Exercise 1 (20 minutes)

Today we ask a new question of the same data: do better-educated Danes trust the police more? — and does the answer depend on whether we use weights?

Do the Setup if you haven't, then start a new R script and copy in this starter code (the same preparation we walked through on the slides):

pacman::p_load(tidyverse, haven, estimatr, modelsummary)

ESS <- read_spss("ESS9e03_1.sav") %>%
  filter(cntry == "DK") %>%
  select(idno, pspwght, gndr, eduyrs, agea, psppsgva, trstlgl, trstplc) %>%
  mutate(across(c(psppsgva, trstlgl, trstplc, pspwght), zap_labels),
         eduyrs = pmin(pmax(eduyrs, 9), 21), # Censor education at 9 & 21
         gndr   = as_factor(gndr)) %>%
  drop_na()

Stuck?

read_spss() can't find the file? ESS9e03_1.sav must sit in your project folder — download it from Absalon and check the Files pane in RStudio.

Did pacman::p_load(...) run without red errors? Fix that first.

Odd results? Session → Restart R, then run your script from the top.

Still stuck? Ask (and answer!) in the t-R-ouble forum on Absalon.

Now write the regression yourself: ignoring weights for a moment, regress trust in the police (trstplc) on years of education (eduyrs) with lm_robust(), and read off the slope. A one-year increase in education goes with a change in police trust of (three digits; point or comma is fine).

mod1 <- lm_robust(trstplc ~ eduyrs, data = ESS)

modelsummary(list("Trust in police" = mod1),
             statistic = NULL, gof_map = c("nobs", "r.squared"))

	Trust in police
(Intercept)	7.530
eduyrs	0.033
Num.Obs.	1511
R2	0.005

Still ignoring weights: is there a gender difference in trust in the police? Regress trstplc on gndr.

mod2 <- lm_robust(trstplc ~ gndr, data = ESS)

modelsummary(list("Trust in police" = mod2),
             statistic = NULL, gof_map = c("nobs", "r.squared"))

	Trust in police
(Intercept)	7.929
gndrFemale	0.159
Num.Obs.	1511
R2	0.002

Predict before you compute: you are about to add survey weights to both models. What do you expect?
Rerun both regressions with weights = pspwght and show all four models in one table. Do the weights matter here?

mod1_w <- lm_robust(trstplc ~ eduyrs, data = ESS, weights = pspwght)
mod2_w <- lm_robust(trstplc ~ gndr,   data = ESS, weights = pspwght)

modelsummary(
  list("Edu (unw.)" = mod1, "Gender (unw.)" = mod2,
       "Edu (wt.)" = mod1_w, "Gender (wt.)" = mod2_w),
  statistic = NULL, gof_map = c("nobs", "r.squared"))

	Edu (unw.)	Gender (unw.)	Edu (wt.)	Gender (wt.)
(Intercept)	7.530	7.929	7.782	7.801
eduyrs	0.033		0.013
gndrFemale		0.159		0.323
Num.Obs.	1511	1511	1511	1511
R2	0.005	0.002	0.001	0.008

Write one sentence (as a # comment) on whether weighting changed your conclusion. Then compare:

Weighting nudged the coefficients only slightly and left the substantive story unchanged: better-educated people trust the police a little more, and the gender difference stays small. That the Danish ESS is already close to representative is exactly why weights move the numbers so little here — in a badly skewed sample they would matter far more.

Bonus (for the fast): how big are the ESS weights? Summarise pspwght with summary() and make a histogram. Which respondents get weights well above 1, and why?

summary(ESS$pspwght)

ggplot(ESS, aes(x = pspwght)) +
  geom_histogram(bins = 30) +
  labs(x = "Post-stratification weight", y = "Count") +
  theme_minimal()

Weights well above 1 belong to under-represented groups (e.g. younger, less-educated, harder-to-reach respondents): each such person "stands in" for several who were missed. Weights below 1 belong to over-represented groups. They cluster tightly around 1 because the ESS sample is already close to representative.

Exercise 1 (20 minutes)

You practice: reading survey data, and how weights change a result. When you're done, assist some of the others …