Nasrawi_Simona_Homework_5
2024-03-19
# 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)
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## [31] "methods" "base"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_datadf <- 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 ))
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,
title = 'Table 1. Regression models for authoritarian attitudes')| (1) | (2) | |
|---|---|---|
| (Intercept) | 57.5 (0.7)*** | 59.6 (0.9)*** |
| polIDModerate | 5.3 (0.7)*** | 2.6 (1.1)* |
| polIDRight | 9.3 (1.1)*** | 3.4 (1.9)+ |
| religious | 0.3 (0.1)** | −0.3 (0.2)+ |
| polIDModerate × religious | 0.8 (0.2)** | |
| polIDRight × religious | 1.5 (0.4)*** | |
| Num.Obs. | 2855 | 2855 |
| R2 | 0.035 | 0.041 |
| R2 Adj. | 0.034 | 0.039 |
| AIC | 24680.0 | 24665.5 |
| BIC | 24709.7 | 24707.2 |
| Log.Lik. | −12334.978 | −12325.764 |
| RMSE | 17.13 | 17.13 |
Interpretation of coefficients for the MLR without the interaction:
polIDModerate (5.3): This coefficient suggests that, comparing individuals with the same religiousness, the average outcome for individuals identifying as politically moderate are 5.3 units higher compared to the reference category (i.e., identifying ideologically as on the ‘left’).
polIDRight (9.3): This coefficient indicates that, comparing individuals with the same religiousness, individuals identifying as politically right are expected to be, on average, 9.3 units higher than the reference category (i.e., identifying ideologically as on the ‘left’) on the authoritarian values scale.
religious (0.3): For the ‘religious’ predictor, a coefficient of 0.3 means that with every one-unit increase in religiousness, there is an associated expected average increase of 0.3 units on the authoritarian values scale, assuming that we are comparing people with the same ideological categorization (i.e., holding ideological self-placement constant).
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.
-The R-squared and adjusted R-squared are higher for the second model – put differently, the first model does not explain much variance in the outcome. In addition, the AIC and BIC are higher for the first model, highlighting that the increase in variance explained is not justified (there is greater complexity or potential underlying issues that the AIC and BIC do not like, comparatively). In sum: it suggests issues with the first model.
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 59.61010 58.93398 57.91980 56.90562 56.22950
## Moderate 62.21299 63.14317 64.53843 65.93370 66.86388
## Right 63.00456 65.26702 68.66072 72.05442 74.31689polID Left: The line for the “Left” category shows a moderate negative slope. As religiousness increases, authoritarian attitudes slightly decrease.
polID Moderate: The “Moderate” category has a moderate positive slope. As religiousness increases, authoritarian attitudes also increase.
polID Right: In the “Right” category the slope is significantly steeper. As religiousness increases, authoritarian attitudes also increase. This distinct incline suggests a non-parallel trend compared to the other two groups. This indicates that the relationship between religiousness and authoritarian attitudes differs for individuals identifying as Right, Left, or Moderate.
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")nd <- netherlands_datand <- nd %>%
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 ))
nd$auth <- scales::rescale(nd$behave +
nd$secure +
nd$safety +
nd$tradition +
nd$rules, to=c(0,100), na.rm=TRUE)
nd <- nd %>% filter(!is.na(auth))nd <- nd %>%
mutate(religion = case_when(
rlgblg == 2 ~ "No",
rlgblg == 1 ~ "Yes",
rlgblg %in% c(7, 8, 9) ~ NA_character_,
TRUE ~ as.character(rlgblg)
))
# check
table(nd$religion)##
## No Yes
## 10913 6750nd <- nd %>%
mutate(ID = case_when(
lrscale >= 0 & lrscale <= 4 ~ "Left",
lrscale >= 6 & lrscale <= 10 ~ "Right",
lrscale > 10 ~ NA_character_,
TRUE ~ NA_character_
))
table(nd$ID)##
## Left Right
## 5449 7010nd <- nd %>%
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).
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)## < table of extent 0 >model5 <- lm(auth ~ religion + ID + gen, data = nd, weights = weight)
model6 <- lm(auth ~ religion + ID + gen + religion*gen, data = nd, weights = weight)modelsummary(
list(model5, model6),
fmt = 1,
estimate = c( "{estimate} ({std.error}){stars}",
"{estimate} ({std.error}){stars}"),
statistic = NULL,
coef_omit = "Intercept",
title = 'Table 2. Regression models for authoritarian attitudes')| (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 of coefficients for the MLR without the interaction:
religionYes (8.2): This coefficient suggests that, comparing individuals with the same religiousness, the average outcome for individuals identifying as religious are 8.2 units higher compared to the reference category (i.e., identifying as non-religious).
IDRight (3.4): This coefficient indicates that, comparing individuals with the same religiousness, individuals identifying as politically right are expected to be, on average, 3.4 units higher than the reference category (i.e., identifying ideologically as on the ‘left’) on the authoritarian values scale.
genBaby Boomers (-5.8): For the generation variable, a coefficient of -5.8 means that individuals belonging to the Baby Boomer generation are expected to have authoritarian values that are 5.8 units lower on average compared to individuals from the omitted generation category (i.e., Interwar generation).
genGen X (-7.3): For the generation variable, a coefficient of -7.3 means that individuals belonging to Generation X are expected to have authoritarian values that are 7.3 units lower on average compared to individuals from the omitted generation category (i.e., Interwar generation).
genMillennials (-8.6): For the generation variable, a coefficient of -8.6 means that individuals belonging to the Millennial generation are expected to have authoritarian values that are 8.6 units lower on average compared to individuals from the omitted generation category (i.e., Interwar generation).
All 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.
-The R-squared and adjusted R-squared are higher for the first model – put differently, the second model does not explain much variance in the outcome. In addition, the AIC and BIC are higher for the second model, highlighting that the increase in variance explained is not justified (there is greater complexity or potential underlying issues that the AIC and BIC do not like, comparatively). In sum: it suggests issues with the second model.
Task 4
Produce the model7 interaction plot from the tutorial, but again using the Netherlands data. Interpret.
nd <- nd %>%
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 = nd, weights = weight)
interact_plot(model7, pred = cohort, modx = polID, jnplot = TRUE)
In the Netherlands, there is a trend of decreasing political authority over time.
-The line representing the “Left” ideology shows a gradual decline in political authority over time. This suggests that individuals identifying with the left have become less authoritarian over the years.
-The “Moderate” category has a similar trend, with a slightly steeper decline. Individuals in this group also show a decrease in political authority over time.
-The “Right” category demonstrates a pronounced decline in political authority. Individuals identifying with the right have experienced a greater reduction in authoritarian attitudes over time.
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 = nd, weights = weight)
interact_plot(model8, pred = religious, modx = ID, jnplot = TRUE)
In the Netherlands, as the level of religiousness increases, there is an increase in authoritarian attitudes. This suggests that individuals who identify as more religious tend to exhibit stronger authoritarian tendencies.
The “Right” line starts at a higher position on the graph compared to the “Left.” This means that individuals with right-leaning political views have higher authoritarian attitudes at lower levels of religiousness.