Virk_MuhammadQasim_Homework5
2024-03-25
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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.
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.
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.
Task 4
Produce the model7 interaction plot from the tutorial, but again using the Netherlands data. Interpret.
Task 5
Produce the model8 interaction plot from the tutorial, but again using the Netherlands data. Interpret.
Setting up the environment:
# 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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Loading data for Germany Renaming the data set so reverting back to original set possible:
germany_data <- read_fst("germany_data.fst")
germany <- germany_dataWeighting scales:
germany$weight <- germany$dweight * germany$pweight
survey_design <- svydesign(ids = ~1, data = germany, weights = ~weight)Using the authoritarian scale, again as conceptualized by Norris and Inglehart.
germany <- germany %>%
mutate(behave = ipbhprp,
secure = impsafe,
safety = ipstrgv,
tradition = imptrad,
rules = ipfrule) %>%
mutate(across(c("behave", "secure", "safety", "tradition", "rules"),
~ na_if(.x, 7) %>% na_if(8) %>% na_if(9))) %>%
# Apply the reverse coding
mutate(across(c("behave", "secure", "safety", "tradition", "rules"), ~ 7 - .x ))
# Now you can calculate 'schwartzauth' after the NA recoding
germany$auth <- scales::rescale(germany$behave +
germany$secure +
germany$safety +
germany$tradition +
germany$rules, to=c(0,100), na.rm=TRUE)Adding some covariates of interest, which will be the lrscale with three categories (left/moderate/right), as well as a cleaned version of ‘how religious’ respondents are (from 0-10).
germany <- germany %>%
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
)
)Running our models.
germany <- germany %>% filter(!is.na(auth))
model3 <- lm(auth ~ polID + religious, data = germany, weights = weight)
model4 <- lm(auth ~ polID + religious + polID*religious, data = germany, weights = weight)Using the modelsummary function to generate our table.
modelsummary(
list(model3, model4),
fmt = 1,
estimate = c( "{estimate} ({std.error}){stars}",
"{estimate} ({std.error}){stars}"),
statistic = NULL)| Â (1) | Â Â (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 |
Interpretation.
A co-efficient of 4.6 for Poll Moderate implies that individuals identifying as politically moderate score 4.6 units higher on the authoritarian scale than those identifying with the left (which is our reference category). The PollDright coefficient is 7.7. This highlights that those identifying with the Right are likely to score, on average, 7.7 points higher than those identifying with the left (reference category). Both of these come with the assumption of keeping religion constant.
In 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. This comes with the assumption of comparing individuals with same ideological categorizations (essentially holding political ideological self-placement as constant).
All 3 of the coefficients have triples asterisks, signifying the p value to be less than 0.001. This implies a less than 0.1% probability that the observed result is due to randomness within our sample. This, under frequentest assumptions, gives us evidence to reject the null hypothesis.
Task 2:
germany_data <- read_fst("germany_data.fst")
interaction_plot <- effect("polID*religious", model4, na.rm=TRUE)
plot(interaction_plot,
main="Interaction effect",
xlab="Religiousness",
ylab="Authoritarian attitudes scale")
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 74.34211Interpretation:
The interaction plot for those identifying Politically with the left shows an upward trend. This implies that as Left-leaning individuals become more religious, they score more on the authoritarian scale on average.
The interaction plot for those identifying Politically with the right also shows an upward trend. This implies that as Right-leaning individuals become more religious, they score higher on the authoritarian scale on average.
The interaction plot for those identifying Politically as moderates shows an upward trend that is similar to those identifying with the right. This implies that as those with moderate political leaning become more religious, they score higher on the authoritarian scale on average. However, in comparison to the Right group, the effect of religiosity is less steep for moderates, as can be seen from the gradient of the two graphs.
The overall trends are quite similar for all 3 cohorts. The difference in Y-intercepts highlights that in the absence of religious identification (religious scale as 0) PolID right score highest on the authoritarian scale, followed by POLidmoderates and last POLID left
Task 3:
Loading data for Netherlands:
netherlands_data <- read_fst("netherlands_data.fst")
netherlands <- netherlands_dataAuthoritarian scale created for Netherlands data
netherlands <- netherlands %>%
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
netherlands$auth <- scales::rescale(netherlands$behave +
netherlands$secure +
netherlands$safety +
netherlands$tradition +
netherlands$rules, to=c(0,100), na.rm=TRUE)
netherlands <- netherlands %>% filter(!is.na(auth))netherlands <- netherlands %>%
mutate(ID = case_when(
lrscale >= 0 & lrscale <= 4 ~ "Left",
lrscale >= 6 & lrscale <= 10 ~ "Right",
lrscale > 10 ~ NA_character_, # Set values above 10 as NA
TRUE ~ NA_character_ # Ensure value 5 and any other unexpected values are set as NA
))
table(netherlands$ID)##
## Left Right
## 5449 7010netherlands <- netherlands %>%
mutate(religion = case_when(
rlgblg == 2 ~ "No",
rlgblg == 1 ~ "Yes",
rlgblg %in% c(7, 8, 9) ~ NA_character_,
TRUE ~ as.character(rlgblg)
))
# check
table(netherlands$religion)##
## No Yes
## 10913 6750netherlands <- netherlands %>%
mutate(
cohort = ifelse(yrbrn < 1930 | yrbrn > 2000, NA, yrbrn),
# Recoding generational cohorts based on the year of birth (yrbrn).
# The year of birth is categorized into different generational cohorts.
# Interwar (1900-1945), Baby Boomers (1946-1964), Gen X (1965-1979), Millennials (1980-1996).
# The 'TRUE' line is a catch-all that keeps the original year of birth for those not in these ranges.
gen = case_when(
yrbrn %in% 1900:1945 ~ "1",
yrbrn %in% 1946:1964 ~ "2",
yrbrn %in% 1965:1979 ~ "3",
yrbrn %in% 1980:1996 ~ "4",
TRUE ~ as.character(yrbrn)
),
# After recoding, the gen variable is converted into a factor with labels for clearer interpretation.
# Factors are used in R to handle categorical variables.
gen = factor(gen,
levels = c("1", "2", "3", "4"),
labels = c("Interwar", "Baby Boomers", "Gen X", "Millennials"))
)
table(netherlands$gen)##
## Interwar Baby Boomers Gen X Millennials
## 3771 6147 4548 2730model5 <- lm(auth ~ religion + ID + gen, data = netherlands, weights = weight)
model6 <- lm(auth ~ religion + ID + gen + religion*gen, data = netherlands, 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 |
interaction_plot <- effect("religion*gen", model6, na.rm=TRUE)
plot(interaction_plot,
main="Interaction effect",
xlab="Generations",
ylab="Authoritarian attitudes scale")
interaction_plot##
## religion*gen effect
## gen
## religion Interwar Baby Boomers Gen X Millennials
## No 66.04811 59.54767 58.45132 57.45886
## Yes 73.53717 68.67842 66.40329 64.39243cat_plot(model5, pred = gen, modx = religion, jnplot = TRUE)## Warning: gen and religion are not included in an interaction with one another in the
## model.
cat_plot(model6, pred = gen, modx = religion, jnplot = TRUE)
Model 5:
The relegionYes coefficient of 8.2 associates identifying as a religious person with an average score on the authoritarian scale to be higher by 8.2 points
IDRright coefficient of 3.4 highlights that those identifying as politically right score 3.4 units higher than our reference category (left identifying individuals) on average.
The adjusted R-squared is 0.123. It highlights that the model explains for 12.3% of the variation within the data.
All generational categories (genBaby Boomers, genGen X, genMillenials) have a triple asterisk, which signifies that the p-value is less than 0.005. This shows that the explanatory variable is statistically significant, giving us evidence to reject the null hypothesis.
The model is thus a valuable predictor, although it does not fully explain all variance and thus other explanatory variables must be explored as well.
Model 6:
The relegionYes coefficient of 7.5 associates identifying as a religious person with an average score on the authoritarian scale to be higher by 7.5 points
IDRright coefficient of 3.4 highlights that those identifying as politically right score 3.4 units higher than our reference category (left identifying individuals) on average.
the adjusted R-squared is 0.121, so the model accounts for 12.1% of the variation in the data. The *** on each coefficient shows that the p-value is less than 0.005, highlighting that they are statistically significant under frequentest assumptions.
Task 4:
Model 7 interaction plot:
netherlands <- netherlands %>%
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 = netherlands, weights = weight)
interact_plot(model7, pred = cohort, modx = polID, jnplot = TRUE)
Interpretation:
We can see a downward trend in authoritarian scale scores for all 3 cohorts (POlID left, POlID right and PolID moderates) over time. In comparison, the steepest slope is for those politically identifying as right, showing the greatest decrease in average authoritarian scales. This is followed by moderates. Those identifying as politically left had the lowest overall decrease. However, the general trend of reducing authoritarian values is similar for all 3 cohorts.
The lines converge, showing that interaction does take place within variables.
Task 5:
Model 8 using Netherlands data.
model8 <- lm(auth ~ religious + ID + religious*ID, data = netherlands, weights = weight)
interact_plot(model8, pred = religious, modx = ID, jnplot = TRUE)
Interpretation:
The general trend is positive for both ID left and ID right groups, showing that as religious identification increases, authoritarian values increase within both groups with a very similar degree since the gradients are very similar.
The ID right cohort has a higher intercept, showing that in the absence of religion as an explanatory variable, ID right cohort will on average score higher than ID left cohort on the authoritarian scale.
Since both lines do not converge (almost parallel) no interaction can be seen.