Uppal_Chetan_Homework_5
2024-03-26
# List of packages
packages <- c("tidyverse", "infer", "fst", "modelsummary", "effects", "survey", "MASS", "aod", "interactions", "kableExtra", "flextable", "scales", "ggeffects") # 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] "datasets" "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 ))
# 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) | 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 |
Explanation: pollDModerate (5.3): indicates that when we compare individuals with the same religiousness, the average outcome is 5.3 units higher for individuals identifying politically moderate than reference identity on the left pollDRight (9.3): indicates that when we compare individuals with the same religiousness, people identifying as politically right are 9.3 units higher than the reference (individuals ideologically on the left) religious (0.3): This indicates that every one unit increase in relgiousness, expected increase 0.3 units on authoritarian scales. This is assumption we are comparing individuals with the same ideological categorization by holding consistently ideological self-placement PollDModerate & PollDRight have, while religious has, indicating a p < 0.001.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).
Fit metric models: model4 has a lower AIC value (24665.5) compared to model 3 (24680.0).BIC model4 has a lower value of 24707.2 than model3 which has 24709.7. The log.lik value of model4 (-12325.76) is less negative than of model3 (-12334.97). Overall, model4 is better for testing and testing the datasets. However, for rmse, both models have the same value of 17.13, making it hard to determine which one is a better fit. The adjusted R-squared value of model3 is 0.034 while model4 has 0.039, suggesting that pollD and religious values explain about 3.4% for model3 and 3.9% for model4. both are statistically signficant; however, they only explain a bit of the variablity. 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.
result <- predict_response(model4, c("religious", "polID"))
plot(result)
PollD = left; religiousnss of those who lean politically left, weaker
their authoritarian attitudes PollD= MODERATE, higher the religiousness
of those who are politically moderate then slower the increase in
authoritarian attitudes
pollD= right, higher the religiousness of those who lean politically right, the stronger their authoritarian attitudes.Given the steeper graph for individuals leaning politically right compared to moderates, my findings suggest a higher variance in authoritarian attitudes among the politically right-leaning, correlating with varying degrees of 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.
netherlands_data <- read_fst("netherlands_data.fst")
df <- netherlands_datadf <- df %>%
mutate(religion = case_when(
rlgblg == 2 ~ "No",
rlgblg == 1 ~ "Yes",
rlgblg %in% c(7, 8, 9) ~ NA_character_,
TRUE ~ as.character(rlgblg)
))
table(df$religion)##
## No Yes
## 11289 7008df <- df %>%
mutate(ID = case_when(
lrscale >= 0 & lrscale <= 4 ~ "Left",
lrscale >= 6 & lrscale <= 10 ~ "Right",
lrscale > 10 ~ NA_character_, # Set values above 10 as NA
TRUE ~ NA_character_ # Ensure value 5 and any other unexpected values are set as NA
))
table(df$ID)##
## Left Right
## 5605 7247df <- df %>%
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(df$gen)##
## Interwar Baby Boomers Gen X Millennials
## 3967 6359 4684 2803df <- df %>%
mutate(behave = ipbhprp,
secure = impsafe,
safety = ipstrgv,
tradition = imptrad,
rules = ipfrule) %>%
mutate(across(c("behave", "secure", "safety", "tradition", "rules"),
~ na_if(.x, 7) %>% na_if(8) %>% na_if(9))) %>%
mutate(across(c("behave", "secure", "safety", "tradition", "rules"), ~ 7 - .x ))
df$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
)
)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 | 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): when comparing individuals with the same political leaning, the average outcome for individuals with religions are 8.2 units higher compared to the reference category.
IDRight (3.4): when comparing individuals with the same religiousness, individuals identifying as politically right are on average 3.4 units higher than the reference category on the authoritarian values scale.
genBaby Boomers (-5.8): Baby Boomers in comparison to the reference cateogry show scores that are, on average, 5.8 points lower on the authoritarian values scale of 0-100
genGen X (-7.3): Generation X shows an decrease as the scores are 7.3 points lower than the reference category on the authoritarian values scale.
genMillennials (-8.6): Millennials have the biggest decrease in authoritarian values, with their scores being 8.6 points lower than the reference category. This marked difference is statistically significant, suggesting that Millennials diverge most strongly from those who lean politically left in comparison to their authoritarian values.
All the coefficients are significant with ***, representing a p < 0.001.There is less than a 0.1% probability that the observed result is due to chance and we incorrectly reject the null, under the frequentist assumptions.
fit metrics models: AIC model5 has a lower value of 9479.3 compared to model6, which means that model5 is better for testing this dataset compared to model6. A similar thing happens for BIC, as model5 shows a smaller BIC value of 9514.7 compared to model6, which has 9535; model5 is better fit for testing this dataset.The log.like value for model6 (−4732.25) is less negative than that of model5 (−4732.66), model6 is better fit for this dataset. Both models have the same value of RMSE (14.94), it is difficult to determine which model is the better fit by considering the value of RMSE only.
As for the adjusted R-squared value of 0.123 (model5) and 0.121 (model6), this indicates that pollD and religious variables, and generation varaibles explain about 12.3% for model5 and 12.1% for model6 for the variance in authoritarian value scales for netherlands.
Both models explain a small portion of variabiluty in authoritarian values, showing a chance for outside differences. Task 4 Produce the model7 interaction plot from the tutorial, but again using the Netherlands data. Interpret.
model7 <- lm(auth ~ + cohort + polID + cohort*polID, data = df, weights = weight)
interact_plot(model7, pred = cohort, modx = polID, jnplot = TRUE)
polIDLeft: the difference between the coded generations in authoritarian
score is the smallest.
polIDModerate: the higher the religiousness of those who are politically moderate
polIDRight: the difference between the coded generations in authoritarian score is the largest, with a steep slope.
The trend is that the younger individuals possess lower authoritarian attitudes scale.Those politically right show the greatest variance in authoritarian attitudes scale and those politically left show the least variance, both relatively with a generation that the individual belongs to. 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 = df, weights = weight)
interact_plot(model8, pred = religious, modx = ID, jnplot = TRUE)
Interpretation: Individuals on the right exhibit a positive correlation
between religiosity and authoritarianism, with a steeper slope observed
among those on the left. Overall, higher religiosity corresponds to
higher values on the authoritarian attitudes scale.