logistic-regression.r

# packages ----------------------------------------------------------------
rm(list = ls())
library(tidyverse)
theme_set(theme_minimal())


# data --------------------------------------------------------------------
n <- 500
df <- data_frame(
  x1 = rnorm(n) + 1,
  x2 = 5 + 2 * rnorm(n)
  )

ggplot(df) + 
  geom_point(aes(x1, x2))

df <- df %>% 
  mutate(y = as.numeric(x1 > (x2 - 5)/2 + rnorm(n)))

ggplot(df) + 
  geom_point(aes(x1, x2, color = y))

ggplot(df) + 
  geom_point(aes(x1, y, color = y), alpha = 0.25)

df

df %>% 
  gather(key, value, -y) %>% 
  ggplot() + 
  geom_point(aes(value, y, color = y), alpha = 0.25) +
  facet_wrap(~ key, scales = "free") 


ggplot(df) + 
  geom_density(aes(x1, fill = y, group = y), alpha = 0.75)





# ajuste visual -----------------------------------------------------------
ggplot(df) + 
  geom_point(aes(x1, y, color = y), alpha = 0.25) + 
  geom_smooth(aes(x1, y), method = "lm")


ggplot(df) + 
  geom_point(aes(x1, y, color = y), alpha = 0.25) + 
  geom_smooth(aes(x1, y), method = "loess")



# logit -------------------------------------------------------------------
df2 <- data_frame(
  s = seq(-10, 10, length.out = 101)  
)

ggplot(df2) + 
  geom_line(aes(s, sin(s)))

ggplot(df2) + 
  geom_line(aes(s, 1 / (1 + exp(s))))

ggplot(df2) + 
  geom_line(aes(s, 1 / (1 + exp(-s))))

ggplot(df2) + 
  geom_line(aes(s, 1 / (1 + exp(-(2 + - 2 * s)))))

s <- seq(-10, 10, length.out = 101)  
s2 <- seq(-5, 5, length.out = 6)  

p <- expand.grid(x = s, b0 = s2, b1 = s2) %>% 
  tbl_df() %>% 
  mutate(y = 1 / (1 + exp(-(b0 + b1 * x)))) %>% 
  ggplot() + 
  geom_line(aes(x, y)) + 
  facet_grid(b0 ~ b1) + 
  theme(axis.title.x = element_blank(), axis.text = element_blank(), axis.ticks = element_blank())

p

p +
  geom_point(data = df, aes(x1, y, color = y), alpha = 0.25) +
  theme(legend.position = "none")


# ajuste parametros -------------------------------------------------------
m1 <- glm(y ~ x1, family = binomial(link = "logit"), data = df)
m1
c <- m1$coefficients
c

ggplot() + 
  geom_jitter(data = df, aes(x1, y, color = y), alpha = 0.2, height = 0.01) + 
  geom_line(data = df2, aes(s,  1 / (1 + exp(-(c[1] + c[2] * s))))) + 
  xlim(-2, 3)

m2 <- glm(y ~ x1 + x2, family = binomial(link = "logit"), data = df)
m2
c <- m2$coefficients
c

df_sur <- expand.grid(
  x1 = seq(min(df$x1), max(df$x1), length.out = 100),
  x2 = seq(min(df$x2), max(df$x2), length.out = 100)
  ) %>% 
  tbl_df() %>% 
  mutate(
    y = predict(m2, newdata = ., type = "response")
  )
df_sur

df_surm <- df_sur %>% 
  spread(x1, y) %>% 
  select(-x2) %>% 
  as.matrix()

library(plotly)
plot_ly() %>% 
  add_surface(x = unique(sort(df_sur$x1)), y = unique(sort(df_sur$x2)), z = df_surm) %>% 
  add_markers(data = df, x = ~x1, y = ~x2, z = ~y, color = ~y)

# evaluar -----------------------------------------------------------------
df <- df %>% 
  mutate(
    p1 = predict(m1, newdata = ., type = "response"),
    p2 = predict(m2, newdata = ., type = "response"),
    l2 = predict(m2, newdata = ., type = "link")
  )

ggplot(df) + 
  geom_density(aes(p1))

df %>% 
  select(y, starts_with("p")) %>% 
  gather(key, value, -y) %>% 
  ggplot() + 
  geom_density(aes(value)) + 
  facet_wrap(~ key)

df %>% 
  select(y, starts_with("p")) %>% 
  gather(key, value, -y) %>% 
  ggplot() + 
  geom_density(aes(value, group = y, fill = y), alpha = 0.75) + 
  facet_wrap(~ key)



# acumulada ---------------------------------------------------------------
x <- 1:10
ecdf_x <- ecdf(x)

plot(ecdf_x)

n <- 5000
plot(ecdf(runif(n)))

plot(ecdf(rnorm(n)))
plot(ecdf(rexp(n)), add = TRUE)
plot(ecdf(runif(n)), add = TRUE)

df <- df %>% 
  mutate()