Zhang_Jack_Homework

packages <- c("tidyverse", "infer", "fst", "modelsummary", "effects", "survey", "MASS", "aod", "interactions", "kableExtra", "flextable", "scales") # 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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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

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))) %>%
  mutate(across(c("behave", "secure", "safety", "tradition", "rules"), ~ 7 - .x ))

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
    )
  )

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

polIDModerate (4.6): This coefficient suggests that, comparing individuals with the same religiousness, the average outcome for individuals identifying as politically moderate are 4.6 units higher compared to the reference category (left).
polIDRight (7.7): This coefficient indicates that, comparing individuals with the same religiousness, individuals identifying as politically right are expected to be, on average, 7.7 units higher than the reference category (left) on the authoritarian values scale.
religious (0.9): For the ‘religious’ predictor, a coefficient of 0.9 means that with 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 ***, 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.

A higher R2, lower AIC, greater Log.Lik, and a lower RMSE indicate that the second model is a better fit.

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

Looking at the lines, they are not really parallel. This difference is most significant between polID left and polID right. This signifies interaction meaning that people who are left will be somewhat authoritarian if they are religious, whereas people who are right will be much more authoritarian if they are religious. Therefore religion plays more of an effect on authoritorian attitudes for those that are right.

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.

netherlands_data <- read_fst("netherlands_data.fst")

BD <- netherlands_data

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

BD <- BD %>%
  mutate(
    cohort = ifelse(yrbrn < 1930 | yrbrn > 2000, NA, yrbrn),
    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(BD$gen)

## 
##     Interwar Baby Boomers        Gen X  Millennials 
##         3967         6359         4684         2803

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

# check
table(BD$religion)

## 
##    No   Yes 
## 11289  7008

BD <- BD %>%
  mutate(ID = case_when(
    lrscale >= 0 & lrscale <= 4 ~ "Left",
    lrscale >= 6 & lrscale <= 10 ~ "Right",
    lrscale > 10 ~ NA_character_,  
    TRUE ~ NA_character_  
  ))
table(BD$ID)

## 
##  Left Right 
##  5605  7247

BD <- BD %>%
  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 ))

BD$auth <- scales::rescale(BD$behave + 
                      BD$secure + 
                      BD$safety + 
                      BD$tradition + 
                      BD$rules, to=c(0,100), na.rm=TRUE)


BD <- BD %>% filter(!is.na(auth))

model5 <- lm(auth ~ religion + ID + gen, data = BD, weights = weight)
model6 <- lm(auth ~ religion + ID + gen + religion*gen, data = BD, 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

religionYes (7.2): People with a religion are expected to be 7.2 points higher on the authoritarian scale compared to those who aren’t religious.
IDRight (4.2): This coefficient indicates that individuals identifying as politically right are expected to be, on average, 4.2 units higher than the reference category (left) on the authoritarian values scale.
genBaby Boomers (-5.2): This coefficient indicates that baby boomers are expected to be, on average, 5.2 units less than the reference category (interwar) on the authoritarian values scale.
genGen X (-7.7): This coefficient indicates that gen x are expected to be, on average, 7.7 units less than the reference category (interwar) on the authoritarian values scale.
genMillenials (-8.4): This coefficient indicates that millenials are expected to be, on average, 8.4 units less than the reference category (interwar) on the authoritarian values scale.

A higher R2, lower AIC, greater Log.Lik, and a lower RMSE indicate that the second model is a better fit.

Task 4

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

BD <- BD %>%
  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
    )
  )

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

The most clear interaction effect is between moderate and right identities meaning someone being right and being older increases their authoritarian values, while someone being old and moderate may have less authoritarian views. On the other hand, someone being young and right may have less authoritarian views, while someone being young and moderate may have more authoritarian views.

Task 5

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

model8 <- lm(auth ~ religious + ID + religious*ID, data = BD, weights = weight)
interact_plot(model8, pred = religious, modx = ID, jnplot = TRUE)

There is no interaction effect as both lines are generally parallel with each other.

Zhang_Jack_Homework _5

2024-03-25

Task 1

Task 2

Task 3

Task 4

Task 5

End