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regression_analysis.R
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regression_analysis.R
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## Loading libraries
library(ggplot2)
library(nnet)
library(reshape2)
library(caret)
library(car)
library(plm)
library(stargazer)
library(mlogit)
library(jtools)
### Reading in the dataset
f = "data.csv"
df_Mig <- read.table(f, sep = ",", header = T)
colnames(df_Mig) <- gsub("\\.", "", colnames(df_Mig))
### Plotting the proportion of each outcome category
barplot(prop.table(table(df_Mig$Migration))* 100)
### Checking and adjusting type of variables
str(df_Mig)
df_Mig$Migration <- as.factor(df_Mig$Migration)
df_Mig$Internalmigration <- as.factor(df_Mig$Internalmigration)
df_Mig$Internationalmigration <- as.factor(df_Mig$Internationalmigration)
# df_Mig$kebele <- as.factor(df_Mig$kebele)
### Definition of the models (multinomial logit)
model_test <- multinom(Migration ~ AgeHHhead + Ethnicminority + Sexratio +
Marriedfemales + Tempanomaly*zone + Precanomaly*zone,data=df_Mig)
# Total migration
model1 <- multinom(Migration ~ AgeHHhead + FemaleHHhead + SecondaryeducationHHhead + HHsize + Ethnicminority
+ Sexratio + Marriedfemales + Marriedmales + lnsavings1 + Nonfarmincome
+ Tempanomaly + Tempanomaly1 + Precanomaly + Precanomaly1 + zone, data=df_Mig)
# Internal migration
model2 <- multinom(Internalmigration ~ AgeHHhead + FemaleHHhead + SecondaryeducationHHhead + HHsize + Ethnicminority
+ Sexratio + Marriedfemales + Marriedmales + lnsavings1 + Nonfarmincome
+ Tempanomaly + Tempanomaly1 + Precanomaly + Precanomaly1 + zone, data=df_Mig)
# International migration
model3 <- multinom(Internationalmigration ~ AgeHHhead + FemaleHHhead + SecondaryeducationHHhead + HHsize + Ethnicminority
+ Sexratio + Marriedfemales + Marriedmales + lnsavings1 + Nonfarmincome
+ Tempanomaly + Tempanomaly1 + Precanomaly + Precanomaly1 + zone, data=df_Mig)
### Adding interaction terms (savings x weather shocks for all three model definitions)
model1_inter = multinom(Migration ~ AgeHHhead + FemaleHHhead + SecondaryeducationHHhead + HHsize + Ethnicminority
+ Sexratio + Marriedfemales + Marriedmales + lnsavings1 + Nonfarmincome
+ Tempanomaly + Tempanomaly1 + Precanomaly + Precanomaly1
+ Tempanomaly:lnsavings1 + Tempanomaly1:lnsavings1 + Precanomaly:lnsavings1 + Precanomaly1:lnsavings1
+ zone, data=df_Mig)
model2_inter = multinom(Internalmigration ~ AgeHHhead + FemaleHHhead + SecondaryeducationHHhead + HHsize + Ethnicminority
+ Sexratio + Marriedfemales + Marriedmales + lnsavings1 + Nonfarmincome
+ Tempanomaly + Tempanomaly1 + Precanomaly + Precanomaly1
+ Tempanomaly:lnsavings1 + Tempanomaly1:lnsavings1 + Precanomaly:lnsavings1 + Precanomaly1:lnsavings1
+ zone, data=df_Mig)
model3_inter = multinom(Internationalmigration ~ AgeHHhead + FemaleHHhead + SecondaryeducationHHhead + HHsize + Ethnicminority
+ Sexratio + Marriedfemales + Marriedmales + lnsavings1 + Nonfarmincome
+ Tempanomaly + Tempanomaly1 + Precanomaly + Precanomaly1
+ Tempanomaly:lnsavings1 + Tempanomaly1:lnsavings1 + Precanomaly:lnsavings1 + Precanomaly1:lnsavings1
+ zone, data=df_Mig)
### Testing alternative model definitions
# First: without zone-specific fixed effects
# Second: only significant variables
# Third: only with intercept
model1_nozone <- multinom(Migration ~ AgeHHhead + FemaleHHhead + SecondaryeducationHHhead + HHsize + Ethnicminority
+ Sexratio + Marriedfemales + Marriedmales + lnsavings1 + Nonfarmincome
+ Tempanomaly + Tempanomaly1 + Precanomaly + Precanomaly1, data=df_Mig)
model1_sig <- multinom(Migration ~ AgeHHhead + FemaleHHhead + HHsize
+ Marriedmales + Nonfarmincome
+ Tempanomaly + Tempanomaly1 + Precanomaly + Precanomaly1 + zone, data=df_Mig)
OIM <- multinom(Migration ~ 1, data = df_Mig)
### Summarizing the model results
summary(model1)
broom::tidy(model1)
broom::tidy(model1_inter)
broom::tidy(model3)
### Anova
Anova(model1_sig)
Anova(model1_inter)
Anova(model3_inter)
# E.g. results of model 1 with interaction terms:
# Analysis of Deviance Table (Type II tests)
# LR Chisq Df Pr(>Chisq)
# AgeHHhead 51.444 2 6.746e-12 ***
# FemaleHHhead 64.184 2 1.155e-14 ***
# SecondaryeducationHHhead 0.000 2 0.9997768
# HHsize 109.037 2 < 2.2e-16 ***
# Ethnicminority 2.521 2 0.2834510
# Sexratio 3.821 2 0.1479939
# Marriedfemales 1.242 2 0.5373002
# Marriedmales 16.120 2 0.0003159 ***
# lnsavings1 4.200 2 0.1224565
# Nonfarmincome 13.482 2 0.0011813 **
# Tempanomaly 0.000 2 1.0000000
# Tempanomaly1 0.000 2 0.9999385
# Precanomaly 0.000 2 1.0000000
# Precanomaly1 0.000 2 1.0000000
# zone 18.369 16 0.3027280
# lnsavings1:Tempanomaly 10.931 2 0.0042308 ** --> interaction with savings significant
# lnsavings1:Tempanomaly1 2.363 2 0.3068885
# lnsavings1:Precanomaly 12.361 2 0.0020693 ** --> interaction with savings significant
# lnsavings1:Precanomaly1 0.421 2 0.8102093
### Comparing the Akaike information criteria
AIC(OIM) # only with intercept: 2418.63
AIC(model1) # 2151.264
AIC(model1_sig) # 2146.35
AIC(model1_inter) # 2146.642
AIC(model2_inter) # 2157.805
AIC(model3_inter) # 1700.358 # model with international migration as dependent variable has the best fit
### Validation based on confusion matrix
test <- predict(model1,data=df_Mig)
real_pred <- data.frame(real=df_Mig$Migration,test=as.character(test))
cmat <- caret::confusionMatrix(real_pred$real,real_pred$test)
test <- predict(model3,data=df_Mig)
real_pred <- data.frame(real=df_Mig$Internationalmigration,test=as.character(test))
cmat <- caret::confusionMatrix(real_pred$real,real_pred$test)
# E.g. results for model 3:
# Confusion Matrix and Statistics
#
# Reference
# Prediction 0 1 2
# 0 706 1 77
# 1 88 1 11
# 2 181 1 136
#
# Overall Statistics
#
# Accuracy : 0.7013
# 95% CI : (0.6746, 0.7271)
# No Information Rate : 0.8111
# P-Value [Acc > NIR] : 1
# Kappa : 0.2913
# Mcnemar's Test P-Value : <2e-16
#
# Statistics by Class:
#
# Class: 0 Class: 1 Class: 2
# Sensitivity 0.7241 0.3333333 0.6071
# Specificity 0.6564 0.9174312 0.8139
# Pos Pred Value 0.9005 0.0100000 0.4277
# Neg Pred Value 0.3565 0.9981851 0.9005
# Prevalence 0.8111 0.0024958 0.1864
# Detection Rate 0.5874 0.0008319 0.1131
# Detection Prevalence 0.6522 0.0831947 0.2646
# Balanced Accuracy 0.6902 0.6253823 0.7105
### Creating output tables for LaTex
pred_names <- c("Age (head)", "Female (head)", "Sec. education (head)",
"HH size", "Ethnic minority", "Sex ratio", "Married females", "Married males",
"Savings", "Nonfarm income",
"Temp. shocks (+)", "Temp. shocks (-)",
"Precip. shocks (+)", "Precip. shocks (-)")
dep_names=c("Migrants (+)", "Migrants (-)")
all_dep_names=c("Internal (+)", "Internal (-)", "Internat.(+)", "Internat.(-)")
stargazer(model1, type="text", out = "R_migrants1.tex",
covariate.labels=pred_names, dep.var.labels=dep_names,
nobs=TRUE, no.space=TRUE)
stargazer(model2, model3, type="text", out = "R_migrants23.tex",
covariate.labels=pred_names, dep.var.labels=all_dep_names,
nobs=TRUE, omit.stat = "aic", no.space=TRUE)
stargazer(model1_inter, type="text", out = "R_migrants1_inter.tex",
covariate.labels=pred_names, dep.var.labels=dep_names,
nobs=TRUE, omit.stat = "aic", no.space=TRUE)
stargazer(model2_inter, model3_inter, type="text", out = "R_migrants23_inter.tex",
covariate.labels=pred_names, dep.var.labels=all_dep_names,
nobs=TRUE, omit.stat = "aic", no.space=TRUE)