require(ISLR)

Loading required package: ISLR

Warning: package 'ISLR' was built under R version 4.3.3

require(MASS)

Loading required package: MASS

Warning: package 'MASS' was built under R version 4.3.2

require(descr)

Loading required package: descr

Warning: package 'descr' was built under R version 4.3.3

attach(Smarket)

## Linear Discriminant Analysis
freq(Direction)

Direction 
      Frequency Percent
Down        602   48.16
Up          648   51.84
Total      1250  100.00

train = Year<2005
lda.fit=lda(Direction~Lag1+Lag2,data=Smarket, subset=Year<2005)
lda.fit

Call:
lda(Direction ~ Lag1 + Lag2, data = Smarket, subset = Year < 
    2005)

Prior probabilities of groups:
    Down       Up 
0.491984 0.508016 

Group means:
            Lag1        Lag2
Down  0.04279022  0.03389409
Up   -0.03954635 -0.03132544

Coefficients of linear discriminants:
            LD1
Lag1 -0.6420190
Lag2 -0.5135293

plot(lda.fit, col="coral")

Smarket.2005=subset(Smarket,Year==2005) # Creating subset with 2005 data for prediction
lda.pred=predict(lda.fit,Smarket.2005)
names(lda.pred)

[1] "class"     "posterior" "x"

lda.class=lda.pred$class
Direction.2005=Smarket$Direction[!train] 
table(lda.class,Direction.2005)

         Direction.2005
lda.class Down  Up
     Down   35  35
     Up     76 106

data.frame(lda.pred)[1:5,]

     class posterior.Down posterior.Up         LD1
999     Up      0.4901792    0.5098208  0.08293096
1000    Up      0.4792185    0.5207815  0.59114102
1001    Up      0.4668185    0.5331815  1.16723063
1002    Up      0.4740011    0.5259989  0.83335022
1003    Up      0.4927877    0.5072123 -0.03792892

table(lda.pred$class,Smarket.2005$Direction)

      
       Down  Up
  Down   35  35
  Up     76 106

mean(lda.pred$class==Smarket.2005$Direction)

[1] 0.5595238

library(haven)

Warning: package 'haven' was built under R version 4.3.2

TEDS_2016 <- read_stata("https://github.com/datageneration/home/blob/master/DataProgramming/data/TEDS_2016.dta?raw=true")

glm.vt <- glm(votetsai~female, data = TEDS_2016, family = binomial)

summary(glm.vt)


Call:
glm(formula = votetsai ~ female, family = binomial, data = TEDS_2016)

Coefficients:
            Estimate Std. Error z value Pr(>|z|)    
(Intercept)  0.54971    0.08245   6.667 2.61e-11 ***
female      -0.06517    0.11644  -0.560    0.576    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 1666.5  on 1260  degrees of freedom
Residual deviance: 1666.2  on 1259  degrees of freedom
  (429 observations deleted due to missingness)
AIC: 1670.2

Number of Fisher Scoring iterations: 4

plot(glm.vt)

library(ggplot2)

ggplot(TEDS_2016, aes(x = female, y = votetsai)) +
  geom_bar(stat = "identity", fill = "skyblue") +
  labs(title = "Females Voting for Tsai", x = "Sex", y = "Votes")

Warning: Removed 429 rows containing missing values (`position_stack()`).

glm.vt <- glm(votetsai~female + KMT + DPP + age + edu + income, data = TEDS_2016, family = binomial)

summary(glm.vt)


Call:
glm(formula = votetsai ~ female + KMT + DPP + age + edu + income, 
    family = binomial, data = TEDS_2016)

Coefficients:
             Estimate Std. Error z value Pr(>|z|)    
(Intercept)  1.618640   0.592084   2.734  0.00626 ** 
female       0.047406   0.177403   0.267  0.78930    
KMT         -3.156273   0.250360 -12.607  < 2e-16 ***
DPP          2.888943   0.267968  10.781  < 2e-16 ***
age         -0.011808   0.007164  -1.648  0.09931 .  
edu         -0.184604   0.083102  -2.221  0.02632 *  
income       0.013727   0.034382   0.399  0.68971    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 1661.76  on 1256  degrees of freedom
Residual deviance:  836.15  on 1250  degrees of freedom
  (433 observations deleted due to missingness)
AIC: 850.15

Number of Fisher Scoring iterations: 6

plot(glm.vt)

glm.vt <- glm(votetsai~female + KMT + DPP + age + edu + income + Independence + Econ_worse + Govt_dont_care + Minnan_father + Mainland_father + Taiwanese, data = TEDS_2016, family = binomial)

summary(glm.vt)


Call:
glm(formula = votetsai ~ female + KMT + DPP + age + edu + income + 
    Independence + Econ_worse + Govt_dont_care + Minnan_father + 
    Mainland_father + Taiwanese, family = binomial, data = TEDS_2016)

Coefficients:
                 Estimate Std. Error z value Pr(>|z|)    
(Intercept)     -0.015976   0.679780  -0.024  0.98125    
female          -0.097996   0.189840  -0.516  0.60571    
KMT             -2.922246   0.259333 -11.268  < 2e-16 ***
DPP              2.468855   0.275350   8.966  < 2e-16 ***
age              0.003287   0.007884   0.417  0.67672    
edu             -0.092110   0.090119  -1.022  0.30674    
income           0.021771   0.036406   0.598  0.54984    
Independence     1.020953   0.251776   4.055 5.01e-05 ***
Econ_worse       0.310462   0.189100   1.642  0.10063    
Govt_dont_care  -0.014295   0.188765  -0.076  0.93964    
Minnan_father   -0.247650   0.253921  -0.975  0.32941    
Mainland_father -1.089332   0.396822  -2.745  0.00605 ** 
Taiwanese        0.909019   0.198930   4.570 4.89e-06 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 1661.76  on 1256  degrees of freedom
Residual deviance:  767.13  on 1244  degrees of freedom
  (433 observations deleted due to missingness)
AIC: 793.13

Number of Fisher Scoring iterations: 6

plot(glm.vt)

Answer

Female voters show a slight tendency to vote less (less likely to vote) for President Tsai, although gender itself (aka. whether a voter is a female or not) is not statistically significant predictor.

The best predictors of whether a voter will for President Tsai are: party affiliations (KMT, DPP), stances on independence, and family background factors such as having a Mainland father or being Taiwanese.