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dceoy/glm_confint.R

Last active August 29, 2015 14:21
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glm_confint.R
#!/usr/bin/env Rscript
# Diabetes survey on Pima Indians
#
# variables:
# 'glucose' Plasma glucose concentration at 2 hours in an oral glucose tolerance test
# 'diabetes' Diabetes pedigree function
# 'test' test whether the patient shows signs of diabetes (coded 0 if negative, 1 if positive)
data(pima, package = 'faraway')
#
# Logistic Regression
#
m <- glm(factor(test) ~ glucose + diabetes, family = binomial, data = pima)
print(summary(m))
#
# Call:
# glm(formula = test ~ glucose + diabetes, family = binomial, data = pima)
#
# Deviance Residuals:
# Min 1Q Median 3Q Max
# -2.7557 -0.7801 -0.5295 0.8460 3.2897
#
# Coefficients:
# Estimate Std. Error z value Pr(>|z|)
# (Intercept) -5.724331 0.447126 -12.803 < 2e-16 ***
# glucose 0.037356 0.003284 11.375 < 2e-16 ***
# diabetes 0.918678 0.273089 3.364 0.000768 ***
# ---
# Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#
# (Dispersion parameter for binomial family taken to be 1)
#
# Null deviance: 993.48 on 767 degrees of freedom
# Residual deviance: 796.99 on 765 degrees of freedom
# AIC: 802.99
#
# Number of Fisher Scoring iterations: 4
#
# Alpha Level
alpha <- 0.05
results <- list()
#
# Profile Likelihood CI
#
results$profile_likelihood_ci <- confint(m, level = 1 - alpha)
#
# Wald CI
#
results$wald_ci <- confint.default(m, level = 1 - alpha)
#
# Wald CI (manual calculation)
#
wald_ci <- function(model, alpha) {
ce <- summary(model)$coefficients[,1:2]
ci <- cbind(ce[,1] - qnorm(1 - alpha / 2) * ce[,2],
ce[,1] + qnorm(1 - alpha / 2) * ce[,2])
colnames(ci) <- c(paste((alpha / 2) * 100, '%'),
paste((1 - alpha / 2) * 100, '%'))
return(ci)
}
results$wald_ci_manual_calc <- wald_ci(m, alpha)
#
# Odds Ratio
#
results$odds_ratio <- exp(cbind(Estimate = m$coefficients, confint(m, level = 1 - alpha)))
print(results)
#
# $profile_likelihood_ci
# 2.5 % 97.5 %
# (Intercept) -6.62859431 -4.87394015
# glucose 0.03109338 0.04398227
# diabetes 0.38948850 1.46127936
#
# $wald_ci
# 2.5 % 97.5 %
# (Intercept) -6.60068146 -4.84798018
# glucose 0.03091909 0.04379221
# diabetes 0.38343319 1.45392188
#
# $wald_ci_manual_calc
# 2.5 % 97.5 %
# (Intercept) -6.60068146 -4.84798018
# glucose 0.03091909 0.04379221
# diabetes 0.38343319 1.45392188
#
# $odds_ratio
# Estimate 2.5 % 97.5 %
# (Intercept) 0.003265538 0.00132202 0.007643191
# glucose 1.038062146 1.03158183 1.044963828
# diabetes 2.505974144 1.47622552 4.311471930
#
Raw
glm_predict.R
#!/usr/bin/env R
sapply(c('dplyr', 'data.table', 'ggplot2'), function(p) require(p, character.only = TRUE))
select <- dplyr::select
# Diabetes survey on Pima Indians
data(pima, package = 'faraway')
#
# Logistic Regression
#
m <- glm(factor(test) ~ glucose + diabetes, family = binomial, data = pima)
# Alpha Level
alpha = 0.05
#
# New Data having various values of Glucose and Diabetes
#
new_d <- with(pima, data.table(glucose = rep(quantile(pima$glucose)[2:4], each = 100),
diabetes = rep(seq(from = min(diabetes),
to = max(diabetes),
length.out = 100)), 3))
#
# Prediction of Probabilities
#
prd_p <- new_d %>%
predict(m, newdata = ., type = 'link', se.fit = TRUE) %>%
as.data.table() %>%
mutate(predicted_prob = plogis(fit),
lower_limit = plogis(fit - qnorm(1 - alpha / 2) * se.fit),
upper_limit = plogis(fit + qnorm(1 - alpha / 2) * se.fit)) %>%
cbind(new_d, .) %>%
select(glucose, diabetes, predicted_prob, lower_limit, upper_limit)
#
# Visualization
#
prd_p$glucose <- factor(prd_p$glucose)
ribbon <- ggplot(prd_p, aes(x = diabetes, y = predicted_prob)) +
geom_ribbon(aes(ymin = lower_limit, ymax = upper_limit, fill = glucose), alpha = 0.2) +
geom_line(aes(colour = glucose), size = 1) +
labs(x = 'diabetes pedigree function', y = 'test of diabetes')
svg('plot.svg', width = 6, height = 4)
plot(ribbon)
dev.off()
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plot.svg
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