10.7 Regressão de Poisson
10.7.1 Clássica
## Dobson (1990) Page 93: Randomized Controlled Trial :
counts <- c(18,17,15,20,10,20,25,13,12)
outcome <- gl(3,1,9)
treatment <- gl(3,3)
data.frame(treatment, outcome, counts) # showing data## treatment outcome counts
## 1 1 1 18
## 2 1 2 17
## 3 1 3 15
## 4 2 1 20
## 5 2 2 10
## 6 2 3 20
## 7 3 1 25
## 8 3 2 13
## 9 3 3 12## Analysis of Deviance Table
##
## Model: poisson, link: log
##
## Response: counts
##
## Terms added sequentially (first to last)
##
##
## Df Deviance Resid. Df Resid. Dev
## NULL 8 10.5814
## outcome 2 5.4523 6 5.1291
## treatment 2 0.0000 4 5.1291##
## Call:
## glm(formula = counts ~ outcome + treatment, family = poisson())
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 3.045e+00 1.709e-01 17.815 <2e-16 ***
## outcome2 -4.543e-01 2.022e-01 -2.247 0.0246 *
## outcome3 -2.930e-01 1.927e-01 -1.520 0.1285
## treatment2 1.398e-16 2.000e-01 0.000 1.0000
## treatment3 -2.416e-16 2.000e-01 0.000 1.0000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 10.5814 on 8 degrees of freedom
## Residual deviance: 5.1291 on 4 degrees of freedom
## AIC: 56.761
##
## Number of Fisher Scoring iterations: 410.7.2 Bayesiana
# library(rstanarm)
# ### Poisson regression (example from help("glm"))
# count_data <- data.frame(
# counts = c(18,17,15,20,10,20,25,13,12),
# outcome = gl(3,1,9),
# treatment = gl(3,3)
# )
# fit3 <- stan_glm(
# counts ~ outcome + treatment,
# data = count_data,
# family = poisson(link="log"),
# prior = normal(0, 2),
# refresh = 0,
# # for speed of example only
# chains = 2, iter = 250
# )
# print(fit3)
#
# bayesplot::color_scheme_set("viridis")
# plot(fit3)
# plot(fit3, regex_pars = c("outcome", "treatment"))
# plot(fit3, plotfun = "combo", regex_pars = "treatment") # ?bayesplot::mcmc_combo
# posterior_vs_prior(fit3, regex_pars = c("outcome", "treatment"))