5  ParlGov losers’ consent

ESS linking example – see also sections “Party-voted-for in government” and “Performance of Party Facts linking” in manuscript.

Code

library(conflicted)

library(tidyverse)
conflicts_prefer(dplyr::filter, .quiet = TRUE)
library(glue)
library(knitr)

library(broom) # tidy model results
library(broom.mixed) # tidy model results for lme4
library(estimatr) # robust standard errors
library(ggeffects) # effects plots
library(lme4) # multi-level models
library(modelsummary) # model tables and coefficient plots
library(patchwork) # combine plots
library(reactable) # dynamic tables
library(skimr) # summary statistics

options(knitr.kable.NA = "")

round_numeric_variables <- function(data, digits = 0) {
  mutate(data, across(
    where(is.numeric),
    \(.x) format(round(.x, digits), scientific = FALSE)
  ))
}

Code

ess_raw <- read_rds("data/02-ess-select.rds")
ess_cabinet_raw <- read_rds("data/07-parlgov-ess_cabinets.rds")

5.1 Losers’ consent models

Satisfaction with democracy by those that voted for parties in government vs. opposition. For a book length discussion and empirical assessment of European democracies see Anderson et.al. (2005) – esp. model page 104. A replication and extension to other regions is provided by Farrer and Zingher (2019, 525)

• Anderson, Christopher, ed. 2005. Losers’ Consent: Elections and Democratic Legitimacy. Oxford ; New York: Oxford University Press.
• Farrer, Benjamin, and Joshua N Zingher. 2019. “A Global Analysis of How Losing an Election Affects Voter Satisfaction with Democracy.” International Political Science Review 40(4): 518–34. — doi: 10.1093/poq/nfad003

5.2 Variables

Variables used in losers’ consent models and context information

• stfdem — How satisfied with the way democracy works in country?
  • 0 // Extremely dissatisfied — 10 // Extremely satisfied
• cabinet — “party-voted-for” (prtv) in government after election
  • ParlGov based calculation
  • excluding caretaker governments
• lrscale — Placement on left right scale
  • 0 // Left — 10 // Right
• gndr — Gender
• agea — Age of respondent, calculated
• eduyrs — Years of full-time education completed
• ESS identifiers
  • cntry — Country
  • essround — ESS round
  • pspwght — Post-stratification weight // see ESS survey weights
  • inw_date — Date of interview // various ESS inw* variables
• Party information
  • prtv — Party voted for in last national election // aggregated ESS IDs
  • prtv_name — Party voted for in last national election // party name
  • first_ess_id — unique ESS party ID used in Party Facts

5.3 Summary statistics

Code

ess_cabinet <-
  ess_cabinet_raw |>
  select(essround, cntry, idno, cabinet = cabinet_party)

ess_lm <-
  ess_raw |>
  left_join(ess_cabinet) |>
  mutate(
    across(c(lrscale, stfdem), \(.x) as.integer(.x) - 1),
    cabinet = case_when(
      cabinet == 1 ~ "Yes",
      cabinet == 0 ~ "No",
      .default = NA
    ),
    cabinet = as.factor(cabinet) |> fct_rev()
  ) |>
  filter(!all(is.na(cabinet)), .by = c(cntry, essround))

ess_lm |>
  select(-idno) |>
  skim() |>
  round_numeric_variables(2)

Data summary

Name	select(ess_lm, -idno)
Number of rows	433599
Number of columns	14
_______________________
Column type frequency:
character	3
Date	1
factor	4
numeric	6
________________________
Group variables	None

Variable type: character

skim_variable	n_missing	complete_rate	min	max	empty	n_unique	whitespace
cntry	0	1.00	2	2	0	32	0
prtv	171780	0.60	8	14	0	2704	0
prtc	240202	0.45	8	10	0	2642	0

Variable type: Date

skim_variable	n_missing	complete_rate	min	max	median	n_unique
inw_date	912	1.00	2002-01-14	2022-09-02	2011-06-03	4827

Variable type: factor

skim_variable	n_missing	complete_rate	ordered	n_unique	top_counts
gndr	331	1.00	FALSE	2	Fem: 231527, Mal: 201741, No : 0
prtv_party	171780	0.60	FALSE	888	Lab: 6580, Con: 6077, Chr: 5660, Soc: 4972
prtc_party	240202	0.45	FALSE	900	Lab: 4949, Con: 4578, Chr: 4290, Soc: 3484
cabinet	209306	0.52	FALSE	2	Yes: 121092, No: 103201

Variable type: numeric

skim_variable	n_missing	complete_rate	mean	sd	p0	p25	p50	p75	p100	hist
essround	0	1.00	5.39	2.80	1	3.0	5.00	8.00	10.00	▇▇▇▇▇
pspwght	0	1.00	1.01	0.52	0	0.7	0.93	1.18	6.85	▇▁▁▁▁
agea	2155	1.00	48.49	18.62	13	33.0	48.00	63.00	123.00	▆▇▆▁▁
eduyrs	5075	0.99	12.43	4.13	0	10.0	12.00	15.00	65.00	▇▅▁▁▁
lrscale	55413	0.87	5.13	2.23	0	4.0	5.00	7.00	10.00	▂▃▇▃▁
stfdem	15516	0.96	5.28	2.51	0	4.0	5.00	7.00	10.00	▅▅▇▇▂

5.4 Multi-level models (ML)

Model variables preparation

• removing outliers age (99% quantile)
• selecting only variables used in models
• removing incomplete observations
• centering of continuous variables (age, education, left-right)

Code

# quantile(ess_lm$eduyrs, probs = c(0, 0.5, 0.9, 0.95, 0.99, 0.999), na.rm = TRUE)
eduyrs_remove <- quantile(ess_lm$eduyrs, probs = 0.99, na.rm = TRUE)

ess_lm_c <-
  ess_lm |>
  filter(eduyrs < eduyrs_remove) |>
  select(stfdem, cabinet, gndr, eduyrs, agea, lrscale, cntry, essround, pspwght) |>
  na.omit() |>
  mutate(
    essround_cntry = paste(essround, cntry),
    across(c(agea, eduyrs, lrscale),
      \(.x) scale(.x, scale = FALSE) |> as.vector(),
      .names = "{.col}_c"
    )
  )

plot_ggpredict <- function(model, plot_terms) {
  ggpredict(model, terms = plot_terms) |>
    plot(show.title = FALSE, show.legend = FALSE)
}

ml_formula <- "stfdem ~ gndr +  cabinet*eduyrs_c + cabinet*poly(agea_c, 2) + cabinet*poly(lrscale_c, 2)"

5.4.1 Three ML models

Multi-level models with quadric terms and interactions. Structure of models:

• Model 1 (ML-1) — ESS-Round/country and country
• Model 2 (ML-2) — ESS-Round and country
• Model 3 (ML-3) — country

Visualization of results in Figure 5.1 and Figure 5.2 – see variable information in Section 5.3

Code

ml1 <- lmer(
  as.formula(glue("{ml_formula} + (1 | cntry/essround_cntry)")),
  weights = pspwght,
  data = ess_lm_c
)

ml2 <- lmer(
  as.formula(glue("{ml_formula} + (1 | essround) + (1 | cntry)")),
  weights = pspwght,
  data = ess_lm_c
)

ml3 <- lmer(
  as.formula(glue("{ml_formula} + (1 | cntry)")),
  weights = pspwght,
  data = ess_lm_c
)

Code

models <- list("ML-1" = ml1, "ML-2" = ml2, "ML-3" = ml3)

if (knitr::is_html_output()) {
  modelsummary(models)
} else {
  modelsummary(models, output = "markdown")
}

	ML-1	ML-2	ML-3
(Intercept)	5.782	5.790	5.775
	(0.169)	(0.184)	(0.172)
gndrFemale	-0.182	-0.178	-0.179
	(0.009)	(0.010)	(0.010)
cabinetNo	-0.637	-0.645	-0.640
	(0.010)	(0.010)	(0.010)
eduyrs_c	0.048	0.045	0.048
	(0.002)	(0.002)	(0.002)
poly(agea_c, 2)1	23.624	21.075	25.719
	(3.151)	(3.192)	(3.189)
poly(agea_c, 2)2	30.470	30.403	31.438
	(2.913)	(2.957)	(2.967)
poly(lrscale_c, 2)1	103.697	105.407	108.606
	(3.333)	(3.204)	(3.208)
poly(lrscale_c, 2)2	35.905	39.358	40.284
	(3.116)	(3.149)	(3.160)
cabinetNo × eduyrs_c	0.013	0.014	0.015
	(0.003)	(0.003)	(0.003)
cabinetNo × poly(agea_c, 2)1	-4.329	-2.065	-3.641
	(4.620)	(4.675)	(4.691)
cabinetNo × poly(agea_c, 2)2	13.465	14.204	13.904
	(4.284)	(4.350)	(4.366)
cabinetNo × poly(lrscale_c, 2)1	-22.081	-23.826	-26.594
	(4.862)	(4.494)	(4.496)
cabinetNo × poly(lrscale_c, 2)2	-108.724	-113.550	-113.758
	(4.367)	(4.397)	(4.413)
SD (Intercept cntry)	0.931	0.965	0.970
SD (Observations)	2.106	2.142	2.150
SD (Intercept essround_cntrycntry)	0.500
SD (Intercept essround)		0.219
:———————————–	———:	———:	———:
Num.Obs.	205611	205611	205611
R2 Marg.	0.040	0.040	0.041
R2 Cond.	0.233	0.209	0.203
AIC	918254.1	924409.6	925869.4
BIC	918417.9	924573.3	926022.9
ICC	0.2	0.2	0.2
RMSE	2.13	2.16	2.17

Analysis of variance (ANOVA) models and refitting with Maximum Likelihood instead of Restricted Maximum Likelihood.

Code

anova(ml1, ml2, ml3) |>
  tidy() |>
  arrange(term)

term	npar	AIC	BIC	logLik	deviance	statistic	df	p.value
ml1	16	918249.0	918412.7	-459108.5	918217.0	7617.436	1	0
ml2	16	924404.7	924568.4	-462186.3	924372.7	0.000	0
ml3	15	925864.4	926017.9	-462917.2	925834.4

5.4.2 Effects plot ML-1

Effects plot Multi-Level Model 1 (ML-1, see Section 5.4.1)

Code

plot_ggpredict(ml1, c("lrscale_c [all]", "cabinet")) +
  plot_ggpredict(ml1, c("agea_c [all]", "cabinet")) +
  plot_ggpredict(ml1, c("eduyrs_c [all]", "cabinet"))

Figure 5.1: Effects plot (95% CIs) — Satisfaction with democracy

Code

pl_dt_lr <- ggpredict(ml1, c("lrscale_c [all]", "cabinet"))
pl_dt_edu <- ggpredict(ml1, c("eduyrs_c [all]", "cabinet"))
pl_dt_age <- ggpredict(ml1, c("agea_c [all]"))

Code

add_plot_layers <- function(pl, var_name = "x") {
  pl +
    geom_hline(yintercept = 5, color = "grey", size = 0.5) +
    geom_ribbon(aes(ymin = conf.low, ymax = conf.high), alpha = 0.1) +
    scale_y_continuous(limits = c(3.5, 7)) +
    labs(x = var_name, y = "") +
    theme_minimal()
}

color_values <- c("Yes" = "#E41A1C", "No" = "#377EB8")

pl_lr <-
  ggplot(pl_dt_lr, aes(x, predicted, fill = group)) |>
  add_plot_layers("left-right") +
  geom_vline(xintercept = median(ess_lm_c$lrscale_c), color = "grey", size = 0.5, linetype = "dashed") +
  geom_line(aes(colour = group)) +
  guides(color = "none", fill = "none") +
  scale_color_manual(values = color_values) +
  scale_fill_manual(values = color_values)

pl_edu <-
  ggplot(pl_dt_edu, aes(x, predicted, fill = group)) |>
  add_plot_layers("education") +
  geom_vline(xintercept = median(ess_lm_c$eduyrs_c), color = "grey", size = 0.5, linetype = "dashed") +
  geom_line(aes(colour = group)) +
  guides(color = "none", fill = "none") +
  scale_color_manual(values = color_values) +
  scale_fill_manual(values = color_values)

pl_age <-
  ggplot(pl_dt_age, aes(x, predicted)) |>
  add_plot_layers("age") +
  geom_vline(xintercept = median(ess_lm_c$agea_c), color = "grey", size = 0.5, linetype = "dashed") +
  geom_line()

pl <- pl_lr + pl_edu + pl_age

ggsave("figures-tables/figure-2_ml-model-effects.png", pl, width = 9, height = 6, dpi = 300)
pl

Figure 5.2: Effects plot (95% CIs) — Satisfaction with democracy // Article version

5.5 Linear effects (ML)

Multi-level model with linear terms and no interactions.

Visualization of results in Figure 5.3 (standardized coefficients) and Figure 5.4 (effects) – see variable information in Section 5.3

Code

ml_le <- lmer(
  "stfdem ~ cabinet + gndr + eduyrs_c + agea_c + lrscale_c + (1 | cntry/essround_cntry)",
  weights = pspwght,
  data = ess_lm_c
)

Code

ml_le |>
  tidy() |>
  kable(digits = 3)

effect	group	term	estimate	std.error	statistic
fixed		(Intercept)	5.775	0.170	33.996
fixed		cabinetNo	-0.636	0.010	-64.341
fixed		gndrFemale	-0.178	0.009	-18.849
fixed		eduyrs_c	0.051	0.001	37.025
fixed		agea_c	0.002	0.000	6.679
fixed		lrscale_c	0.094	0.002	44.172
ran_pars	essround_cntry:cntry	sd__(Intercept)	0.503
ran_pars	cntry	sd__(Intercept)	0.934
ran_pars	Residual	sd__Observation	2.112

Code

cm <- c(
  "cabinetNo" = "Opposition voter",
  "eduyrs_c" = "Education years",
  "gndrFemale" = "Women",
  "agea_c" = "Age",
  "lrscale_c" = "Left-right"
)

# parameters::parameters(ml1, standardize = "refit")
# modelplot(ml_le)

modelplot(ml_le, coef_map = rev(cm), standardize = "refit") +
  labs(x = "")

Figure 5.3: Standardized coefficients (95% CIs)– Linear effects model

Code

plot_ggpredict(ml_le, c("lrscale_c [all]", "cabinet")) +
  plot_ggpredict(ml_le, c("agea_c [all]", "cabinet")) +
  plot_ggpredict(ml_le, c("eduyrs_c [all]", "cabinet"))

Figure 5.4: Linear effects plot (95% CIs) — Satisfaction with democracy

5.6 Fixed effects model

Fixed effects model with quadric terms and interactions.

Visualization of results in Figure 5.5 and variable information in Section 5.3

Code

m_fe <-
  lm_robust(as.formula(glue("{ml_formula} + cntry + factor(essround)")),
    weights = pspwght,
    data = ess_lm_c
  )

Code

m_fe |>
  tidy() |>
  mutate(term = str_remove_all(term, "poly\\(|, 2\\)1") |> str_replace(fixed(", 2)2"), "^2")) |>
  filter(!str_starts(term, "cntry|factor")) |>
  select(-df, -outcome) |>
  kable(digits = 3)

term	estimate	std.error	statistic	p.value	conf.low	conf.high
(Intercept)	6.407	0.037	173.718	0.000	6.335	6.479
gndrFemale	-0.178	0.011	-16.569	0.000	-0.199	-0.157
cabinetNo	-0.645	0.011	-58.835	0.000	-0.667	-0.624
eduyrs_c	0.045	0.002	21.591	0.000	0.041	0.050
agea_c	21.004	3.505	5.993	0.000	14.135	27.874
agea_c^2	30.381	3.306	9.190	0.000	23.901	36.860
lrscale_c	105.418	3.903	27.011	0.000	97.769	113.068
lrscale_c^2	39.400	4.134	9.531	0.000	31.297	47.502
cabinetNo:eduyrs_c	0.014	0.003	4.744	0.000	0.008	0.020
cabinetNo:agea_c	-2.033	5.236	-0.388	0.698	-12.295	8.229
cabinetNo:agea_c^2	14.216	4.958	2.867	0.004	4.499	23.933
cabinetNo:lrscale_c	-23.832	5.585	-4.267	0.000	-34.779	-12.885
cabinetNo:lrscale_c^2	-113.566	5.823	-19.502	0.000	-124.979	-102.153

Fixed effects for countries (“cnty”) and ESS rounds (“essround”) not shown.

Code

m_fe |>
  glance() |>
  kable(digits = 2)

r.squared	adj.r.squared	statistic	p.value	df.residual	nobs	se_type
0.18	0.18	756.54	0	205558	205611	HC2

Code

plot_ggpredict(m_fe, c("lrscale_c [all]", "cabinet")) +
  plot_ggpredict(m_fe, c("agea_c [all]", "cabinet")) +
  plot_ggpredict(m_fe, c("eduyrs_c [all]", "cabinet"))

Figure 5.5: Fixed effects model (95% CIs) — Satisfaction with democracy

5.7 Share covered

Code

id_select <- "parlgov_id" # "ches_id" + "parlgov_id"
ess_check <- ess_cabinet_raw # ess_raw + ess_cabinet_raw
tbl_file_name <- "figures-tables/table-2b_parlgov-coverage.csv"

We calculate the share of matches for the “party-voted-for” (prtv) question. Excluded from the calculation are instances of other, independent, and technical (see Party Facts codebook).

Code

link_table_technical <-
  read_rds("data/03-party-facts-links-technical.rds")

prtv <-
  ess_check |>
  left_join(link_table_technical, by = c("prtv" = "ess_id")) |>
  select(cntry, essround, prtv, prtv_party, all_of(id_select), partyfacts_name, technical) |>
  filter(!is.na(prtv)) |>
  mutate(is_match = if_else(is.na(.data[[id_select]]), 0, 1))

prtv_match <-
  prtv |>
  filter(technical != 7 & technical != 8 & technical != 12 | is.na(technical)) |>
  summarise(
    prvt_n = n(),
    is_match = first(is_match),
    .by = c(cntry, essround, prtv, prtv_party)
  )

prtv_share <-
  prtv_match |>
  summarise(
    share_match = (sum(prvt_n * is_match) * 100 / sum(prvt_n)) |> round(1),
    .by = c(cntry, essround)
  )

The table summarizes the share of party matches across all countries and ESS rounds.

Code

tbl_out <-
  prtv_share |>
  reframe(
    enframe(
      quantile(share_match, c(0, 0.1, 0.25, 0.5, 0.75, 1)),
      "quantile", "share_match"
    )
  ) |>
  mutate(share_match = round(share_match, 1))

write_csv(tbl_out, tbl_file_name)
tbl_out

quantile	share_match
0%	11.4
10%	65.4
25%	81.9
50%	95.8
75%	99.2
100%	100.0

The share of matched parties is weighted by the number of “party-voted-for” responses and is calculated for each country in every ESS round.

The next table summarizes the country level share of party matches for ESS rounds with data set matches.

Code

tbl_out <-
  prtv_share |>
  summarise(
    min = min(share_match),
    median = median(share_match) |> round(1),
    max = max(share_match),
    ess_rounds = n_distinct(essround),
    .by = cntry
  ) |>
  filter(max > 0) |>
  arrange(min, median)

if (knitr::is_html_output()) {
  tbl_out |>
    reactable(searchable = TRUE, striped = TRUE)
} else {
  tbl_out
}