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R version 3.2.1 (2015-06-18) -- "World-Famous Astronaut"
Copyright (C) 2015 The R Foundation for Statistical Computing
Platform: i686-pc-linux-gnu (32-bit)
R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.
R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.
Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.
>
> epsilon <- 1e-15
>
> library(mcmc)
>
> RNGkind("Marsaglia-Multicarry")
> set.seed(42)
>
> options(digits = 3)
>
> n <- 100
> rho <- 0.5
> beta0 <- 0.25
> beta1 <- 1
> beta2 <- 0.5
>
> x1 <- rnorm(n)
> x2 <- rho * x1 + sqrt(1 - rho^2) * rnorm(n)
> eta <- beta0 + beta1 * x1 + beta2 * x2
> p <- 1 / (1 + exp(- eta))
> y <- as.numeric(runif(n) < p)
>
> out <- glm(y ~ x1 + x2, family = binomial())
> summary(out)
Call:
glm(formula = y ~ x1 + x2, family = binomial())
Deviance Residuals:
Min 1Q Median 3Q Max
-2.064 -0.821 -0.246 0.840 2.070
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 0.0599 0.2477 0.24 0.80905
x1 1.3682 0.3844 3.56 0.00037 ***
x2 0.4760 0.3135 1.52 0.12886
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 138.469 on 99 degrees of freedom
Residual deviance: 99.293 on 97 degrees of freedom
AIC: 105.3
Number of Fisher Scoring iterations: 5
>
> mlogl <- function(beta) {
+ if (length(beta) != 3) stop("length(beta) != 3")
+ beta0 <- beta[1]
+ beta1 <- beta[2]
+ beta2 <- beta[3]
+ eta <- beta0 + beta1 * x1 + beta2 * x2
+ p <- exp(eta) / (1 + exp(eta))
+ return(- sum(log(p[y == 1])) - sum(log(1 - p[y == 0])))
+ }
>
> out.nlm <- nlm(mlogl, coefficients(out), print.level = 2)
iteration = 0
Parameter:
[1] 0.0599 1.3682 0.4760
Function Value
[1] 49.6
Gradient:
[1] 8.24e-06 5.50e-06 6.08e-06
Relative gradient close to zero.
Current iterate is probably solution.
>
> logl <- function(beta) {
+ if (length(beta) != 3) stop("length(beta) != 3")
+ beta0 <- beta[1]
+ beta1 <- beta[2]
+ beta2 <- beta[3]
+ eta <- beta0 + beta1 * x1 + beta2 * x2
+ p <- exp(eta) / (1 + exp(eta))
+ return(sum(log(p[y == 1])) + sum(log(1 - p[y == 0])))
+ }
>
> out.metro <- metrop(logl, coefficients(out), 1e3, scale = 0.01)
> out.metro$accept
[1] 0.982
>
> out.metro <- metrop(out.metro, scale = 0.1)
> out.metro$accept
[1] 0.795
>
> out.metro <- metrop(out.metro, scale = 0.5)
> out.metro$accept
[1] 0.264
>
> apply(out.metro$batch, 2, mean)
[1] 0.0608 1.4230 0.5263
> var(out.metro$batch)
[,1] [,2] [,3]
[1,] 0.06755 -0.0108 0.00989
[2,] -0.01080 0.1758 -0.06155
[3,] 0.00989 -0.0615 0.10483
> olbm(out.metro$batch, 25)
[,1] [,2] [,3]
[1,] 4.54e-04 9.47e-05 -1.92e-05
[2,] 9.47e-05 1.84e-03 -6.45e-04
[3,] -1.92e-05 -6.45e-04 9.09e-04
>
> saveseed <- .Random.seed
> out.metro <- metrop(logl, as.numeric(coefficients(out)), 1e2,
+ scale = 0.5, debug = TRUE)
>
> all(out.metro$batch[- out.metro$nbatch, ] == out.metro$current[- 1, ])
[1] TRUE
> all(out.metro$current[1, ] == out.metro$initial)
[1] TRUE
> all(out.metro$batch[out.metro$nbatch, ] == out.metro$final)
[1] TRUE
>
> .Random.seed <- saveseed
> d <- ncol(out.metro$proposal)
> n <- nrow(out.metro$proposal)
> my.proposal <- matrix(NA, n, d)
> my.u <- double(n)
> ska <- out.metro$scale
> for (i in 1:n) {
+ my.proposal[i, ] <- out.metro$current[i, ] + ska * rnorm(d)
+ if (is.na(out.metro$u[i])) {
+ my.u[i] <- NA
+ } else {
+ my.u[i] <- runif(1)
+ }
+ }
> max(abs(out.metro$proposal - my.proposal)) < epsilon
[1] TRUE
> all(is.na(out.metro$u) == is.na(my.u))
[1] TRUE
> all(out.metro$u[!is.na(out.metro$u)] == my.u[!is.na(my.u)])
[1] TRUE
>
> my.curr.log.green <- apply(out.metro$current, 1, logl)
> my.prop.log.green <- apply(out.metro$proposal, 1, logl)
> all(is.na(out.metro$u) == (my.prop.log.green > my.curr.log.green))
[1] TRUE
> foo <- my.prop.log.green - my.curr.log.green
> max(abs(foo - out.metro$log.green)) < epsilon
[1] TRUE
>
> my.accept <- is.na(my.u) | my.u < exp(foo)
> sum(my.accept) == round(n * out.metro$accept)
[1] TRUE
>
> my.path <- matrix(NA, n, d)
> my.path[my.accept, ] <- out.metro$proposal[my.accept, ]
> my.path[! my.accept, ] <- out.metro$current[! my.accept, ]
>
> all(my.path == out.metro$batch)
[1] TRUE
>
>
> proc.time()
user system elapsed
0.532 0.028 0.551
|
