Shackleton_Jaime_Homework_5
Jaime Shackleton
2024-03-26
Initial set-up
# 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")
gd <- germany_data
gd <- gd %>%
mutate(behave = ipbhprp,
secure = impsafe,
safety = ipstrgv,
tradition = imptrad,
rules = ipfrule) %>%
mutate(across(c(behave, secure, safety, tradition, rules),
~ replace(., . %in% c(7, 8, 9), NA))) %>%
# Apply the reverse coding
mutate(across(c(behave, secure, safety, tradition, rules), ~ 7 - .))
# Now you can calculate 'schwartzauth' after the NA recoding
gd$auth <- rowSums(gd[c("behave", "secure", "safety", "tradition", "rules")], na.rm = TRUE)
gd$auth <- scales::rescale(gd$auth, to = c(0, 100), na.rm = TRUE)
gd <- gd %>% filter(!is.na(auth))gd <- gd %>%
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 = gd, weights = weight)
model4 <- lm(auth ~ polID + religious + polID*religious, data = gd, weights = weight)modelsummary(
list(model3, model4),
fmt = 1,
estimate = c( "{estimate} ({std.error}){stars}",
"{estimate} ({std.error}){stars}"),
statistic = NULL)| Â (1) | Â Â (2) | |
|---|---|---|
| (Intercept) | 63.4 (0.6)*** | 64.9 (0.8)*** |
| polIDModerate | 4.1 (0.7)*** | 2.2 (1.1)* |
| polIDRight | 7.4 (1.1)*** | 3.1 (1.8)+ |
| religious | 0.4 (0.1)*** | −0.1 (0.2) |
| polIDModerate × religious | 0.6 (0.2)* | |
| polIDRight × religious | 1.1 (0.3)** | |
| Num.Obs. | 2919 | 2919 |
| R2 | 0.027 | 0.031 |
| R2 Adj. | 0.026 | 0.030 |
| AIC | 24899.2 | 24892.0 |
| BIC | 24929.1 | 24933.8 |
| Log.Lik. | −12444.607 | −12438.984 |
| RMSE | 15.75 | 15.76 |
polIDModerate (4.1): This coefficient suggests that, comparing individuals with the same religiousness , the average outcome for individuals identifying as politically moderate are 4.1 units higher compared to the reference category.
polIDRight (7.4): This coefficient indicates that, comparing individuals with the same religiousness, individuals identifying as politically right are, on average, expected to be, 7.4 units higher than the reference category
religious (0.4): a coefficient of 0.4 means that with every one-unit increase in religiousness, there is an expected average increase of 0.4 units on the authoritarian values scale
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
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 64.88845 64.64671 64.28411 63.92151 63.67977
## Moderate 67.07983 67.98847 69.35143 70.71439 71.62303
## Right 67.97977 69.89936 72.77874 75.65812 77.57770The lines between polID left and polID right are not parallel, therefore indicating there is an interaction between them. The polID part showcases that those politically identifying as aligned with the left have lower, consistent rates of religiousness and authoritative values, with lower the more religious someone is. The polID for those politically inclined to the right shows an increase in authoritative attitudes in relation to religiousness.
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.
# Read data from file
netherlands_data <- read_fst("netherlands_data.fst")
nd <- netherlands_data
# Mutate variables
nd <- nd %>%
mutate(
religion = case_when(
rlgblg == 2 ~ "No",
rlgblg == 1 ~ "Yes",
rlgblg %in% c(7, 8, 9) ~ NA_character_,
TRUE ~ as.character(rlgblg)
),
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"))
)
nd <- 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 ))
# Calculate 'auth'
nd$auth <- scales::rescale(nd$behave +
nd$secure +
nd$safety +
nd$tradition +
nd$rules, to=c(0,100), na.rm=TRUE)
# Filter out rows with missing values in 'auth'
nd <- nd %>% filter(!is.na(auth))
# Check frequency of 'religion'
table(nd$religion)##
## No Yes
## 10913 6750nd <- nd %>%
mutate(ID = case_when(
lrscale >= 0 & lrscale <= 4 ~ "Left",
lrscale >= 6 & lrscale <= 10 ~ "Right",
lrscale > 10 ~ NA_character_, # Set values above 10 as NA
TRUE ~ NA_character_ # Ensure value 5 and any other unexpected values are set as NA
))
table(nd$ID)##
## Left Right
## 5449 7010model5 <- 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")| Â (1) | Â Â (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 |
religionYes (8.2): This coefficient suggests that, comparing individuals with the same religiousness , the average outcome for individuals identifying as politically moderate are 8.2 units higher compared to the reference category.
IDRight (3.4): This coefficient indicates that, comparing individuals with the same religiousness, individuals identifying as politically right are, on average, expected to be, 3.4 units higher than the reference category
genBaby Boomers (-5.8): a negative coefficient of 5.8 means that, comparing individuals from the generation of baby boomers, the average outcome for individuals is that they are 5.8 units less religious than the reference category
-genGen X (-7.3): a negative coefficient of 7.3 means that, comparing individuals from the generation of baby boomers, the average outcome for individuals is that they are 7.3 units less religious than the reference category
- genMillenials (-8.6): a negative coefficient of 8.6 means that, comparing individuals from the generation of baby boomers, the average outcome for individuals is that they are 8.6 units less religious than the reference category
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
interaction_plot <- effect("religion*gen", model5, na.rm=TRUE)## NOTE: religion:gen does not appear in the modelplot(interaction_plot,
main="Interaction effect",
xlab="Generation",
ylab="Religiousness")
interaction_plot##
## religion*gen effect
## gen
## religion Interwar Baby Boomers Gen X Millennials
## No 65.70179 59.89227 58.37776 57.12389
## Yes 73.87429 68.06478 66.55026 65.29640These lines are almost equivalent in shape and direction, their individual parts being quite parallel, such as the lines between interwar and baby boomers, and so on. As such, that implies there is not much interaction between religion = no and religion = yes.However, they are not the same, being at different heights, therefore implying there may still be some interaction.
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)
It is much more clear here that there is an interaction as the lines for left and right are not parallel, therefore indicating an interaction.
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)
Here it can be seen that the lines of left and right are quite similar,
nearly parallel. That implies there may be little to no interaction
between the factors.