loading in packages

# 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.

loading dataset

germany_data <- read_fst("germany_data.fst")

renaming dataset to df

df <- germany_data

Survey weight

df$weight <- df$dweight * df$pweight
survey_design <- svydesign(ids = ~1, data = df, weights = ~weight)

MLR

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
    )
  )

Modelling

model3 <- lm(auth ~ polID + religious, data = df, weights = weight)
model4 <- lm(auth ~ polID + religious + polID*religious, data = df, weights = weight)
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 of the coefficients for the MLR without the interaction (i.e., the first displayed model), and interpretation for the model fit metrics for both models.

polIDModerate 4.6 - For every one-unit increase in the “polIDModerate” variable, we expect the dependent variable to increase by approximately 4.6 units, holding all other predictors constant. This coefficient is statistically significant (p < 0.001), indicating that there is a strong relationship between the “polIDModerate” variable and the dependent variable.

polIDRight 7.7 - For every one-unit increase in the “polIDRight” variable, we expect the dependent variable to increase by approximately 7.7 units, holding all other predictors constant. This coefficient is also statistically significant (p < 0.001), suggesting a significant relationship between the “polIDRight” variable and the dependent variable.

religious 0.9 - For every one-unit increase in the “religious” variable, we expect the dependent variable to increase by approximately 0.9 units, assuming all other predictors remain constant. Like the other coefficients, this one is statistically significant (p < 0.001), indicating a meaningful association between the “religious” variable and the dependent variable.

All three coefficients have ***, indicating a p < 0.001. Meaning: There is less than a 0.1% probability that the observed result is due to chance and we incorrectly reject the null, under frequentist assumptions.

R Square 0.048 model 3 - The R-squared value for Model 1 is 0.048, meaning that approximately 4.8% of the variance in the dependent variable is explained by the independent variables included in the model.

R Square 0.050 mode 4 - The R-squared value for Model 2 is 0.050, indicating that approximately 5% of the variance in the dependent variable is explained by the independent variables in this model.

Comparing the two models, Model 4 has a slightly higher R-squared value, suggesting that it provides a slightly better fit to the data compared to Model 3. However, it’s important to note that both R-squared values are relatively low, indicating that the independent variables included in the models may not fully explain the variability in the dependent variable

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.

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

base on the visual there is no parallel trend

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 dataset

netherlands_data <- read_fst("netherlands_data.fst")

renaming dataset to df

df <- netherlands_data

Survey weight

df$weight <- df$dweight * df$pweight
survey_design <- svydesign(ids = ~1, data = df, weights = ~weight)

MLR

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(religion = case_when(
    rlgblg == 2 ~ "No",
    rlgblg == 1 ~ "Yes",
    rlgblg %in% c(7, 8, 9) ~ NA_character_,
    TRUE ~ as.character(rlgblg)
  ))

# check
table(df$religion)
## 
##    No   Yes 
## 10913  6750
df <- df %>%
  mutate(ID = case_when(
    lrscale >= 0 & lrscale <= 4 ~ "Left",
    lrscale >= 6 & lrscale <= 10 ~ "Right",
    lrscale > 10 ~ NA_character_,  # Set values above 10 as NA
    TRUE ~ NA_character_  # Ensure value 5 and any other unexpected values are set as NA
  ))
table(df$ID)
## 
##  Left Right 
##  5449  7010
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

Modelling

model5 <- lm(auth ~ religion + ID + gen, data = df, weights = weight)
model6 <- lm(auth ~ religion + ID + gen + religion*gen, data = df, weights = weight)
modelsummary(
  list(model5, model6),
  fmt = 1,
  estimate  = c( "{estimate} ({std.error}){stars}",
                "{estimate} ({std.error}){stars}"),
  statistic = NULL,
  coef_omit = "Intercept")
 (1)   (2)
religionYes 7.2 (0.3)*** 5.7 (0.7)***
IDRight 4.2 (0.3)*** 4.3 (0.3)***
genBaby Boomers −5.2 (0.4)*** −5.9 (0.6)***
genGen X −7.7 (0.4)*** −8.8 (0.6)***
genMillennials −8.4 (0.5)*** −9.7 (0.6)***
religionYes × genBaby Boomers 1.1 (0.8)
religionYes × genGen X 2.3 (0.9)**
religionYes × genMillennials 2.9 (1.0)**
Num.Obs. 12116 12116
R2 0.124 0.125
R2 Adj. 0.124 0.125
AIC 101219.3 101213.5
BIC 101271.2 101287.5
Log.Lik. −50602.672 −50596.757
RMSE 15.27 15.26

Interpretation of the coefficients for the MLR without the interaction (i.e., the first displayed model), and interpretation for the model fit metrics for both models.

religionYes 7.2 - is associated with an increase of 7.2 units in the dependent variable compared to not being part of the religion group.

IDRight 4.2 - Holding all other variables constant, a one-unit increase in IDRight is associated with a 4.2 unit increase in the dependent variable.

genBaby Boomers 5.2 - associated with a decrease of 5.2 units in the dependent variable compared to not being classified as a Baby Boomer.

genGen X 7.7 - associated with a decrease of 7.7 units in the dependent variable compared to not being classified as Gen X.

genMillennials 8.4 - associated with a decrease of 8.4 units in the dependent variable compared to not being classified as a Millennial.

R-squared model5 0.124 - this means that approximately 12.4% of the variance in the dependent variable is explained by the independent variables in the model without interaction terms. In other words, the model without interactions accounts for 12.4% of the variability observed in the dependent variable.

R-squared model6 0.125 - this indicates that approximately 12.5% of the variance in the dependent variable is explained by the independent variables in the model with interaction terms. Comparing this with the R-squared value of the model without interactions, the addition of interaction terms has slightly improved the model’s explanatory power by 0.1%. However, the improvement is marginal.

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_      
    )
  )
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
model7 <- lm(auth ~ + cohort + polID + cohort*polID, data = df, weights = weight)
interact_plot(model7, pred = cohort, modx = polID, jnplot = TRUE)

## Interpretation base on the visual there is no parallel trend

Task 5

Produce the model8 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(
   religious = case_when(
      rlgdgr %in% c(77, 88, 99) ~ NA_real_,
      TRUE ~ rlgdgr
    )
  )
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 base on the visual there is a parallel trend

End