VIla_Lacey_Homework_5
Lacey Vila
2024-03-25
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# 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
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## [31] "methods" "base"# 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
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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$weight <- df$dweight * df$pweight
survey_design <- svydesign(ids = ~1, data = df, weights = ~weight)
# Setting values greater than 10 to NA
df$trstplt <- ifelse(df$trstplt > 10, NA, df$trstplt)
df$trstprl <- ifelse(df$trstprl > 10, NA, df$trstprl)
df$trstprt <- ifelse(df$trstprt > 10, NA, df$trstprt)
# Creating and rescaling the trust variable
df$trust <- scales::rescale(df$trstplt + df$trstprl + df$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
df$populist <- scales::rescale(df$trust, na.rm = TRUE, to=c(100,0))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
)
)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 |
#Model 3’s coefficient interpretation for MLR without the interaction term # The intercept (57.6): This shows that, for those # on the ‘left’ with a religiousness score of 0, the predicted authoritarian score is 57.6, with strong statistical significance. religion Yes (8.9): Compared to non-religious people, religious people have an 8.9 unit higher authoritarian score #; political identification is same. #IDRight (3.9): Keeping religiousness constant, identifying as politically right is linked to a 3.9 unit rise in the #authoritarian score relative to those on the left. # Model fit metrics interpretation: # Num.Obs.: Eleven76 observations were used to fit the model. # R2 (0.095): Relatively little, 9.5% of the variation in the authoritarian score is explained by the model. # R2 Adj. (0.093): The model accounts for 9.3% of the variance after correcting for the number of predictors. # BIC (9780.9 vs. 9788.0) and AIC (9760.7 vs. 9762.6): Model 4 has slightly higher AIC and BIC values, indicating that the interaction term does not significantly enhance the model fit. # Log.Lik. (−4876.334): Models 3 and 4 have approximately the same log-likelihood, suggesting a comparable fit. # RMSE (15.28): Both models have the same root mean square error, showing comparable prediction accuracy.
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)
# Plotting the interaction effect
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#Examining the interaction plot of model 4: # The interaction effect plot shows how political membership (Left, Moderate, Right) modifies the relationship between authoritarianism and religiosity. The slopes of the lines show that religiousness increases the authoritarian attitudes scale, with a greater association for politically conservative individuals. Specifically, the steepest slope in the ‘Right’ category indicates a stronger association between religiousness # and authoritarian viewpoints for this specific population. Conversely, those who identify as “Left” or “Moderate” had a less strong but still positive connection. # The non-parallel nature of the lines supports the possibility of an interaction effect by indicating that political affiliation alters the connection between religiousness and authoritarian ideas.
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")
dn <- netherlands_datadn$weight <- dn$dweight * dn$pweight
survey_design <- svydesign(ids = ~1, data = dn, weights = ~weight)
# Setting values greater than 10 to NA
dn$trstplt <- ifelse(dn$trstplt > 10, NA, dn$trstplt)
dn$trstprl <- ifelse(dn$trstprl > 10, NA, dn$trstprl)
dn$trstprt <- ifelse(dn$trstprt > 10, NA, dn$trstprt)
# Creating and rescaling the trust variable
dn$trust <- scales::rescale(dn$trstplt + dn$trstprl + dn$trstprt, na.rm = TRUE, to = c(0, 100))
dn$populist <- scales::rescale(dn$trust, na.rm = TRUE, to=c(100,0))dn <- dn %>%
mutate(
Capital = case_when(
ppltrst %in% c(77, 88, 99) ~ NA_character_,
ppltrst >= 0 & ppltrst <= 3 ~ "Low",
ppltrst >= 4 & ppltrst <= 6 ~ "Mid",
ppltrst >= 7 & ppltrst <= 10 ~ "High",
TRUE ~ as.character(ppltrst)
),
Politically = case_when(
polintr %in% c(1, 2) ~ "Interested",
polintr %in% c(3, 4) ~ "Not Interested",
polintr %in% c(7, 8, 9) ~ NA_character_
)
)dn <- dn %>%
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 ))
dn$auth <- scales::rescale(dn$behave +
dn$secure +
dn$safety +
dn$tradition +
dn$rules, to=c(0,100), na.rm=TRUE)
dn <- dn %>% filter(!is.na(auth))dn <- dn %>%
mutate(religion = case_when(
rlgblg == 2 ~ "No",
rlgblg == 1 ~ "Yes",
rlgblg %in% c(7, 8, 9) ~ NA_character_,
TRUE ~ as.character(rlgblg)
))
table(dn$religion)##
## No Yes
## 10913 6750dn <- dn %>%
mutate(ID = case_when(
lrscale >= 0 & lrscale <= 4 ~ "Left",
lrscale >= 6 & lrscale <= 10 ~ "Right",
lrscale > 10 ~ NA_character_,
TRUE ~ NA_character_
))
table(dn$ID)##
## Left Right
## 5449 7010dn <- dn %>%
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(dn$gen)##
## Interwar Baby Boomers Gen X Millennials
## 3771 6147 4548 2730model5 <- lm(auth ~ religion + ID + gen, data = dn, weights = weight)
model6 <- lm(auth ~ religion + ID + gen + religion*gen, data = dn, 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 MLR without interaction (model 5): #religionYes (7.2 ): When a person is religious, their level of authoritarian attitudes increases by 7.2 units, holding political affiliation and generational category constant. This is a very important relationship. #IDRight (4.2 ): Political identification on the right is very significant when contrasted to a 4.2 unit rise in authoritarian beliefs when compared to the left, assuming all other factors remain constant. #genBaby Boomers (-5.2 ): Compared to the Interwar generation, there is a 5.2 unit decrease in authoritarian beliefs for every Baby Boomer, assuming all other factors remain similar. As opposed to the Interwar generation, being a member of Gen X is strongly associated with a 7.7 unit reduction in authoritarian beliefs (#genGen X) (-7.7 ). # Num.Obs.: 12116 observations in total were utilised to fit the two models. # R2 (0.124): The models very slightly explain 12.4% of the diversity in beliefs held by authoritarians. # R2 Adj. (0.124 vs. 0.125): Including the interaction terms nearly entirely maintains the adjusted R-squared, suggesting that their addition does not much boost the explanatory capacity of the model. The model with interactions (model 6) has a little lower AIC (101219.3 vs. 101213.5) despite its complexity, indicating a noticeably better match to the data.
Task 4
Produce the model7 interaction plot from the tutorial, but again using the Netherlands data. Interpret.
dn <- dn %>%
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 = dn, weights = weight)
interact_plot(model7, pred = cohort, modx = polID, jnplot = TRUE)
# The trend lines demonstrate that for all political identifications
(Left, Moderate, Right), authoritarian sentiments tend to decrease with
more recent birth cohorts. Younger generations have less respect for
authority than older generations do. # However, the slopes of the lines
differ according on political identification. The ‘Left’ group has the
shallowest slope, #indicating a less sharp decline in authoritarian
beliefs across several cohorts. # The ‘Moderate’ and ‘Right’ political
groups have steeper slopes, but younger individuals within them show a
more noticeable shift away from authoritarian viewpoints. Older
generations are often more authoritarian than the ‘Right,’ as seen by
the ‘Right’ and ‘Moderate’ lines crossing; however, this trend reverses
with younger cohorts when the ‘Moderate’ shows a little rise in contrast
to the right
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 = dn, weights = weight)
interact_plot(model8, pred = religious, modx = ID, jnplot = TRUE)
#As religiousness increases, so does the authoritarian attitude score,
as seen by the positive slopes for both groups. According to the
‘Right’s’ steeper slope, there is a noticeable increase in authoritarian
inclinations and religiosity among individuals who identify as
politically right-leaning. For those on the “Left,” the correlation
between religiosity and authoritarian inclinations is less pronounced,
despite the positive link still existing. It is implied that political
identification may act as a moderator in the relationship between
religion and authoritarian ideas.Given that there are no crossing lines
between left and right political identifications, it seems likely that
religiousness has a constant impact on authoritarian viewpoints over the
whole spectrum of observed religiousness.
#end.