R version 3.1.1 (2014-07-10) -- "Sock it to Me"
Copyright (C) 2014 The R Foundation for Statistical Computing
Platform: x86_64-unknown-linux-gnu (64-bit)

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> 
>  pdf(file = "glm-plots.pdf")
>  
>  set.seed(42)
> 
>  x <- 1:81
>  z <- (x - mean(x)) / sd(x)
>  z <- z / max(z) * 3.0
>  range(z)
[1] -3  3
>  fred <- function(x) ifelse(x > 0, 1 / (1 + exp(- x)), exp(x) / (1 + exp(x)))
>  moo <- fred(z)
> 
>  plot(x, moo, ylim = c(0, 1))
>  title(main = "Simulation Truth Mean Values")
> 
>  y <- as.numeric(runif(length(x)) < moo)
>  plot(x, y)
>  title(main = "Simulated Data")
> 
>  # logistic regression
>  plot(x, y)
>  out <- glm(y ~ x, family = binomial)
>  curve(predict(out, type = "response", newdata = data.frame(x = x)), add = TRUE)
>  title(main = "Logistic Regression")
> 
>  # linear regression (justified by Gauss-Markov theorem)
>  plot(x, y)
>  out <- lm(y ~ x)
>  curve(predict(out, newdata = data.frame(x = x)), add = TRUE)
>  title(main = "Linear Regression")
> 
>  # three types of latent variable woof regression
>  cc <- c("black", "red", "darkseagreen")
>  plot(x, y)
>  out <- glm(y ~ x, family = binomial)
>  curve(predict(out, type = "response", newdata = data.frame(x = x)),
+      add = TRUE, col = cc[1])
>  out <- glm(y ~ x, family = binomial(link = "probit"))
>  curve(predict(out, type = "response", newdata = data.frame(x = x)),
+      add = TRUE, col = cc[2])
>  out <- glm(y ~ x, family = binomial(link = "cauchit"))
>  curve(predict(out, type = "response", newdata = data.frame(x = x)),
+      add = TRUE, col = cc[3])
>  legend(0, 0.8, legend = c("logit", "probit", "cauchit"),
+      col = cc, lwd = 2)
>  title(main = "Various Latent Variable Distribution Regressions")
> 
>  plot(x, y)
>  out <- glm(y ~ x, family = binomial(link = "cloglog"))
>  curve(predict(out, type = "response", newdata = data.frame(x = x)),
+      add = TRUE)
>  title(main = "Complementary Log Log")
> 
>  plot(x, y)
>  out <- glm(y ~ x, family=quasi(variance="mu(1-mu)"),
+     start = c(0.5, 0))
There were 25 warnings (use warnings() to see them)
>  summary(out, dispersion=1)

Call:
glm(formula = y ~ x, family = quasi(variance = "mu(1-mu)"), start = c(0.5, 
    0))

Deviance Residuals: 
     Min        1Q    Median        3Q       Max  
-1.69563  -0.80198  -0.00001   0.75853   1.76001  

Coefficients:
              Estimate Std. Error z value Pr(>|z|)    
(Intercept) -1.250e-02  7.266e-06   -1720   <2e-16 ***
x            1.250e-02  1.957e-06    6388   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for quasi family taken to be 1)

    Null deviance: 112.277  on 80  degrees of freedom
Residual deviance:  63.395  on 79  degrees of freedom
AIC: NA

Number of Fisher Scoring iterations: 24

>  curve(predict(out, type = "response", newdata = data.frame(x = x),
+      dispersion = 1), add = TRUE)
>  title(main = "Quasi-Likelihood, Identity Link")
> 
>  plot(x, y)
>  out <- glm(y ~ x, family = binomial(link = "log"), start = c(-1, 0))
There were 28 warnings (use warnings() to see them)
>  warnings()
Warning messages:
1: step size truncated due to divergence
2: step size truncated: out of bounds
3: step size truncated: out of bounds
4: step size truncated: out of bounds
5: step size truncated: out of bounds
6: step size truncated: out of bounds
7: step size truncated: out of bounds
8: step size truncated: out of bounds
9: step size truncated: out of bounds
10: step size truncated: out of bounds
11: step size truncated: out of bounds
12: step size truncated: out of bounds
13: step size truncated: out of bounds
14: step size truncated: out of bounds
15: step size truncated: out of bounds
16: step size truncated: out of bounds
17: step size truncated: out of bounds
18: step size truncated: out of bounds
19: step size truncated: out of bounds
20: step size truncated: out of bounds
21: step size truncated: out of bounds
22: step size truncated: out of bounds
23: step size truncated: out of bounds
24: step size truncated: out of bounds
25: step size truncated: out of bounds
26: step size truncated: out of bounds
27: glm.fit: algorithm did not converge
28: glm.fit: algorithm stopped at boundary value
>  curve(predict(out, type = "response", newdata = data.frame(x = x)),
+      add = TRUE)
>  title(main = "Log")
> 
>  # all links
>  okLinks <- c("logit", "probit", "cloglog", "cauchit", "log")
>  cc <- c("black", "red", "darkgreen", "blue", "magenta")
>  plot(x, y)
>  for (i in seq(along = okLinks)) {
+      out <- glm(y ~ x, family = binomial(link = okLinks[i]),
+          start = c(-1, 0))
+      curve(predict(out, type = "response", newdata = data.frame(x = x)),
+          add = TRUE, col = cc[i])
+  }
There were 28 warnings (use warnings() to see them)
>  legend(0, 0.8, legend = okLinks, col = cc, lwd = 2)
>  title(main = "All Link Functions R Function GLM Knows About")
> 
> 
> 
> proc.time()
   user  system elapsed 
  0.349   0.034   0.506