jbkunst · November 30, 2017 21:25 · Nov 30, 2017
diff --git a/logistic-regression.r b/logistic-regression.r
@@ -0,0 +1,167 @@
+# 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()
+