1.3)*** −6.5 (1.7)***
genGen X −7.3 (1.4)*** −7.6 (1.8)***
genMillennials −8.6 (1.5)*** −8.6 (1.9)***
religionYes × genBaby Boomers 1.6 (2.6)
religionYes × genGen X 0.5 (2.8)
religionYes × genMillennials −0.6 (3.2)
Num.Obs. 1147 1147
R2 0.126 0.127
R2 Adj. 0.123 0.121
AIC 9479.3 9484.5
BIC 9514.7 9535.0
Log.Lik. −4732.669 −4732.251
RMSE 14.94 14.94

Interpretation

ReligionYes (8.2)*: According to this coefficient, the average authoritarian value of religious people is 8.2 units greater than that of non-religious people when comparing people who share the same political ideology (i.e., holding constant). The nonreligious people are the reference group here.

IDRight (3.4)*: According to this coefficient, people who identify as politically right should be, on average, 3.4 units higher on the authoritarian values scale than people who identify ideologically as on the “left,” which is the reference category, when comparing people with the same degree of religiosity.

genMillennials (-8.6)*, genGenX (-7.3), and genBabyBoomers (-5.8): According to these coefficients, Baby Boomers, Generation X, and Millennials have, on average, -5.8, -7.3, and -8.6 units lower authoritarian values than the reference category, which is the Interwar generation, while holding religiousness and political ideology constant.

All coefficients have triple asterisks, indicating a p value less than 0.001. This means a less than 0.1% chance that the observed outcome is due to randomness in our sample. This, under the most common assumptions, provides evidence to reject the null hypothesis. The model is thus a valuable predictor.

For model 5 (excluding interaction terms):

R-squared (0.126): The model’s predictors account for 12.6% of the variation in the authoritarian values scale. In other words, this model represents a small fraction of the diversity in authoritarian values.

Adjusted R-squared (0.123): An adjusted R-squared of 0.123 indicates that, after accounting for the number of predictors, the explanatory power remains comparable to the R-squared, indicating that the model is not excessively complex for the amount of data.

For model 6 (with interaction terms):

R-squared (0.127): A slightly higher R-squared value than model 5 indicates that the addition of interaction variables adds just a small increase in explaining the variance in authoritarian values.

Adjusted R-squared (0.121): Despite the minor rise in R-squared, the adjusted R-squared is lower than that of model5, demonstrating that the addition of interaction variables does not significantly improve the model’s explanatory power when accounting for the penalty for additional predictors.

##Task 4 Produce the model7 interaction plot from the tutorial, but again using the Netherlands data. Interpret.

netherlands_data <- read_fst("netherlands_data.fst")

df <- netherlands_data
df <- df %>%
  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))) %>%
  # Apply the reverse coding
  mutate(across(c("behave", "secure", "safety", "tradition", "rules"), ~ 7 - .x ))

# Now you can calculate 'schwartzauth' after the NA recoding
df$auth <- scales::rescale(df$behave + 
                      df$secure + 
                      df$safety + 
                      df$tradition + 
                      df$rules, to=c(0,100), na.rm=TRUE)


df <- df %>% filter(!is.na(auth))
df <- df %>%
  mutate(
    polID = case_when(
      lrscale %in% 0:3 ~ "Left",                    
      lrscale %in% 7:10 ~ "Right",                     
      lrscale %in% 4:6 ~ "Moderate",                  
      lrscale %in% c(77, 88, 99) ~ NA_character_      
    ),
   religious = case_when(
      rlgdgr %in% c(77, 88, 99) ~ NA_real_,
      TRUE ~ rlgdgr
    )
  )
df <- df %>%
  mutate(
    cohort = ifelse(yrbrn < 1930 | yrbrn > 2000, NA, yrbrn),
    # Recoding generational cohorts based on the year of birth (yrbrn).
    # The year of birth is categorized into different generational cohorts.
    # Interwar (1900-1945), Baby Boomers (1946-1964), Gen X (1965-1979), Millennials (1980-1996).
    # The 'TRUE' line is a catch-all that keeps the original year of birth for those not in these ranges.
    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(yrbrn)  
    ),
 
    gen = factor(gen,
                 levels = c("1", "2", "3", "4"),
                 labels = c("Interwar", "Baby Boomers", "Gen X", "Millennials"))
  )
table(df$gen)
## 
##     Interwar Baby Boomers        Gen X  Millennials 
##         3771         6147         4548         2730
model7 <- lm(auth ~ + cohort + polID + cohort*polID, data = df, weights = weight)
interact_plot(model7, pred = cohort, modx = polID, jnplot = TRUE)

Interpretation:

The slopes are not parallel suggesting that that a person’s political affiliation and authoritarian score have an interaction impact andr that the relationship between cohort and autharitarian scores differs by political ideology.

Over time, we can detect a decrease in authoritarian scale scores across all three cohorts (POlID left, POlID right, and PolID moderate). In comparison, those ideologically identifying as right have the steepest slope, with the highest fall in average authoritarian scales, followed by moderates. Those identifying as politically left experienced the greatest total decrease. The slope for the Left is relatively flatter, indicating a more stable authoritarian score across generations.

##Task 5 Produce the model8 interaction plot from the tutorial, but again using the Netherlands data. Interpret.

df <- df %>%
  mutate(ID = case_when(
    lrscale >= 0 & lrscale <= 4 ~ "Left",
    lrscale >= 6 & lrscale <= 10 ~ "Right",
    lrscale > 10 ~ NA_character_,  # Set values above 10 as NA
    TRUE ~ NA_character_  # Ensure value 5 and any other unexpected values are set as NA
  ))
table(df$ID)
## 
##  Left Right 
##  5449  7010
model8 <- lm(auth ~ religious + ID + religious*ID, data = df, weights = weight)
interact_plot(model8, pred = religious, modx = ID, jnplot = TRUE)

Interpretation: The overall trend is positive for both Left and Right groups, indicating that as religious affiliation increases, authoritarian attitudes rise in both groups to a very similar degree because the slopes are quite similar.

The slopes are not parallel suggesting that that a person’s political affiliation and authoritarian score have an interaction impact andr that the relationship between cohort and authoritarian scores differs by political ideology. However, as religiousness increases for the right, authoritarian values decrease more than the left meaning that increases in religiousness are associated with a greater increase in auth for those on the Left compared to those on the Right, but each slope displays a steady upward trend.