Class Project Assignment 2

Matt Eckstein

Author

Matt Eckstein

Published

August 18, 2023

Code

library(tidyverse)
library(AER)
library(dplyr)
library(readxl)

knitr::opts_chunk$set(echo = TRUE)

1. Multiple regression models

\[ NetApprove_{i} = \beta_{0} + \beta _{1} × pctox \]

\[ NetApprove_{i} = \beta_{0} + \beta _{1} × pctox + \beta _{2} × netsentiment \] \[ NetApprove_{i} = \beta_{0} + \beta _{1} × pctox + \beta _{2} × bordruua \] \[ NetApprove_{i} = \beta_{0} + \beta _{1} × pctox + \beta _{2} × netsentiment + \beta _{3} × bordruua \] \[ NetApprove_{i} = \beta_{0} + \beta _{1} × pctox + \beta _{2} × strongru \] \[ NetApprove_{i} = \beta_{0} + \beta _{1} × pctox + \beta _{2} × closewest \]

#2a.

Code

data <- read_csv("Eckstein_data/Orthodoxy_and_US_leadership_cleaned.csv")

Rows: 17 Columns: 18
-- Column specification --------------------------------------------------------
Delimiter: ","
chr  (4): Country, Estimated 2010
Catholic Population, Estimated 2010
Protes...
dbl (12): bordru, bordua, bordruua, pctox, approve, disapprove, dkref, 20212...
num  (2): Estimated 2010
Orthodox Population, totalpop

i Use `spec()` to retrieve the full column specification for this data.
i Specify the column types or set `show_col_types = FALSE` to quiet this message.

Code

data$pctox <- data$pctox * 100
summary(data)

   Country          Estimated 2010\nCatholic Population
 Length:17          Length:17                          
 Class :character   Class :character                   
 Mode  :character   Mode  :character                   
                                                       
                                                       
                                                       
 Estimated 2010\nProtestant Population Estimated 2010\nOrthodox Population
 Length:17                             Min.   :    20000                  
 Class :character                      1st Qu.:   250000                  
 Mode  :character                      Median :  2680000                  
                                       Mean   : 11231176                  
                                       3rd Qu.:  6730000                  
                                       Max.   :101450000                  
 Estimated 2010 Population of Other Christians    totalpop        
 Length:17                                     Min.   :  1331535  
 Class :character                              1st Qu.:  3678186  
 Mode  :character                              Median :  7291436  
                                               Mean   : 18790613  
                                               3rd Qu.: 11033783  
                                               Max.   :143242599  
     bordru           bordua          bordruua          pctox      
 Min.   :0.0000   Min.   :0.0000   Min.   :0.0000   Min.   : 0.20  
 1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.: 5.42  
 Median :0.0000   Median :0.0000   Median :1.0000   Median :70.82  
 Mean   :0.4118   Mean   :0.3529   Mean   :0.5882   Mean   :51.39  
 3rd Qu.:1.0000   3rd Qu.:1.0000   3rd Qu.:1.0000   3rd Qu.:90.96  
 Max.   :1.0000   Max.   :1.0000   Max.   :1.0000   Max.   :99.56  
    approve         disapprove         dkref          202122chg  
 Min.   :0.0400   Min.   :0.0800   Min.   :0.1200   Min.   :-31  
 1st Qu.:0.2700   1st Qu.:0.2900   1st Qu.:0.1900   1st Qu.: -9  
 Median :0.3300   Median :0.3400   Median :0.2000   Median : -3  
 Mean   :0.3653   Mean   :0.3918   Mean   :0.2424   Mean   :  0  
 3rd Qu.:0.4100   3rd Qu.:0.4700   3rd Qu.:0.3000   3rd Qu.:  9  
 Max.   :0.8000   Max.   :0.7700   Max.   :0.4200   Max.   : 30  
   netapprove         strongru    closewest      netsentiment   
 Min.   :-73.000   Min.   :22   Min.   :48.00   Min.   :-30.00  
 1st Qu.:-21.000   1st Qu.:40   1st Qu.:61.00   1st Qu.: -8.00  
 Median :  2.000   Median :52   Median :66.00   Median : 18.00  
 Mean   : -2.647   Mean   :53   Mean   :64.76   Mean   : 11.76  
 3rd Qu.: 14.000   3rd Qu.:61   3rd Qu.:69.00   3rd Qu.: 30.00  
 Max.   : 72.000   Max.   :85   Max.   :82.00   Max.   : 40.00

#2b. Customizing variable names

Code

#Most of my variable names are good as they are; though, here, I create and name additional variables that will be helpful in my analysis 

# Create a vector to store the oxbucket values
oxbucket <- character(length(data$pctox))

# Assign values to oxbucket based on pctox
oxbucket[data$pctox < 2] <- "<2%"
oxbucket[data$pctox >= 2 & data$pctox < 5] <- "2-5%"
oxbucket[data$pctox >= 5 & data$pctox < 10] <- "5-10%"
oxbucket[data$pctox >= 10 & data$pctox < 25] <- "10-25%"
oxbucket[data$pctox >= 25 & data$pctox < 50] <- "25-50%"
oxbucket[data$pctox >= 50 & data$pctox < 75] <- "50-75%"
oxbucket[data$pctox >= 75 & data$pctox < 100] <- "75-100%"

# Add the oxbucket variable to the data frame
data$oxbucket <- oxbucket

avgs <- data %>%
  group_by(bordruua, oxbucket) %>%
  summarize(mean(netapprove),
  sd(netapprove),
  n())

`summarise()` has grouped output by 'bordruua'. You can override using the
`.groups` argument.

Code

border <- avgs %>% dplyr::filter(bordruua == 1)
noborder <- avgs %>% dplyr::filter(bordruua == 0)


colnames(border) <- c("Border_war", "Percent_orthodox", "mean_net_approval", "SD_net_approval", "number")
colnames(noborder) <- c("Border_war", "Percent_orthodox", "mean_net_approval", "SD_net_approval", "number")

#2c. Designating regressors and reporting means and SDs

Code

vars <- c("pctox", "netsentiment", "bordruua", "strongru", "closewest")

cbind(allvars_mean = sapply(data[, vars], mean),
allvars_sd = sapply(data[, vars], sd))

             allvars_mean allvars_sd
pctox          51.3911765 40.9699643
netsentiment   11.7647059 22.5652648
bordruua        0.5882353  0.5072997
strongru       53.0000000 18.2688259
closewest      64.7647059  8.0972944

#2d. Basic linear equation

Code

model <- lm(data$netapprove ~ data$pctox)
model


Call:
lm(formula = data$netapprove ~ data$pctox)

Coefficients:
(Intercept)   data$pctox  
     9.8367      -0.2429

Code

summary(model)


Call:
lm(formula = data$netapprove ~ data$pctox)

Residuals:
    Min      1Q  Median      3Q     Max 
-65.633 -22.724   0.684  21.560  62.484 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)
(Intercept)   9.8367    14.3169   0.687    0.503
data$pctox   -0.2429     0.2204  -1.102    0.288

Residual standard error: 36.11 on 15 degrees of freedom
Multiple R-squared:  0.07494,   Adjusted R-squared:  0.01327 
F-statistic: 1.215 on 1 and 15 DF,  p-value: 0.2877

#2e. (Prompt 2e is identical to prompt 2d; see answer 2d)

#2f. Linear-log model

Code

Linearlog_model <- lm(netapprove ~ log(pctox), data = data)
Linearlog_model


Call:
lm(formula = netapprove ~ log(pctox), data = data)

Coefficients:
(Intercept)   log(pctox)  
      9.870       -4.233

Code

summary(Linearlog_model)


Call:
lm(formula = netapprove ~ log(pctox), data = data)

Residuals:
    Min      1Q  Median      3Q     Max 
-64.839 -17.429  -2.699  18.278  63.305 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)
(Intercept)    9.870     15.581   0.633    0.536
log(pctox)    -4.233      4.341  -0.975    0.345

Residual standard error: 36.41 on 15 degrees of freedom
Multiple R-squared:  0.05961,   Adjusted R-squared:  -0.003086 
F-statistic: 0.9508 on 1 and 15 DF,  p-value: 0.345

#2g. Cubic model

Code

cubic_model <- lm(netapprove ~ I(pctox) + I(pctox^2) + I(pctox^3), data =
data)
cubic_model


Call:
lm(formula = netapprove ~ I(pctox) + I(pctox^2) + I(pctox^3), 
    data = data)

Coefficients:
(Intercept)     I(pctox)   I(pctox^2)   I(pctox^3)  
 15.0842278   -0.5664232   -0.0102011    0.0001475

Code

summary(cubic_model)


Call:
lm(formula = netapprove ~ I(pctox) + I(pctox^2) + I(pctox^3), 
    data = data)

Residuals:
    Min      1Q  Median      3Q     Max 
-49.206 -26.290  -4.445  10.840  71.997 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)
(Intercept) 15.0842278 19.7419850   0.764    0.458
I(pctox)    -0.5664232  2.6229253  -0.216    0.832
I(pctox^2)  -0.0102011  0.0659589  -0.155    0.879
I(pctox^3)   0.0001475  0.0004444   0.332    0.745

Residual standard error: 37.58 on 13 degrees of freedom
Multiple R-squared:  0.132, Adjusted R-squared:  -0.06826 
F-statistic: 0.6592 on 3 and 13 DF,  p-value: 0.5916

#2h. Plot the observations and add the linear, log-linear, and cubic models

Code

plot <- plot(data$pctox, data$netapprove,
pch = 20,
col = "steelblue",
xlab = "Percent Orthodox",
ylab = "Net Approval of US Leadership",
xlim = c(0, 100),
ylim = c(-100, 100))
abline(model, lwd = 2)
order_id <- order(data$pctox)
lines(data$pctox[order_id],
fitted(Linearlog_model)[order_id],
col = "darkgreen",
lwd = 2)
lines(x = data$pctox[order_id],
y = fitted(cubic_model)[order_id],
col = "orange",
lwd = 2)
legend("topleft",
legend = c("Linear", "Linear-Log", "Cubic"),
lty = 1,
col = c("Black", "darkgreen", "orange"))

#3:

Visually speaking, none of the three representations (linear, linear-log, or cubic) is drastically different from the other two. The linear and linear-log models are extremely similar except for a slight upward hook at the left side of the graph in the linear-log model, and this makes the model neither noticeably better nor noticeably worse than the linear model.

The cubic model arguably follows the points slightly better than the other two models, but this is thanks to a dip in the model line at around 70% Orthodox that appears to be driven in large part by one point (Russia’s) with the lowest net approval of US leadership of any country in the dataset. Given the apparent ability of the curve to be noticeably influenced by this single point, it is likely that this model is overfitted. As such, there is no apparent advantage to choosing a non-linear model for this analysis.

#4a.

Code

model <- lm(data$netapprove ~ data$pctox)
model2 <- lm(data$netapprove ~ data$pctox + data$netsentiment)
model3 <- lm(data$netapprove ~ data$pctox + data$bordruua)
model4 <- lm(data$netapprove ~ data$pctox + data$bordruua + data$netsentiment)
model5 <- lm(data$netapprove ~ data$pctox + data$strongru)
model6 <- lm(data$netapprove ~ data$pctox + data$closewest)
print(model)


Call:
lm(formula = data$netapprove ~ data$pctox)

Coefficients:
(Intercept)   data$pctox  
     9.8367      -0.2429

Code

print(model2)


Call:
lm(formula = data$netapprove ~ data$pctox + data$netsentiment)

Coefficients:
      (Intercept)         data$pctox  data$netsentiment  
         -27.9698             0.1812             1.3610

Code

print(model3)


Call:
lm(formula = data$netapprove ~ data$pctox + data$bordruua)

Coefficients:
  (Intercept)     data$pctox  data$bordruua  
      -5.9958        -0.2082        23.8848

Code

print(model4)


Call:
lm(formula = data$netapprove ~ data$pctox + data$bordruua + data$netsentiment)

Coefficients:
      (Intercept)         data$pctox      data$bordruua  data$netsentiment  
         -27.4665             0.1861            -1.7612             1.3849

Code

print(model5)


Call:
lm(formula = data$netapprove ~ data$pctox + data$strongru)

Coefficients:
  (Intercept)     data$pctox  data$strongru  
      72.0073         0.1514        -1.5553

Code

print(model6)


Call:
lm(formula = data$netapprove ~ data$pctox + data$closewest)

Coefficients:
   (Intercept)      data$pctox  data$closewest  
     -125.7743         -0.1266          2.0016

Code

summary(model)


Call:
lm(formula = data$netapprove ~ data$pctox)

Residuals:
    Min      1Q  Median      3Q     Max 
-65.633 -22.724   0.684  21.560  62.484 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)
(Intercept)   9.8367    14.3169   0.687    0.503
data$pctox   -0.2429     0.2204  -1.102    0.288

Residual standard error: 36.11 on 15 degrees of freedom
Multiple R-squared:  0.07494,   Adjusted R-squared:  0.01327 
F-statistic: 1.215 on 1 and 15 DF,  p-value: 0.2877

Code

summary(model2)


Call:
lm(formula = data$netapprove ~ data$pctox + data$netsentiment)

Residuals:
    Min      1Q  Median      3Q     Max 
-20.565 -17.029  -7.454   5.419  64.628 

Coefficients:
                  Estimate Std. Error t value Pr(>|t|)   
(Intercept)       -27.9698    14.0341  -1.993  0.06613 . 
data$pctox          0.1812     0.1907   0.950  0.35831   
data$netsentiment   1.3610     0.3463   3.930  0.00151 **
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 25.78 on 14 degrees of freedom
Multiple R-squared:  0.5602,    Adjusted R-squared:  0.4973 
F-statistic: 8.915 on 2 and 14 DF,  p-value: 0.003184

Code

summary(model3)


Call:
lm(formula = data$netapprove ~ data$pctox + data$bordruua)

Residuals:
    Min      1Q  Median      3Q     Max 
-76.142 -10.584  -5.222  10.310  54.936 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)
(Intercept)    -5.9958    18.0802  -0.332    0.745
data$pctox     -0.2082     0.2157  -0.966    0.351
data$bordruua  23.8848    17.4168   1.371    0.192

Residual standard error: 35.1 on 14 degrees of freedom
Multiple R-squared:  0.1845,    Adjusted R-squared:  0.06798 
F-statistic: 1.584 on 2 and 14 DF,  p-value: 0.2399

Code

summary(model4)


Call:
lm(formula = data$netapprove ~ data$pctox + data$bordruua + data$netsentiment)

Residuals:
    Min      1Q  Median      3Q     Max 
-20.476 -15.797  -7.179   5.867  64.086 

Coefficients:
                  Estimate Std. Error t value Pr(>|t|)   
(Intercept)       -27.4665    15.2018  -1.807  0.09398 . 
data$pctox          0.1861     0.2024   0.919  0.37463   
data$bordruua      -1.7612    15.3332  -0.115  0.91031   
data$netsentiment   1.3849     0.4152   3.336  0.00536 **
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 26.74 on 13 degrees of freedom
Multiple R-squared:  0.5606,    Adjusted R-squared:  0.4592 
F-statistic: 5.529 on 3 and 13 DF,  p-value: 0.0114

Code

summary(model5)


Call:
lm(formula = data$netapprove ~ data$pctox + data$strongru)

Residuals:
    Min      1Q  Median      3Q     Max 
-23.523 -17.892  -3.459   3.915  73.318 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)   
(Intercept)    72.0073    21.5210   3.346  0.00480 **
data$pctox      0.1514     0.2062   0.734  0.47502   
data$strongru  -1.5553     0.4624  -3.363  0.00464 **
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 27.8 on 14 degrees of freedom
Multiple R-squared:  0.4884,    Adjusted R-squared:  0.4153 
F-statistic: 6.681 on 2 and 14 DF,  p-value: 0.009179

Code

summary(model6)


Call:
lm(formula = data$netapprove ~ data$pctox + data$closewest)

Residuals:
    Min      1Q  Median      3Q     Max 
-48.347 -22.549  -6.299  16.072  61.334 

Coefficients:
                Estimate Std. Error t value Pr(>|t|)  
(Intercept)    -125.7743    74.5317  -1.688   0.1136  
data$pctox       -0.1266     0.2139  -0.592   0.5633  
data$closewest    2.0016     1.0825   1.849   0.0857 .
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 33.51 on 14 degrees of freedom
Multiple R-squared:  0.2565,    Adjusted R-squared:  0.1503 
F-statistic: 2.415 on 2 and 14 DF,  p-value: 0.1256

#4b.

Code

rob_se <- list(sqrt(diag(vcovHC(model, type = "HC1"))),
sqrt(diag(vcovHC(model2, type = "HC1"))),
sqrt(diag(vcovHC(model3, type = "HC1"))),
sqrt(diag(vcovHC(model4, type = "HC1"))),
sqrt(diag(vcovHC(model5, type = "HC1"))),
sqrt(diag(vcovHC(model6, type = "HC1"))))

#4c.

Code

library(stargazer)


Please cite as:

 Hlavac, Marek (2022). stargazer: Well-Formatted Regression and Summary Statistics Tables.

 R package version 5.2.3. https://CRAN.R-project.org/package=stargazer

Code

stargazer(model, model2, model3,
model4, model5, model6,
title = "Regressions of Orthodox Christian Religious ID and Net Approval of US Leadership",
type = "html",
digits = 3,
header = FALSE,
se = rob_se,
object.names = TRUE,
model.numbers = FALSE,
column.labels = c("(I)", "(II)", "(III)", "(IV)", "(V)", "(VI)"))

**Regressions of Orthodox Christian Religious ID and Net Approval of US Leadership**

	Dependent variable:

	netapprove
	(I)	(II)	(III)	(IV)	(V)	(VI)
	model	model2	model3	model4	model5	model6

pctox	-0.243	0.181	-0.208	0.186	0.151	-0.127
	(0.207)	(0.131)	(0.189)	(0.153)	(0.116)	(0.183)

netsentiment		1.361^***		1.385^***
		(0.318)		(0.287)

bordruua			23.885	-1.761
			(15.950)	(11.926)

strongru					-1.555^***
					(0.514)

closewest						2.002^**
						(0.780)

Constant	9.837	-27.970^***	-5.996	-27.466^**	72.007^***	-125.774^**
	(12.324)	(10.611)	(11.042)	(11.524)	(25.230)	(52.850)


Observations	17	17	17	17	17	17
R²	0.075	0.560	0.184	0.561	0.488	0.257
Adjusted R²	0.013	0.497	0.068	0.459	0.415	0.150
Residual Std. Error	36.114 (df = 15)	25.776 (df = 14)	35.098 (df = 14)	26.735 (df = 13)	27.801 (df = 14)	33.512 (df = 14)
F Statistic	1.215 (df = 1; 15)	8.915^*** (df = 2; 14)	1.584 (df = 2; 14)	5.529^** (df = 3; 13)	6.681^*** (df = 2; 14)	2.415 (df = 2; 14)

Note:	p<0.1; p<0.05; p<0.01

#4d. Linear hypothesis tests (F-tests) for each model:

Code

#Note the white.adjust robust fix for handling heteroskedasticity

linearHypothesis(model, c("data$pctox=0"), white.adjust = "hc1")

Linear hypothesis test

Hypothesis:
data$pctox = 0

Model 1: restricted model
Model 2: data$netapprove ~ data$pctox

Note: Coefficient covariance matrix supplied.

  Res.Df Df     F Pr(>F)
1     16                
2     15  1 1.382 0.2581

Code

linearHypothesis(model2, c("data$netsentiment=0", "data$pctox=0"), white.adjust = "hc1")

Linear hypothesis test

Hypothesis:
data$netsentiment = 0
data$pctox = 0

Model 1: restricted model
Model 2: data$netapprove ~ data$pctox + data$netsentiment

Note: Coefficient covariance matrix supplied.

  Res.Df Df      F   Pr(>F)   
1     16                      
2     14  2 10.277 0.001793 **
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Code

linearHypothesis(model3, c("data$bordruua=0", "data$pctox=0"), white.adjust = "hc1")

Linear hypothesis test

Hypothesis:
data$bordruua = 0
data$pctox = 0

Model 1: restricted model
Model 2: data$netapprove ~ data$pctox + data$bordruua

Note: Coefficient covariance matrix supplied.

  Res.Df Df     F Pr(>F)
1     16                
2     14  2 1.525 0.2517

Code

linearHypothesis(model4, c("data$netsentiment=0", "data$pctox=0", "data$bordruua=0"), white.adjust = "hc1")

Linear hypothesis test

Hypothesis:
data$netsentiment = 0
data$pctox = 0
data$bordruua = 0

Model 1: restricted model
Model 2: data$netapprove ~ data$pctox + data$bordruua + data$netsentiment

Note: Coefficient covariance matrix supplied.

  Res.Df Df      F   Pr(>F)   
1     16                      
2     13  3 7.8231 0.003093 **
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Code

linearHypothesis(model5, c("data$pctox=0", "data$strongru=0"), white.adjust = "hc1")

Linear hypothesis test

Hypothesis:
data$pctox = 0
data$strongru = 0

Model 1: restricted model
Model 2: data$netapprove ~ data$pctox + data$strongru

Note: Coefficient covariance matrix supplied.

  Res.Df Df      F  Pr(>F)  
1     16                    
2     14  2 5.6243 0.01612 *
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Code

linearHypothesis(model6, c("data$pctox=0", "data$closewest=0"), white.adjust = "hc1")

Linear hypothesis test

Hypothesis:
data$pctox = 0
data$closewest = 0

Model 1: restricted model
Model 2: data$netapprove ~ data$pctox + data$closewest

Note: Coefficient covariance matrix supplied.

  Res.Df Df     F  Pr(>F)  
1     16                   
2     14  2 3.505 0.05833 .
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#5.

I have examined the influence of the percentage of Eastern European countries’ populations that identify as Orthodox Christian, as measured by Pew Research, on their populations’ net approval of US leadership in the world (the difference between the share of people who expressed approval and the share who expressed disapproval), as measured by Gallup.

I have considered a series of six models for examining contributing factors in this relationship:

-model (I), which uses the percentage of countries’ populations identifying as Orthodox (pctox) as the sole independent variable to explain variation in net approval of US leadership (netapprove) -model (II), which uses both pctox and netsentiment, a variable that measures the difference in each surveyed country between the percentages of respondents who agree with the statements “It is in our country’s interest to work closely with the U.S. and other Western powers” and “A strong Russia is necessary to balance the influence of the West.” -model (III), which uses both pctox and bordruua, a dummy variable that accounts for geographic proximity to the Russia-Ukraine conflict and takes the value 1 in countries that border Russia and/or Ukraine and 0 in countries that do not border either -model (IV), which uses pctox, netsentiment, and bordruua together -model (V), which uses pctox and strongru, a variable that codes for levels of agreement with the statement “A strong Russia is necessary to balance the influence of the West” -model (VI), which uses pctox and closewest, a variable that codes for levels of agreement with the statement “It is in our country’s interest to work closely with the U.S. and other Western powers”

I began this analysis hypothesizing that the share of countries’ populations that identify as Orthodox would negatively predict public approval of US leadership, due to Russia’s history as a major influence on public opinion in the Orthodox world and its use of Orthodox religious themes in anti-Western political propaganda attempting to justify actions such as its invasion of Ukraine. When I used pctox as my sole independent variable in model (I), it was negatively signed, but not statistically significant. In the other models where it was included alongside other variables, its sign was sometimes positive and sometimes negative, but it never attained statistical significance, meaning that I did not find evidence in favor of my initial hypothesis.

I did find, though, that inclusion of the netsentiment variable measuring the difference between respondents’ endorsement of the pro-Western statement and their endorsement of the pro-Russian statement resulted in its significance as a predictor of net approval of US leadership. Similarly, including the pro-Western statement or the pro-Russian statement alone without making any reference to the other also resulted in statistical significance as a predictor of net approval of US leadership. In model II, the coefficient on netsentiment of 1.361 was statistically significant at the 1% level, meaning that an increase in netsentiment of one percentage point, holding all else constant, led to an increase in US leadership approval of 1.361 percentage points and that there was a less than one percent chance of the study finding a value at least as extreme as the one observed in the absence of a true relationship. In model IV, the coefficient on netsentiment was a very similar 1.385, also significant at the 1% level. Model V found that the coefficient on strongru, measuring agreement with the pro-Russian statement, was -1.555, and that this finding was also significant at the 1% level. This means that, if all other variables’ values are held constant, increasing a surveyed country’s agreement that a strong Russia is necessary to balance the West by one percentage point led to a 1.555 percentage point decrease in net approval of US leadership. Conversely, in Model VI, the coefficient on closewest was 2.002, meaning that, holding all else constant, increasing a country’s agreement with the pro-Western statement by one percentage point led to a 2.002 percentage point increase in net approval of US leadership. However, this was a somewhat weaker finding, being statistically significant at the 5% level, meaning that there was a less than 5% but greater than 1% chance of finding a value at least as extreme as the one observed in the absence of a true relationship.

In no model was the bordruua variable, measuring whether or not a country borders Russia and/or Ukraine, statistically significant, meaning that this analysis did not find evidence of geographic proximity to the Russian invasion of Ukraine as a meaningful predictor of attitudes towards US leadership.

Considering these factors, although no model found statistical significance of the predictor I set out to investigate, the model that best explains the relationship between Orthodox Christian religious affiliation and views of US leadership is model (II). It finds a potential alternative explanation, netsentiment, highly statistically significant. Furthermore, an F-test finds that the model has a p-value of 0.001793, meaning that, if the model’s variables were collectively not truly related to net approval of US leadership, there would be only a 1 in 558 chance of data at least as extreme as what was observed occurring by chance. The significance of netsentiment sheds light on where some of the impact I expected to come from pctox is actually coming from and thus provides insights into why pctox lacks significance.

This analysis has a few limitations. Notably, it does not include a variable measuring the percentage of ethnic Russians in the included countries, because no dataset was available that measured this variable across countries in a consistent manner. This poses a risk of omitted variable bias, meaning that the absence of this factor from the analysis could cause have distorted the estimates of some coefficients. Of the included countries, those with large minorities of ethnic Russians and where the majority ethnic group has few adherents of Orthodox Christianity - that is, Estonia and Latvia - are most likely to be affected, since some of the effects the model is attributing to Orthodox religious affiliation may in fact be caused at least in part by Russian ethnic identity. Also, the small sample size of 17 countries can result in large confidence intervals for some estimates, meaning that there is a risk of some estimated values being further from their true values than they would have been with a larger sample. The scope of this risk, though, is limited, since the small number of countries in Eastern Europe will automatically limit the scope of the data - the sample of 17 is a relatively large share of the entire universe of Eastern European countries. Additionally, this analysis would have benefited from, and future analysis would benefit from, availability of data at a more granular level, to analyze the relationship between Orthodox identity and approval of US leadership in the world broken down by sub-national dimensions such as administrative division (province, oblast, etc.), age, gender, and ethnicity.

While the missing data on Russian ethnicity threatens some aspects of internal validity, the scope of this threat is limited. While the lack of data on Russian ethnicity may cause some distortion of results when it comes to Estonia and Latvia, the risk of distortion of results via conflation of the impacts of Russian ethnicity with those of Orthodox religious affiliation is relatively low elsewhere. The netsentiment variable, by measuring the difference between national publics’ feelings towards the West and their feelings towards Russia, is a suitable regressor for accounting for non-religious political factors that impact Eastern Europeans’ views of US leadership in the world. The credibility of the Pew Research Center and Gallup as data sources likely means the risk of an errors-in-variables bias caused by mismeasuring values of variables is quite low. Furthermore, the risk of simultaneous causality bias, the phenomenon wherein a dependent and an independent variable are causes of each other, is also low, since it seems much less likely (although theoretically possible) for a person to change their religious affiliation as a result of their views of US leadership than it does for a person’s pre-existing religious affiliation to affect their views of US leadership.

External validity of this analysis is likely strong, because the countries included in the study are roughly representative of Eastern European countries as a whole, and each variable has a consistent time and source for every included country.