Online appendix for “Pandemic Pass? Treaty Derogations and Human Rights Practices During COVID-19”

(Research note)

Authors
Affiliations

Lewis and Clark College

Arizona State University

Georgia State University

Latest version

July 25, 2024

Modeling approach

We use Stan 2.34.1 (Stan Development Team 2023) through R 4.4.0 (R Core Team 2023) and {brms} 2.21.0 (Bürkner 2017) to estimate our models. We generate 4 MCMC chains for each model with 2,000 iterations in each chain, 1,000 of which are used for warmup. All chains converge; we assess convergence with visual inspection.

Complete results from all the models, along with posterior predictive checks, goodness-of-fit measures, and prediction diagnostics are all available at a companion statistical analysis compendium at https://doi.org/10.17605/OSF.IO/7GVDA.

Priors

We follow the suggestion of Gelman et al. (2008) and use weakly informative priors for our logistic and ordered logistic regression models. For consistency with prior specification, and for computation efficiency, we mean-center all nonbinary variables so that parameter estimates represent changes from the mean. We use two general priors (see Figure 1):

  • For all \(\beta\) terms, we use a Student t distribution with a mean of 0 and a standard deviation of 3. This keeps most parameter estimates around −5 to 5, with thicker tails that allow for some possibility of extreme values.
  • For \(\sigma\) terms related to the variance or standard deviation of parameter distributions, which must be positive, we use a half Cauchy distribution, centered at 0 with a \(\gamma\) of 1

These priors give more weight to realistic areas of parameter values and downweight values in unrealistic spaces. For instance, since logit-scale coefficient values greater than 4 or 5 are highly unlikely, our Student t prior puts more weight on smaller values. Additionally, weakly informative priors allow reasonable and considerable uncertainty in possible parameter estimates.

Figure A 1: Density plots of prior distributions for model parameters

Model definitions

H1: Logistic regression

Figure A 2: Hierarchy of country-week data, showing location and frequency of measured variables

\[ \begin{aligned} &\ \mathrlap{\textbf{Binary outcome $i$ across week $t$ within each country $j$}} \\ \text{Outcome}_{it_j} \sim&\ \operatorname{Bernoulli}(\pi_{it_j}) \\[0.75em] &\ \textbf{Distribution parameters} \\ \pi_{it_j} =&\ (\beta_0 + b_{0_j}) + \beta_1 \text{Derogation in effect}_{it} + \\ &\ \beta_2\ \text{New cases}_{it}\ + \beta_3\ \text{Cumulative cases}_{it}\ + \\ &\ \beta_4\ \text{New deaths}_{it}\ + \beta_5\ \text{Cumulative deaths}_{it}\ + \\ &\ \beta_6\ \text{Past ICCPR derogation}_{it}\ + \beta_7\ \text{Past ICCPR action}_{it}\ + \\ &\ \beta_8\ \text{Rule of law index}_{it}\ + \beta_9\ \text{Civil liberties index}_{it}\ + \\ &\ \beta_{10}\ \text{Core civil society index}_{it}\ + \beta_{11}\ \text{Week number}_{it} \\ b_{0_j} \sim&\ \mathcal{N}(0, \sigma_0) \\[0.75em] &\ \textbf{Priors} \\ \beta_{0 \dots 11} \sim&\ \operatorname{Student\ t}(\nu = 1, \mu = 0, \sigma = 3) \\ \sigma_0 \sim&\ \operatorname{Cauchy}(x = 0, \gamma = 1) \text{, lower bound} = 0 \end{aligned} \]

The actual R code for these models is included in the replication code at https://doi.org/10.17605/OSF.IO/ANONYMIZED-FOR-NOW This is a simplified representation of the {brms} (Bürkner 2017) model code:

# H1: Logistic regression for binary outcomes
brm(
  bf(outcome ~ derogation_ineffect + 
      new_cases_z + cumulative_cases_z + 
      new_deaths_z + cumulative_deaths_z +
      prior_iccpr_derogations + prior_iccpr_other_action + 
      v2x_rule + v2x_civlib + v2xcs_ccsi + 
      year_week_num + (1 | country_name)),
  family = bernoulli(),
  prior = c(
    prior(student_t(1, 0, 3), class = Intercept),
    prior(student_t(1, 0, 3), class = b),
    prior(cauchy(0, 1), class = sd, lb = 0)),
  ...
)

H2: Ordered logistic regression

Figure A 3: Hierarchy of region-quarter data, showing location and frequency of measured variables

\[ \begin{aligned} &\ \mathrlap{\textbf{Model of outcome level $i$ across quarter $t$ within each region $j$}} \\ \text{Outcome}_{it_j} \sim&\ \operatorname{Ordered\ logit}(\phi_{it_j}, \alpha_k) \\[0.75em] &\ \textbf{Models for distribution parameters} \\ \phi_{it_j} =&\ (\beta_0 + b_{0_j}) + \beta_1 \text{Derogation in effect}_{it} + \\ &\ \beta_2\ \text{New cases}_{it}\ + \beta_3\ \text{Cumulative cases}_{it}\ + \\ &\ \beta_4\ \text{New deaths}_{it}\ + \beta_5\ \text{Cumulative deaths}_{it}\ + \\ &\ \beta_6\ \text{Past ICCPR derogation}_{it}\ + \beta_7\ \text{Past ICCPR action}_{it}\ + \\ &\ \beta_8\ \text{Rule of law index}_{it}\ + \beta_9\ \text{Civil liberties index}_{it}\ + \\ &\ \beta_{10}\ \text{Core civil society index}_{it}\ + \beta_{11}\ \text{Quarter number}_{it} \\ b_{0_j} \sim&\ \mathcal{N}(0, \sigma_0) \\[0.75em] &\ \textbf{Priors} \\ \beta_{0 \dots 11} \sim&\ \operatorname{Student\ t}(\nu = 1, \mu = 0, \sigma = 3) \\ \sigma_0 \sim&\ \operatorname{Cauchy}(x = 0, \gamma = 1) \text{, lower bound} = 0 \\ \alpha_k \sim&\ \mathcal{N}(0, 1) \end{aligned} \]

The actual R code for these models is included in the replication code at https://doi.org/10.17605/OSF.IO/ANONYMIZED-FOR-NOW This is a simplified representation of the {brms} (Bürkner 2017) model code:

# H2: Ordinal logistic regression for ordered outcomes
brm(
  bf(outcome ~ derogation_ineffect + 
      new_cases_z + cumulative_cases_z + 
      new_deaths_z + cumulative_deaths_z +
      prior_iccpr_derogations + prior_iccpr_other_action + 
      v2x_rule + v2x_civlib + v2xcs_ccsi + 
      year_quarter_num + (1 | who_region)),
  family = cumulative(),
  prior = c(
    prior(student_t(1, 0, 3), class = Intercept),
    prior(student_t(1, 0, 3), class = b),
    prior(cauchy(0, 1), class = sd, lb = 0)),
  ...
)

H1: Derogations and emergency policies

Predicted probabilities and group contrasts

Table A 1: Summary of predicted probabilities and minimum and maximum contrasts between derogating and non-derogating countries for emergency policy models
Predicted probabilities Smallest difference Largest difference
Derogation March 2020 June 2021 Week \(\Delta\) p > 0 Week \(\Delta\) p > 0
No 0.98
[0.95–0.99]
0.93
[0.82–0.97]
2020-03-09 0.02
[0.01–0.05]
1.000 2021-06-28 0.07
[0.03–0.17]
1.000
Yes 1.00
[0.99–1.00]
1.00
[0.98–1.00]
No 0.91
[0.79–0.96]
0.89
[0.77–0.95]
2020-03-09 0.09
[0.04–0.21]
1.000 2021-06-28 0.11
[0.05–0.23]
1.000
Yes 1.00
[1.00–1.00]
1.00
[1.00–1.00]
No 0.49
[0.33–0.65]
0.32
[0.20–0.48]
2020-03-09 0.23
[0.15–0.32]
1.000 2021-03-29 0.25
[0.15–0.34]
1.000
Yes 0.73
[0.56–0.86]
0.58
[0.39–0.76]
No 0.66
[0.49–0.80]
0.18
[0.10–0.30]
2020-03-09 0.25
[0.15–0.36]
1.000 2021-02-01 0.39
[0.28–0.49]
1.000
Yes 0.91
[0.82–0.96]
0.54
[0.34–0.74]
No 0.99
[0.93–1.00]
1.00
[1.00–1.00]
2021-06-28 0.00
[0.00–0.00]
0.999 2020-03-09 0.01
[0.00–0.07]
0.999
Yes 1.00
[1.00–1.00]
1.00
[1.00–1.00]

Complete model results

Table A 2: Complete results from models showing relationship between derogations and emergency policies (H1)
Cancel Public Events Gathering Restrictions Close Public Transit Movement International Travel
Note: Estimates are median posterior log odds from ordered logistic and binary logistic regression models; 95% credible intervals (highest density posterior interval, or HDPI) in brackets. Total \(R^2\) considers the variance of both population and group effects; marginal \(R^2\) only takes population effects into account.
Derogation in effect 3.4 11 1.04 1.7 7.27
[1.3, 5.9] [3, 57] [0.64, 1.45] [1.2, 2.2] [0.08, 40.80]
New cases (standardized) 2.19 8.5 -0.68 0.75 6.41
[-0.53, 5.76] [5.8, 11.4] [-0.88, -0.48] [0.31, 1.25] [-0.34, 16.49]
Cumulative cases (standardized) 3.3 4.7 -0.367 -0.18 1.4
[1.3, 5.6] [2.9, 6.7] [-0.810, 0.035] [-0.57, 0.23] [-6.0, 13.6]
New deaths (standardized) 8.2 2.4 1.24 0.74 -1.62
[4.9, 11.3] [1.1, 3.9] [0.97, 1.54] [0.38, 1.12] [-3.24, -0.31]
Cumulative deaths (standardized) -0.899 -2.7 0.70 0.17 6.07
[-1.864, 0.089] [-3.6, -1.8] [0.29, 1.15] [-0.23, 0.58] [0.42, 11.59]
Past ICCPR derogation 0.38 -1.29 0.081 0.16 -1.2
[-0.75, 1.63] [-2.37, -0.19] [-0.704, 0.837] [-0.69, 0.93] [-3.4, 1.0]
Past ICCPR action -0.14 0.17 -0.18 0.072 0.31
[-1.13, 1.00] [-0.80, 1.10] [-0.92, 0.56] [-0.719, 0.812] [-1.73, 2.47]
Rule of law 3.3 0.72 -0.81 -0.77 -0.066
[1.3, 5.5] [-1.18, 2.38] [-2.15, 0.54] [-2.12, 0.63] [-4.058, 3.360]
Civil liberties -3.99 1.2 1.1 -0.68 0.87
[-7.70, -0.65] [-1.4, 4.4] [-1.3, 3.4] [-3.10, 1.51] [-4.33, 7.96]
Core civil society index 0.26 -0.022 -0.76 -0.57 -1.9
[-1.90, 2.75] [-2.017, 2.149] [-2.58, 0.87] [-2.22, 1.00] [-7.7, 2.2]
Constant 8.1 4.8 1.29 3.6 10.8
[6.6, 9.5] [3.7, 6.0] [0.47, 2.02] [2.6, 4.4] [7.3, 15.5]
Year-week -0.021 -0.0030 -0.0103 -0.032 0.050
[-0.026, -0.015] [-0.0079, 0.0021] [-0.0131, -0.0073] [-0.035, -0.029] [0.031, 0.068]
Country random effects σ 2.4 2.3 1.8 1.9 3.9
[2.0, 2.9] [2.0, 2.7] [1.5, 2.1] [1.7, 2.2] [2.6, 5.5]
N 9453 9522 8832 9246 9591
\(R^2\) (total) 0.31 0.41 0.36 0.40 0.32
\(R^2\) (marginal) 0.01 0.03 0.07 0.12 0.00

H2: Derogations and human rights

Predicted probabilities and group contrasts

Predicted probabilities Smallest difference Largest difference
Derogation Level 2020-Q2 2021-Q2 Week \(\Delta\) p > 0 Week \(\Delta\) p > 0
No None 0.87
[0.79–0.93]
0.94
[0.89–0.97]
2021-Q2 0.02
[-0.04–0.06]
0.81600 2020-Q2 0.04
[-0.08–0.13]
0.81600
Yes None 0.92
[0.78–0.98]
0.96
[0.89–0.99]
No Minor 0.06
[0.03–0.10]
0.03
[0.01–0.05]
2020-Q2 -0.02
[-0.06–0.03]
0.18400 2021-Q2 -0.01
[-0.03–0.02]
0.18400
Yes Minor 0.04
[0.01–0.10]
0.02
[0.00–0.06]
No Moderate 0.01
[0.01–0.02]
0.01
[0.00–0.01]
2020-Q2 0.00
[-0.01–0.01]
0.18400 2021-Q2 0.00
[-0.01–0.00]
0.18400
Yes Moderate 0.01
[0.00–0.02]
0.00
[0.00–0.01]
No Major 0.05
[0.03–0.10]
0.02
[0.01–0.05]
2020-Q2 -0.02
[-0.06–0.03]
0.18400 2021-Q2 -0.01
[-0.03–0.02]
0.18400
Yes Major 0.03
[0.01–0.10]
0.01
[0.00–0.05]
No 0.03
[0.01–0.06]
0.02
[0.01–0.04]
2021-Q2 0.00
[-0.02–0.04]
0.54075 2020-Q2 0.00
[-0.03–0.06]
0.54075
Yes 0.03
[0.01–0.10]
0.02
[0.00–0.07]
No None 0.66
[0.55–0.76]
0.61
[0.49–0.71]
2020-Q2 0.22
[0.11–0.33]
0.99975 2021-Q2 0.25
[0.12–0.36]
0.99975
Yes None 0.89
[0.76–0.95]
0.86
[0.71–0.94]
No Minor 0.02
[0.01–0.03]
0.02
[0.01–0.03]
2020-Q2 -0.01
[-0.02–0.00]
0.00025 2021-Q2 -0.01
[-0.02–0.00]
0.00025
Yes Minor 0.01
[0.00–0.02]
0.01
[0.00–0.02]
No Moderate 0.32
[0.23–0.43]
0.37
[0.27–0.49]
2021-Q2 -0.24
[-0.35–-0.11]
0.00025 2020-Q2 -0.21
[-0.32–-0.10]
0.00025
Yes Moderate 0.11
[0.04–0.22]
0.13
[0.05–0.28]
No None 0.66
[0.55–0.75]
0.92
[0.88–0.95]
2020-Q2 -0.05
[-0.19–0.08]
0.23250 2021-Q2 -0.02
[-0.09–0.02]
0.23250
Yes None 0.60
[0.44–0.76]
0.90
[0.81–0.95]
No Minor 0.19
[0.15–0.24]
0.05
[0.03–0.08]
2021-Q2 0.01
[-0.01–0.05]
0.76750 2020-Q2 0.02
[-0.03–0.08]
0.76750
Yes Minor 0.21
[0.14–0.28]
0.06
[0.03–0.12]
No Moderate 0.11
[0.07–0.16]
0.02
[0.01–0.04]
2021-Q2 0.01
[-0.01–0.03]
0.76750 2020-Q2 0.02
[-0.03–0.08]
0.76750
Yes Moderate 0.13
[0.07–0.21]
0.03
[0.01–0.06]
No Major 0.04
[0.02–0.06]
0.01
[0.00–0.01]
2021-Q2 0.00
[0.00–0.01]
0.76750 2020-Q2 0.01
[-0.01–0.05]
0.76750
Yes Major 0.05
[0.02–0.10]
0.01
[0.00–0.02]

Complete model results

Table A 3: Complete results from models showing relationship between derogations and human rights (H2)
Discriminatory Policy Non-Derogable Rights No Time Limit Measures Abusive Enforcement
Note: Estimates are median posterior log odds from ordered logistic and binary logistic regression models; 95% credible intervals (highest density posterior interval, or HDPI) in brackets. Total \(R^2\) considers the variance of both population and group effects; marginal \(R^2\) only takes population effects into account.
Derogation in effect -0.49 0.066 -1.4 0.22
[-1.73, 0.59] [-1.262, 1.174] [-2.3, -0.6] [-0.37, 0.76]
New cases (standardized) 0.26 0.051 -0.12 0.028
[-0.49, 1.09] [-1.596, 1.614] [-0.98, 0.69] [-0.510, 0.640]
Cumulative cases (standardized) -0.11 -0.11 -0.49 0.17
[-1.04, 0.98] [-2.04, 1.78] [-1.43, 0.40] [-0.51, 0.95]
New deaths (standardized) -0.27 -0.056 0.089 0.21
[-1.16, 0.54] [-1.223, 1.151] [-0.526, 0.639] [-0.33, 0.81]
Cumulative deaths (standardized) 0.12 -0.42 0.26 -0.29
[-0.91, 1.13] [-2.16, 0.94] [-0.44, 0.99] [-1.03, 0.39]
Past ICCPR derogation 0.95 0.36 0.13 0.457
[0.41, 1.53] [-0.42, 1.07] [-0.32, 0.56] [0.064, 0.852]
Past ICCPR action 0.27 1.38 -0.53 0.04
[-0.27, 0.75] [0.77, 2.01] [-0.99, -0.12] [-0.35, 0.42]
Rule of law 1.04 0.88 0.72 -0.75
[-0.26, 2.38] [-0.84, 2.59] [-0.26, 1.67] [-1.66, 0.14]
Civil liberties 1.2 -3.93 -1.39 0.24
[-1.1, 3.7] [-7.15, -0.89] [-3.37, 0.46] [-1.56, 2.01]
Core civil society index -2.24 0.6 -0.28 -0.3
[-3.92, -0.73] [-1.5, 2.8] [-1.57, 1.08] [-1.6, 1.0]
Constant -1.33
[-2.59, -0.17]
Cut 1 1.26 0.54 -0.71
[-0.25, 2.75] [-0.50, 1.48] [-1.53, 0.05]
Cut 2 1.98 0.62 0.38
[0.46, 3.50] [-0.43, 1.54] [-0.41, 1.15]
Cut 3 2.20 1.9
[0.52, 3.55] [1.0, 2.7]
Region random effects σ 1.30 0.71 0.83 0.57
[0.58, 2.60] [0.17, 1.62] [0.34, 1.67] [0.23, 1.17]
N 834 834 834 834
\(R^2\) (total) 0.15 0.11 0.07 0.15
\(R^2\) (marginal) 0.08 0.08 0.04 0.10
Table A 4: WHO regions
AFRO: Regional Office for Africa
Algeria, Angola, Benin, Botswana, Burkina Faso, Burundi, Cape Verde, Cameroon, Central African Republic, Chad, Comoros, Congo - Brazzaville, Côte d’Ivoire, Congo - Kinshasa, Equatorial Guinea, Eritrea, Eswatini, Ethiopia, Gabon, Gambia, Ghana, Guinea, Guinea-Bissau, Kenya, Lesotho, Liberia, Madagascar, Malawi, Mali, Mauritania, Mauritius, Mozambique, Namibia, Niger, Nigeria, Rwanda, St. Helena, São Tomé & Príncipe, Senegal, Seychelles, Sierra Leone, South Africa, South Sudan, Togo, Uganda, Tanzania, Zambia, and Zimbabwe
AMRO: Regional Office for the Americas
Anguilla, Antigua & Barbuda, Argentina, Aruba, Bahamas, Barbados, Belize, Bermuda, Bolivia, Brazil, British Virgin Islands, Canada, Cayman Islands, Chile, Colombia, Costa Rica, Cuba, Curaçao, Dominica, Dominican Republic, Ecuador, El Salvador, French Guiana, Grenada, Guatemala, Guyana, Haiti, Honduras, Jamaica, Mexico, Nicaragua, Panama, Paraguay, Peru, St. Barthélemy, St. Kitts & Nevis, St. Lucia, Saint Martin (French part), St. Vincent & Grenadines, Sint Maarten, Suriname, Trinidad & Tobago, Turks & Caicos Islands, United States, Uruguay, and Venezuela
EMRO: Regional Office for the Eastern Mediterranean
Afghanistan, Bahrain, Djibouti, Egypt, Iran, Iraq, Jordan, Kuwait, Lebanon, Libya, Morocco, Palestinian Territories, Oman, Pakistan, Qatar, Saudi Arabia, Somalia, Sudan, Syria, Tunisia, United Arab Emirates, and Yemen
EURO: Regional Office for Europe
Albania, Andorra, Armenia, Austria, Azerbaijan, Belarus, Belgium, Bosnia & Herzegovina, Bulgaria, Croatia, Cyprus, Czechia, Denmark, Estonia, Finland, France, Georgia, Germany, Greece, Hungary, Iceland, Ireland, Israel, Italy, Kazakhstan, Kosovo, Kyrgyzstan, Latvia, Liechtenstein, Lithuania, Luxembourg, Malta, Monaco, Montenegro, Netherlands, North Macedonia, Norway, Poland, Portugal, Moldova, Romania, Russia, San Marino, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Tajikistan, United Kingdom, Türkiye, Turkmenistan, Ukraine, and Uzbekistan
SEARO: Regional Office for South-East Asia
Bangladesh, Bhutan, North Korea, India, Indonesia, Maldives, Myanmar (Burma), Nepal, Sri Lanka, Thailand, and Timor-Leste
WPRO: Regional Office for the Western Pacific
American Samoa, Australia, Brunei, Cambodia, China, Cook Islands, Fiji, French Polynesia, Japan, Kiribati, Laos, Malaysia, Marshall Islands, Micronesia (Federated States of), Mongolia, Nauru, New Zealand, Palau, Papua New Guinea, Philippines, South Korea, Samoa, Singapore, Solomon Islands, Tonga, Tuvalu, Vanuatu, and Vietnam
Table A 5: States that derogated from regional human rights conventions
States that derogated from the ACHR Also submitted ICCPR derogation States that derogated from the ECHR Also submitted ICCPR derogation
ACHR = American Convention on Human Rights; ECHR = European Convention on Human Rights
Argentina Yes Albania No
Bolivia No Armenia Yes
Chile Yes Azerbaijan Yes
Colombia Yes Estonia Yes
Dominican Republic Yes Georgia Yes
Ecuador Yes Latvia Yes
El Salvador Yes Moldova Yes
Guatemala Yes North Macedonia No
Honduras No Romania Yes
Jamaica No San Marino Yes
Panama No Serbia No
Paraguay Yes
Peru Yes
Suriname No
Venezuela No
Table A 6: Results from Chaudhry, Comstock, and Heiss (2024) showing the determinants of derogation
Model 1 Model 2
Dependent variable = derogation submission
Logistic regression models; odds ratios (standard error)
* p < 0.1, ** p < 0.05, *** p < 0.01
Intercept 0.00217 (0.00093)*** 0.0044 (0.0021)***
Pandemic backsliding (PanBack) 7.1 (6.5)**
Pandemic violations of democratic standards (PanDem) 0.29 (0.29)
New cases (standardized) 0.33 (0.40) 0.42 (0.51)
New deaths (standardized) 1.66 (0.44)* 1.64 (0.43)*
Cumulative cases (standardized) 0.015 (0.033)* 0.0067 (0.0152)**
Cumulative deaths (standardized) 3.6 (1.7)*** 4.3 (2.1)***
Rule of law index 1.99 (0.87) 1.27 (0.58)
N 9591 9591

References

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