Problem Set 6
Anum Peshimam
2024-08-06
# Display the first few rows and structure of the dataset
head(corruption)## country_name country_text_id year region
## 1 Mexico MEX 2020 Latin America and the Caribbean
## 2 Suriname SUR 2020 Latin America and the Caribbean
## 3 Sweden SWE 2020 Western Europe and North America
## 4 Switzerland CHE 2020 Western Europe and North America
## 5 Ghana GHA 2020 Sub-Saharan Africa
## 6 South Africa ZAF 2020 Sub-Saharan Africa
## disclose_donations_ord public_sector_corruption polyarchy civil_liberties
## 1 3 48.8 64.7 71.2
## 2 1 24.8 76.1 87.7
## 3 2 1.3 90.8 96.9
## 4 0 1.4 89.4 94.8
## 5 2 65.2 72.0 90.4
## 6 1 57.1 70.3 82.2
## disclose_donations iso2c population gdp_percapita capital longitude
## 1 TRUE MX 128932753 8922.612 Mexico City -99.1276
## 2 FALSE SR 586634 7529.614 Paramaribo -55.1679
## 3 FALSE SE 10353442 51541.656 Stockholm 18.0645
## 4 FALSE CH 8636561 85685.290 Bern 7.44821
## 5 FALSE GH 31072945 2020.624 Accra -0.20795
## 6 FALSE ZA 59308690 5659.207 Pretoria 28.1871
## latitude income log_gdp_percapita
## 1 19.427 Upper middle income 9.096344
## 2 5.8232 Upper middle income 8.926599
## 3 59.3327 High income 10.850146
## 4 46.948 High income 11.358436
## 5 5.57045 Lower middle income 7.611162
## 6 -25.746 Upper middle income 8.641039str(corruption)## 'data.frame': 168 obs. of 17 variables:
## $ country_name : chr "Mexico" "Suriname" "Sweden" "Switzerland" ...
## $ country_text_id : chr "MEX" "SUR" "SWE" "CHE" ...
## $ year : num 2020 2020 2020 2020 2020 2020 2020 2020 2020 2020 ...
## $ region : Factor w/ 6 levels "Eastern Europe and Central Asia",..: 2 2 5 5 4 4 6 6 1 1 ...
## $ disclose_donations_ord : num 3 1 2 0 2 1 3 2 3 2 ...
## $ public_sector_corruption: num 48.8 24.8 1.3 1.4 65.2 57.1 3.7 36.8 70.6 71.2 ...
## $ polyarchy : num 64.7 76.1 90.8 89.4 72 70.3 83.2 43.6 26.2 48.5 ...
## $ civil_liberties : num 71.2 87.7 96.9 94.8 90.4 82.2 92.8 56.9 43 85.5 ...
## $ disclose_donations : logi TRUE FALSE FALSE FALSE FALSE FALSE ...
## $ iso2c : chr "MX" "SR" "SE" "CH" ...
## $ population : num 1.29e+08 5.87e+05 1.04e+07 8.64e+06 3.11e+07 ...
## ..- attr(*, "label")= chr "Population, total"
## $ gdp_percapita : num 8923 7530 51542 85685 2021 ...
## ..- attr(*, "label")= chr "GDP per capita (constant 2015 US$)"
## $ capital : chr "Mexico City" "Paramaribo" "Stockholm" "Bern" ...
## $ longitude : chr "-99.1276" "-55.1679" "18.0645" "7.44821" ...
## $ latitude : chr "19.427" "5.8232" "59.3327" "46.948" ...
## $ income : chr "Upper middle income" "Upper middle income" "High income" "High income" ...
## $ log_gdp_percapita : num 9.1 8.93 10.85 11.36 7.61 ...
## ..- attr(*, "label")= chr "GDP per capita (constant 2015 US$)"TASK 1 Using the Civil dataset, perform a simple linear regression with public_sector_corruption as the dependent variable and polyarchy as the independent variable. Visualize the relationship with a scatter plot and overlay the regression line. Use the sjPlot package to create regression tables and interpret the results.
# Load necessary libraries
library(ggplot2)
library(sjPlot)
# Perform the linear regression
model <- lm(public_sector_corruption ~ polyarchy, data = corruption)
# Summarize the regression results
summary(model)##
## Call:
## lm(formula = public_sector_corruption ~ polyarchy, data = corruption)
##
## Residuals:
## Min 1Q Median 3Q Max
## -69.498 -14.334 1.448 16.985 44.436
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 89.44444 3.95373 22.62 <2e-16 ***
## polyarchy -0.82641 0.06786 -12.18 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 21.68 on 166 degrees of freedom
## Multiple R-squared: 0.4718, Adjusted R-squared: 0.4686
## F-statistic: 148.3 on 1 and 166 DF, p-value: < 2.2e-16# Scatter plot with regression line
ggplot(corruption, aes(x = polyarchy, y = public_sector_corruption)) +
geom_point() + # Scatter plot
geom_smooth(method = "lm", col = "blue") + # Regression line
labs(title = "Relationship between Polyarchy and Public Sector Corruption",
x = "Polyarchy",
y = "Public Sector Corruption")## `geom_smooth()` using formula = 'y ~ x'
# Regression table
tab_model(model, show.ci = TRUE, show.se = TRUE, show.p = TRUE)| Â | public_sector_corruption | |||
|---|---|---|---|---|
| Predictors | Estimates | std. Error | CI | p |
| (Intercept) | 89.44 | 3.95 | -Inf – Inf | <0.001 |
| polyarchy | -0.83 | 0.07 | -Inf – Inf | <0.001 |
| Observations | 168 | |||
| R2 / R2 adjusted | 0.472 / 0.469 | |||
The regression analysis results show that the intercept is estimated at 89.44, with a standard error of 3.95. The p-value is less than 0.001, indicating statistical significance. Polyarchy, the model’s main predictor, has a coefficient of -0.83, indicating that public sector corruption decreases (0.83 units) with polyarchy. The standard error is 0.07 and the p-value is less than 0.001, making this relationship statistically significant. The R² value of 0.472 indicates that the model explains 47.2% of public sector corruption variance. The adjusted R² is slightly lower at 0.469. The analysis included 168 observations. However, the confidence intervals for both the intercept and the polyarchy coefficient are reported as Infinty - Infinity, indicating a problem with their calculation, which could be due to data characteristics or other technical factors in the estimation of the model.
TASK 2 Extend the model from Task 1 by adding a quadratic term for polyarchy to capture potential non-linear relationships. Visualize the polynomial relationship using ggplot2. Calculate the marginal effects of polyarchy at different levels (30, 60, 90) using both manual calculations and the marginaleffects package. Interpret the results.
# Extend the model with a quadratic term
model_quad <- lm(public_sector_corruption ~ polyarchy + I(polyarchy^2), data = corruption)
# Summarize the extended model
summary(model_quad)##
## Call:
## lm(formula = public_sector_corruption ~ polyarchy + I(polyarchy^2),
## data = corruption)
##
## Residuals:
## Min 1Q Median 3Q Max
## -64.462 -7.475 1.418 14.107 35.187
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 53.116104 7.019792 7.567 2.55e-12 ***
## polyarchy 0.974653 0.305335 3.192 0.00169 **
## I(polyarchy^2) -0.017310 0.002874 -6.023 1.08e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 19.69 on 165 degrees of freedom
## Multiple R-squared: 0.567, Adjusted R-squared: 0.5618
## F-statistic: 108 on 2 and 165 DF, p-value: < 2.2e-16# Load necessary libraries
library(ggplot2)
library(marginaleffects)
# Create the scatter plot with polynomial regression line
ggplot(corruption, aes(x = polyarchy, y = public_sector_corruption)) +
geom_point() + # Scatter plot
stat_smooth(method = "lm", formula = y ~ poly(x, 2), col = "blue") + # Polynomial regression line
labs(title = "Polynomial Relationship between Polyarchy and Public Sector Corruption",
x = "Polyarchy",
y = "Public Sector Corruption")
# Coefficients from the quadratic model
coef_linear <- coef(model_quad)["polyarchy"]
coef_quadratic <- coef(model_quad)["I(polyarchy^2)"]
# Manual marginal effects calculation
marginal_effect_30 <- coef_linear + 2 * coef_quadratic * 30
marginal_effect_60 <- coef_linear + 2 * coef_quadratic * 60
marginal_effect_90 <- coef_linear + 2 * coef_quadratic * 90
# Display the results
marginal_effect_30## polyarchy
## -0.06392759marginal_effect_60## polyarchy
## -1.102508marginal_effect_90## polyarchy
## -2.141088# Calculate marginal effects using marginaleffects package
marginal_effects <- slopes(model_quad, newdata = data.frame(polyarchy = c(30, 60, 90)))
# Display the marginal effects
summary(marginal_effects)## rowid term estimate std.error
## Min. :1.0 Length:3 Min. :-2.14109 Min. :0.07681
## 1st Qu.:1.5 Class :character 1st Qu.:-1.62180 1st Qu.:0.10882
## Median :2.0 Mode :character Median :-1.10251 Median :0.14083
## Mean :2.0 Mean :-1.10251 Mean :0.14815
## 3rd Qu.:2.5 3rd Qu.:-0.58322 3rd Qu.:0.18381
## Max. :3.0 Max. :-0.06393 Max. :0.22680
## statistic p.value s.value conf.low
## Min. :-14.3535 Min. :0.0000 Min. : 0.6218 Min. :-2.5856
## 1st Qu.:-11.8970 1st Qu.:0.0000 1st Qu.: 34.2455 1st Qu.:-1.9193
## Median : -9.4405 Median :0.0000 Median : 67.8693 Median :-1.2531
## Mean : -8.0827 Mean :0.2166 Mean : 73.7606 Mean :-1.3929
## 3rd Qu.: -4.9472 3rd Qu.:0.3249 3rd Qu.:110.3301 3rd Qu.:-0.7965
## Max. : -0.4539 Max. :0.6499 Max. :152.7908 Max. :-0.3399
## conf.high predicted_lo predicted_hi predicted
## Min. :-1.6966 Min. : 0.6361 Min. : 0.6169 Min. : 0.6265
## 1st Qu.:-1.3243 1st Qu.:24.9607 1st Qu.:24.9462 1st Qu.:24.9535
## Median :-0.9520 Median :49.2854 Median :49.2755 Median :49.2805
## Mean :-0.8121 Mean :38.8996 Mean :38.8897 Mean :38.8946
## 3rd Qu.:-0.3699 3rd Qu.:58.0313 3rd Qu.:58.0261 3rd Qu.:58.0287
## Max. : 0.2121 Max. :66.7773 Max. :66.7767 Max. :66.7770
## polyarchy public_sector_corruption
## Min. :30 Min. :48.8
## 1st Qu.:45 1st Qu.:48.8
## Median :60 Median :48.8
## Mean :60 Mean :48.8
## 3rd Qu.:75 3rd Qu.:48.8
## Max. :90 Max. :48.8The marginal effects calculated manually at polyarchy levels of 30, 60, and 90 show different slopes at these points. Specifically, the marginal effect at polyarchy = 30 is approximately -0.064, indicating that polyarchy has a slight negative impact on public sector corruption at low levels. At polyarchy = 60, the marginal effect is -1.103, indicating a stronger negative relationship as polyarchy approaches a medium level. At polyarchy = 90, the marginal effect is -2.141, with a stronger negative impact at higher polyarchy levels. The marginal effects at these levels have been confirmed using the marginaleffects package. The marginal effects decrease, supporting the idea that polyarchy reduces public sector corruption more as it increases. Countries with more polyarchy reduce public sector corruption more.
TASK 3 Using the Civil dataset, fit a logistic regression model predicting the presence of campaign finance disclosure laws (disclose_donations) with public_sector_corruption and log_gdp_percapita as predictors. Use the sjPlot package to create regression tables and interpret the results.
# Fit the logistic regression model
model_logistic <- glm(disclose_donations ~ public_sector_corruption + log_gdp_percapita,
data = corruption,
family = binomial)
# Summarize the model
summary(model_logistic)##
## Call:
## glm(formula = disclose_donations ~ public_sector_corruption +
## log_gdp_percapita, family = binomial, data = corruption)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.50466 2.18953 -0.230 0.818
## public_sector_corruption -0.05964 0.01191 -5.007 5.54e-07 ***
## log_gdp_percapita 0.24907 0.21785 1.143 0.253
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 217.79 on 167 degrees of freedom
## Residual deviance: 131.30 on 165 degrees of freedom
## AIC: 137.3
##
## Number of Fisher Scoring iterations: 5# Create the regression table
tab_model(model_logistic, show.ci = TRUE, show.se = TRUE, show.p = TRUE)| Â | disclose_donations | |||
|---|---|---|---|---|
| Predictors | Odds Ratios | std. Error | CI | p |
| (Intercept) | 0.60 | 1.32 | 0.00 – Inf | 0.818 |
| public_sector_corruption | 0.94 | 0.01 | 0.00 – Inf | <0.001 |
|
GDP per capita (constant 2015 US$) |
1.28 | 0.28 | 0.00 – Inf | 0.253 |
| Observations | 168 | |||
| R2 Tjur | 0.454 | |||
The logistic regression model shows that the intercept has an odds ratio of 0.60, a standard error of 1.32, and a p-value of 0.818. This implies that when both public sector corruption and log GDP per capita are zero, the chances of having campaign finance disclosure laws are slightly lower than one, but this effect is not statistically significant. The odds ratio for public sector corruption is 0.94, which means that for every unit increase in public sector corruption, the chances of having campaign finance disclosure laws fall by about 6%. This estimate has a standard error of 0.01, indicating high precision, and a p-value less than 0.001, confirming that this relationship is statistically significant. The odds ratio for log GDP per capita is 1.28, indicating that higher GDP per capita increases the likelihood of campaign finance disclosure laws by 28%. The standard error is 0.28, and the p-value is 0.253, suggesting that this predictor is not statistically significant in the model. Tjur’s R² is 0.454, indicating that the model explains 45.4% of the variation in campaign finance disclosure laws. However, the confidence intervals for all predictors range from 0.00 to infinity, suggesting potential issues with the model’s fit or data.
TASK 4 Calculate the marginal effects of public_sector_corruption from the logistic regression model in Task 3 at representative values (20, 50, 80). Use the marginaleffects and emmeans packages to compute these effects. Visualize the predicted probabilities of having campaign finance disclosure laws across a range of public_sector_corruption values using ggplot2.
# Ensure the original data is used
newdata_for_slopes <- data.frame(public_sector_corruption = c(20, 50, 80),
log_gdp_percapita = mean(corruption$log_gdp_percapita))
# Calculate marginal effects using slopes()
marginal_effects_slopes <- slopes(model_logistic, newdata = newdata_for_slopes)
summary(marginal_effects_slopes)## rowid term estimate std.error
## Min. :1.00 Length:6 Min. :-0.014221 Min. :0.0008188
## 1st Qu.:1.25 Class :character 1st Qu.:-0.007893 1st Qu.:0.0018280
## Median :2.00 Mode :character Median : 0.003760 Median :0.0070514
## Mean :2.00 Mean : 0.013936 Mean :0.0179391
## 3rd Qu.:2.75 3rd Qu.: 0.032965 3rd Qu.:0.0307530
## Max. :3.00 Max. : 0.059394 Max. :0.0539726
## statistic p.value s.value conf.low
## Min. :-6.060 Min. :0.0000000 Min. : 1.321 Min. :-0.046391
## 1st Qu.:-5.134 1st Qu.:0.0009582 1st Qu.: 1.876 1st Qu.:-0.028727
## Median :-1.025 Median :0.1374871 Median : 4.955 Median :-0.015987
## Mean :-1.966 Mean :0.1580304 Mean :11.739 Mean :-0.021224
## 3rd Qu.: 1.033 3rd Qu.:0.2724973 3rd Qu.:22.915 3rd Qu.:-0.013022
## Max. : 1.100 Max. :0.4002592 Max. :29.451 Max. :-0.003973
## conf.high predicted_lo predicted_hi predicted
## Min. :-0.009621 Min. :0.04141 Min. :0.04141 Min. :0.04142
## 1st Qu.:-0.005059 1st Qu.:0.08243 1st Qu.:0.08241 1st Qu.:0.08242
## Median : 0.016083 Median :0.20546 Median :0.20542 Median :0.20544
## Mean : 0.049096 Mean :0.28477 Mean :0.28474 Mean :0.28476
## 3rd Qu.: 0.093239 3rd Qu.:0.50692 3rd Qu.:0.50687 3rd Qu.:0.50692
## Max. : 0.165178 Max. :0.60749 Max. :0.60743 Max. :0.60742
## public_sector_corruption log_gdp_percapita disclose_donations
## Min. :20.0 Min. :8.567 Mode:logical
## 1st Qu.:27.5 1st Qu.:8.567 TRUE:6
## Median :50.0 Median :8.567
## Mean :50.0 Mean :8.567
## 3rd Qu.:72.5 3rd Qu.:8.567
## Max. :80.0 Max. :8.567# Load the packages
library(emmeans)## Welcome to emmeans.
## Caution: You lose important information if you filter this package's results.
## See '? untidy'# Calculate marginal effects using emmeans
em_marginal_effects <- emmeans(model_logistic, ~ public_sector_corruption, at = list(public_sector_corruption = c(20, 50, 80)))
# Summarize the results
summary(em_marginal_effects)## public_sector_corruption emmean SE df asymp.LCL asymp.UCL
## 20 0.436 0.300 Inf -0.152 1.024
## 50 -1.353 0.279 Inf -1.899 -0.806
## 80 -3.142 0.567 Inf -4.252 -2.031
##
## Results are given on the logit (not the response) scale.
## Confidence level used: 0.95# Generate a sequence of public_sector_corruption values for prediction
public_sector_corruption_seq <- data.frame(public_sector_corruption = seq(0, 100, by = 1),
log_gdp_percapita = mean(corruption$log_gdp_percapita))
# Predict probabilities using the logistic model
predicted_probs <- predict(model_logistic, newdata = public_sector_corruption_seq, type = "response")
# Combine the predictions with the sequence of public_sector_corruption values
prediction_data <- cbind(public_sector_corruption_seq, predicted_probs)
# Plot the predicted probabilities using ggplot2
library(ggplot2)
ggplot(prediction_data, aes(x = public_sector_corruption, y = predicted_probs)) +
geom_line(color = "blue") +
labs(title = "Predicted Probabilities of Campaign Finance Disclosure Laws",
x = "Public Sector Corruption",
y = "Predicted Probability") +
theme_minimal()
TASK 5 Explore the interaction effect between public_sector_corruption and region in the logistic regression model from Task 3. Use the datagrid() function from the marginaleffects package to create a dataset with representative values for regions. Fit the logistic regression model with the interaction term and visualize the interaction effects using ggplot2. Interpret the results and discuss the implications of the interaction effect.
# Create a dataset with representative values for regions using datagrid()
representative_data <- datagrid(model = model_logistic,
region = unique(corruption$region),
public_sector_corruption = seq(0, 100, by = 10))## Warning: Some of the variable names are missing from the model data: region# Display the first few rows of the representative dataset
head(representative_data)## log_gdp_percapita region public_sector_corruption
## 1 8.567353 Latin America and the Caribbean 0
## 2 8.567353 Latin America and the Caribbean 10
## 3 8.567353 Latin America and the Caribbean 20
## 4 8.567353 Latin America and the Caribbean 30
## 5 8.567353 Latin America and the Caribbean 40
## 6 8.567353 Latin America and the Caribbean 50
## rowid
## 1 1
## 2 2
## 3 3
## 4 4
## 5 5
## 6 6# Fit the logistic regression model with the interaction term
model_interaction <- glm(disclose_donations ~ public_sector_corruption * region + log_gdp_percapita,
data = corruption,
family = binomial)
# Summarize the model
summary(model_interaction)##
## Call:
## glm(formula = disclose_donations ~ public_sector_corruption *
## region + log_gdp_percapita, family = binomial, data = corruption)
##
## Coefficients:
## Estimate
## (Intercept) 3.21658
## public_sector_corruption -0.06335
## regionLatin America and the Caribbean -2.47593
## regionMiddle East and North Africa -0.65585
## regionSub-Saharan Africa -1.61845
## regionWestern Europe and North America -1.05205
## regionAsia and Pacific -0.92044
## log_gdp_percapita 0.01539
## public_sector_corruption:regionLatin America and the Caribbean 0.02499
## public_sector_corruption:regionMiddle East and North Africa -0.05436
## public_sector_corruption:regionSub-Saharan Africa -0.02279
## public_sector_corruption:regionWestern Europe and North America -0.03829
## public_sector_corruption:regionAsia and Pacific -0.03145
## Std. Error
## (Intercept) 3.52849
## public_sector_corruption 0.02299
## regionLatin America and the Caribbean 1.53294
## regionMiddle East and North Africa 2.36552
## regionSub-Saharan Africa 1.79649
## regionWestern Europe and North America 1.57290
## regionAsia and Pacific 1.85141
## log_gdp_percapita 0.34500
## public_sector_corruption:regionLatin America and the Caribbean 0.03045
## public_sector_corruption:regionMiddle East and North Africa 0.06720
## public_sector_corruption:regionSub-Saharan Africa 0.03978
## public_sector_corruption:regionWestern Europe and North America 0.07872
## public_sector_corruption:regionAsia and Pacific 0.04645
## z value
## (Intercept) 0.912
## public_sector_corruption -2.755
## regionLatin America and the Caribbean -1.615
## regionMiddle East and North Africa -0.277
## regionSub-Saharan Africa -0.901
## regionWestern Europe and North America -0.669
## regionAsia and Pacific -0.497
## log_gdp_percapita 0.045
## public_sector_corruption:regionLatin America and the Caribbean 0.821
## public_sector_corruption:regionMiddle East and North Africa -0.809
## public_sector_corruption:regionSub-Saharan Africa -0.573
## public_sector_corruption:regionWestern Europe and North America -0.486
## public_sector_corruption:regionAsia and Pacific -0.677
## Pr(>|z|)
## (Intercept) 0.36198
## public_sector_corruption 0.00586 **
## regionLatin America and the Caribbean 0.10628
## regionMiddle East and North Africa 0.78158
## regionSub-Saharan Africa 0.36764
## regionWestern Europe and North America 0.50358
## regionAsia and Pacific 0.61908
## log_gdp_percapita 0.96442
## public_sector_corruption:regionLatin America and the Caribbean 0.41188
## public_sector_corruption:regionMiddle East and North Africa 0.41851
## public_sector_corruption:regionSub-Saharan Africa 0.56671
## public_sector_corruption:regionWestern Europe and North America 0.62666
## public_sector_corruption:regionAsia and Pacific 0.49833
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 217.79 on 167 degrees of freedom
## Residual deviance: 114.37 on 155 degrees of freedom
## AIC: 140.37
##
## Number of Fisher Scoring iterations: 7# Create the regression table
tab_model(model_interaction, show.ci = TRUE, show.se = TRUE, show.p = TRUE)| Â | disclose_donations | |||
|---|---|---|---|---|
| Predictors | Odds Ratios | std. Error | CI | p |
| (Intercept) | 24.94 | 88.01 | 0.00 – Inf | 0.362 |
| public_sector_corruption | 0.94 | 0.02 | 0.00 – Inf | 0.006 |
|
region: Latin America and the Caribbean |
0.08 | 0.13 | 0.00 – Inf | 0.106 |
|
region: Middle East and North Africa |
0.52 | 1.23 | 0.00 – Inf | 0.782 |
|
region: Sub-Saharan Africa |
0.20 | 0.36 | 0.00 – Inf | 0.368 |
|
region: Western Europe and North America |
0.35 | 0.55 | 0.00 – Inf | 0.504 |
| region: Asia and Pacific | 0.40 | 0.74 | 0.00 – Inf | 0.619 |
|
GDP per capita (constant 2015 US$) |
1.02 | 0.35 | 0.00 – Inf | 0.964 |
| public_sector_corruption:regionLatin America and the Caribbean | 1.03 | 0.03 | 0.00 – Inf | 0.412 |
| public_sector_corruption:regionMiddle East and North Africa | 0.95 | 0.06 | 0.00 – Inf | 0.419 |
| public_sector_corruption:regionSub-Saharan Africa | 0.98 | 0.04 | 0.00 – Inf | 0.567 |
| public_sector_corruption:regionWestern Europe and North America | 0.96 | 0.08 | 0.00 – Inf | 0.627 |
| public_sector_corruption:regionAsia and Pacific | 0.97 | 0.05 | 0.00 – Inf | 0.498 |
| Observations | 168 | |||
| R2 Tjur | 0.521 | |||
# Predict probabilities using the interaction model for the representative data
predicted_probs_interaction <- predict(model_interaction, newdata = representative_data, type = "response")
# Combine the predictions with the representative dataset
interaction_data <- cbind(representative_data, predicted_probs_interaction)
# Plot the interaction effects using ggplot2
library(ggplot2)
ggplot(interaction_data, aes(x = public_sector_corruption, y = predicted_probs_interaction, color = region)) +
geom_line() +
labs(title = "Interaction Effect of Public Sector Corruption and Region on Campaign Finance Disclosure Laws",
x = "Public Sector Corruption",
y = "Predicted Probability",
color = "Region") +
theme_minimal()
The logistic regression model shows that public sector corruption has a
significant negative effect on the likelihood of having campaign finance
disclosure laws, with an odds ratio of 0.94. This implies that for every
unit increase in public sector corruption, the odds of having such laws
decreases by about 6%. This relationship is statistically significant
(p-value = 0.006). However, the interaction terms between public sector
corruption and region are not statistically significant, implying that
the effect of corruption on the likelihood of enforcing disclosure laws
does not vary significantly across regions. The visualization of
interaction effects further supports these findings. As public sector
corruption increases, the predicted probability of having campaign
finance disclosure laws decreases, and this trend is observed across all
regions. However, the slopes of the lines are similar, indicating that
the impact of corruption on the likelihood of adopting disclosure laws
is not significantly different across regions. For example, in Eastern
Europe and Central Asia, the probability begins high but gradually
declines as corruption increases, similar to patterns seen in other
regions such as Latin America and the Caribbean, Western Europe, and
North America. The uniformity of these slopes suggests that, while
corruption reduces the likelihood of disclosure laws, this effect is not
significantly influenced by regional differences.