The `extended_uds`

dataset can be generated with the following code:

`library(dplyr)`

`## Warning: package 'dplyr' was built under R version 3.4.2`

```
##
## Attaching package: 'dplyr'
```

```
## The following objects are masked from 'package:stats':
##
## filter, lag
```

```
## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union
```

`library(QuickUDS)`

`## Loading required package: mirt`

`## Warning: package 'mirt' was built under R version 3.4.3`

`## Loading required package: stats4`

`## Loading required package: lattice`

```
measures <- c("pmm_arat", "blm",
"bmr_democracy_femalesuffrage",
"bnr_extended", "pmm_bollen", "csvmdi",
"doorenspleet", "eiu",
"wgi_democracy","fh_total_reversed",
"fh_electoral", "gwf_democracy_extended",
"pmm_hadenius", "kailitz_tri",
"lexical_index", "mainwaring",
"magaloni_democracy_extended",
"pmm_munck", "pacl", "PEPS1v",
"pitf", "polity2", "reign_democracy",
"polyarchy_original_contestation",
"prc", "svolik_democracy",
"ulfelder_democracy_extended",
"utip_dichotomous_strict", "v2x_polyarchy",
"vanhanen_democratization", "wth_democ1")
# Generate Extended UDS
extended_model <- democracy_model(measures,
verbose = FALSE,
technical = list(NCYCLES = 2500))
```

```
## Warning: Log-likelihood was decreasing near the ML solution. EM method may
## be unstable
```

`extended_scores <- democracy_scores(model = extended_model)`

The model takes about 1-2 minutes to converge on my machine, and accounts for more than 90 per cent of the variance in the various democracy indexes used:

`extended_model@time`

```
## TOTAL: Data Estep Mstep SE Post
## 68.45 1.24 9.59 43.90 13.62 0.00
```

```
# Number of iterations, log likelihood, etc.
extended_model
```

```
##
## Call:
## mirt::mirt(data = data %>% select(cols$measures), model = 1,
## itemtype = "graded", SE = TRUE, verbose = verbose, technical = technical)
##
## Full-information item factor analysis with 1 factor(s).
## Converged within 1e-04 tolerance after 343 EM iterations.
## mirt version: 1.26.3
## M-step optimizer: BFGS
## EM acceleration: Ramsay
## Number of rectangular quadrature: 61
##
## Information matrix estimated with method: Oakes
## Condition number of information matrix = 15874.99
## Second-order test: model is a possible local maximum
##
## Log-likelihood = -230681.4
## Estimated parameters: 229
## AIC = 461820.9; AICc = 461824.8
## BIC = 463700.6; SABIC = 462972.8
```

```
# Correlations of latent factor with source variables, variance accounted for, etc.
summary(extended_model)
```

```
## F1 h2
## pmm_arat 0.904 0.818
## blm 0.981 0.961
## bmr_democracy_femalesuffrage 0.976 0.953
## bnr_extended 0.964 0.929
## pmm_bollen 0.927 0.860
## csvmdi 0.942 0.888
## doorenspleet 0.972 0.944
## eiu 0.955 0.912
## wgi_democracy 0.959 0.919
## fh_total_reversed 0.937 0.878
## fh_electoral 0.985 0.971
## gwf_democracy_extended 0.954 0.909
## pmm_hadenius 0.956 0.915
## kailitz_tri 0.939 0.882
## lexical_index 0.923 0.853
## mainwaring 0.971 0.943
## magaloni_democracy_extended 0.969 0.938
## pmm_munck 0.939 0.881
## pacl 0.956 0.914
## PEPS1v 0.991 0.982
## pitf 0.971 0.942
## polity2 0.985 0.969
## reign_democracy 0.950 0.903
## polyarchy_original_contestation 0.946 0.896
## prc 0.956 0.914
## svolik_democracy 0.959 0.919
## ulfelder_democracy_extended 0.969 0.939
## utip_dichotomous_strict 0.951 0.905
## v2x_polyarchy 0.945 0.893
## vanhanen_democratization 0.938 0.879
## wth_democ1 0.991 0.983
##
## SS loadings: 28.391
## Proportion Var: 0.916
##
## Factor correlations:
##
## F1
## F1 1
```

The cutpoints and discrimination parameters of these scores can be obtained as follows:

```
library(ggplot2)
dichotomous <- cutpoints(extended_model) %>%
group_by(variable) %>%
filter(n()==1) %>%
ungroup() %>%
summarise(avg_estimate = mean(estimate),
avg_se = sqrt(sum(se^2)/n() ^ 2 )) %>%
mutate(avg_pct975 = avg_estimate + 1.96*avg_se,
avg_pct025 = avg_estimate - 1.96*avg_se)
xmax <- cutpoints(extended_model) %>%
pull(variable) %>%
unique() %>%
length()
xmax <- xmax + 1
cutpoints(extended_model) %>%
ggplot(aes(x=variable,
y = estimate,
ymin = pct025,
ymax=pct975)) +
theme_bw() +
geom_rect(ymin = dichotomous$avg_pct025, ymax = dichotomous$avg_pct975,
xmin = 0, xmax = xmax, alpha = 0.2, fill = "grey") +
geom_hline(yintercept = dichotomous$avg_estimate,
color="black", linetype = 2) +
labs(x = "",
y = "Unified democracy level rater cutoffs",
title = "Rater cutoffs",
subtitle = "Grey band represents the average cutoff for dichotomous measures of democracy") +
geom_point() +
geom_errorbar() +
geom_hline(yintercept = 0,
color="red")+
coord_flip()
```

```
cutpoints(extended_model, type ="discrimination") %>%
ggplot(aes(x=reorder(variable, estimate),
y = estimate, ymin = pct025, ymax = pct975)) +
theme_bw() +
labs(x="",y="Discrimination parameter for each rater
\n(higher value means fewer idiosyncratic\nerrors relative to latent score)",
title = "Discrimination parameters",
subtitle = "Measures with higher discrimination are less likely \nto make idiosyncratic judgments relative to the rest") +
geom_point() +
geom_errorbar() +
coord_flip()
```

The `democracy_scores`

function produces three types of scores: the original latent variable (`z1`

), an “adjusted” score where 0 equals the cutpoint of the dichotomous democracy indexes (`z1_adj`

) and a probability score (`z1_*_as_prob`

) that is normalizes the other two to a 0-1 index, and can be interepreted as a kind of probability measure: country-years with scores close to 1 are almost certainly democratic, while country-years with scores close to 0 are almost certainly not, while 0.5 represents the cut-off between democracy and non-democracy.

These extended UD scores are available for `27133`

country-years (`248`

unique countries and non-sovereign territories):

(Grey shaded areas represent 95% confidence intervals; blue shaded areas are periods where the country is either deemed to be a member of the system of states in the Gleditsch and Ward list of state system membership since 1816, i.e., independent, or is a microstate in Gleditsch’s tentative list).