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psr_ex.rmd
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---
title: "Posterior check (Probability scale residuals) Bayesian CPM example"
output:
html_document:
toc: no
toc_depth: 3
number_sections: false
code_folding: hide
theme: paper
---
```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
#rm(list=ls())
libs <- c("rstan", "rms", "dplyr", "stringr", "readr", "pammtools", "bayesCPM")
invisible(lapply(libs, library, character.only = TRUE))
dir <- file.path("/home/nathan/Dropbox/njames/school/PhD/orise_ra/bayes_cpm")
# CPM functions
#source(file.path(dir,"cpm_functions.r"))
# dir for figures
#figdir <- file.path(dir,"biostat_sem","fig")
# call this once to distribute MCMC chains across cpu cores:
options(mc.cores=parallel::detectCores())
```
<!-- similar to orm() example 4a -->
```{r ex4a.1, cache=TRUE, eval=FALSE}
# Compare predicted mean with ols for a continuous x
set.seed(1567)
n <- 100
x1 <- rnorm(n)
# y <- 0.9*x1 + rnorm(n) # old w/ normal error
y <- 0.9*x1 + rlogis(n)
dat3 <- data.frame(y=ordered(y),y_num=y,x1)
```
```{r ex4a.2, cache=TRUE, eval=FALSE}
# mod_data <- mkStanDat(dat3, outcome="y", preds = c("x1"), link=2) # probit link
mod_data <- mkStanDat(dat3, outcome="y", preds = c("x1"), link=1)
bg <- bayes_cpm(mod_data, seed=6472,
iter=3250, warmup=2000, chains=4,
control = list(adapt_delta = 0.8))
#bg <- sampling(ord_mod1, data=mod_data, seed=6472,
# iter=3250, warmup=2000, chains=4,
# control = list(adapt_delta = 0.8))
```
```{r, eval=FALSE}
#plots, etc for biostat seminar
bg_df <- as.data.frame(bg)
#head(bg_df[,c("cutpoints[98]")])
#head(bg_df[,c("b[1]")])
head(bg_df[,c("cutpoints[1]","cutpoints[2]","cutpoints[3]","cutpoints[98]","cutpoints[99]","b[1]")])
```
```{r, eval=FALSE}
cdf_bg <- getCDF(bg, mod_data, newdata=data.frame(x1=c(-2,0,2)))
cdf_bg %>% filter(ndrow %in% c(1,2,3)) %>% ggplot(aes(group=ndrow)) +
geom_stepribbon(aes(x=yval, ymin=cdf_q5, ymax=cdf_q95,
fill=factor(ndrow)) , alpha=0.4) +
geom_step(aes(x=yval, y=med_cdf,color=factor(ndrow))) +
xlab("y") + ylab("Conditional CDF") +
scale_fill_discrete(name = "covariate value",
labels=c("x = -2", "x = 0", "x = 2")) +
scale_color_discrete(name = "covariate value",
labels=c("x = -2", "x = 0", "x = 2")) +
stat_function(fun=plogis,color="darkgreen",
linetype=2, alpha=0.4) +
stat_function(fun=function(x) plogis(x,2*0.9), color="blue",
linetype=2, alpha=0.4) +
stat_function(fun=function(x) plogis(x,-2*0.9),color="red",
linetype=2, alpha=0.4)
ggsave(file.path(figdir,"cond_cdf2.png"),width=6,height=3)
mn_dat<-getMean(bg, mod_data, newdata=data.frame(x1=c(-2,0,2)),summ=FALSE)
ggplot(mn_dat,aes(x=mn,fill=factor(x1)))+geom_density(alpha=0.6,color=NA)+
scale_fill_discrete(name = "covariate value",
labels=c("x = -2", "x = 0", "x = 2")) +
xlab("") + ylab("conditional mean density")
ggsave(file.path(figdir,"cond_mn2.png"),width=6,height=3)
mn_dat %>% filter(x1==2) %>% pull(mn) %>% quantile(probs=c(0.025,0.975))
q50_dat <- getQuantile(bg, mod_data, newdata=data.frame(x1=c(-2,0,2)),q=0.50,summ=FALSE)
ggplot(q50_dat,aes(x=qtile,fill=factor(x1)))+
geom_density(alpha=0.6, color=NA, adjust=3)+
scale_fill_discrete(name = "covariate value",
labels=c("x = -2", "x = 0", "x = 2")) +
xlab("") + ylab("conditional median density")
ggsave(file.path(figdir,"cond_md2.png"),width=6,height=3)
q50_x0_samps<-q50_dat %>% filter(x1==0) %>% pull(qtile)
mean(q50_x0_samps > 0.25 | q50_x0_samps < -0.25)
```
```{r, eval=FALSE}
# posterior predictive check
# cdf_dat <- getCDF(bg, mod_data, newdata=data.frame(x1=rnorm(10)),summ=FALSE)
cdf_dat <- getCDF(bg, mod_data, newdata=data.frame(x1=x1),summ=FALSE)
y_rep <- cdf_dat %>% filter(Var1 %in% LETTERS[1:10]) %>% group_by(Var1,ndrow) %>% mutate(rand=runif(1)) %>% filter(cdf<rand) %>% slice_tail(n=1) %>% ungroup()
ggplot(data=y_rep, aes(x=yval, group=Var1)) +
geom_density(col="lightblue") +
geom_density(data=data.frame(yval=y), aes(x=yval),color="blue", inherit.aes = FALSE)
```
```{r}
# try with new data
set.seed(237)
n <- 100
x1 <- rnorm(n)
x2 <- x1^2
x3 <- rexp(n)
y2 <- 0.9*x1 + 1.2*x2 - 3.7*x3 + rlogis(n)
# try with categorized y2, trad. ordinal model
y2 <- cut(y2,breaks=15) %>% as.numeric()
dat4 <- data.frame(y=ordered(y2), y_num=y2, x1, x2, x3)
# mod_data <- mkStanDat(dat3, outcome="y", preds = c("x1"), link=2) # probit link
mod_data4 <- mkStanDat(dat4, outcome="y", preds = c("x1","x2","x3"), link=1)
bg2 <- bayes_cpm(mod_data4, seed=2782,
iter=2500, warmup=2000, chains=4,
control = list(adapt_delta = 0.85))
summary(bg2,pars="b")$summary
cdf_dat2 <- getCDF(bg2, mod_data4, newdata=data.frame(x1=x1,x2=x2,x3=x3),summ=FALSE)
```
```{r}
# prob scale residuals
cdf_dat_tst2 <- cdf_dat2 %>% filter(Var1 %in% LETTERS[1:20])
# prob scale residuals
# verify calcs are correct!!
# check Liu_orm_code.r for presid.orm()
# pr(y>Y) - pr(y<Y) = - pr(y<Y) + pr(y>Y)
cdf_mrg2 <- merge(dat4, cdf_dat_tst2, by=c("x1","x2","x3")) %>% mutate(y_chk=as.numeric(as.character(y)), flg=(y_chk==yval),
surv=1-cdf, psr=surv-cdf) %>%
filter(flg==TRUE)
cdf_mrg2 %>% ggplot(aes(sample=psr,group=Var1)) +
# geom_qq(distribution = stats::qunif,
# dparams=list(min=-1,max=1),
# alpha=0.2) +
geom_qq(distribution = stats::qunif,
dparams=list(min=-1,max=1),
geom="path", alpha=0.2) +
geom_qq_line(aes(sample=psr),
distribution = stats::qunif,
dparams=list(min=-1,max=1),line.p=c(0.01,0.99),
inherit.aes=FALSE)
```
```{r}
cdf_mrg2 %>% ggplot(aes(x=x1,y=psr,group=Var1))+
geom_point(alpha=0.2)+
geom_smooth(se=FALSE,alpha=0.2)
```
```{r}
# posterior predictive check?
y_rep2 <- cdf_dat2 %>% filter(Var1 %in% paste0(LETTERS,1:50)) %>% mutate(yy=yval,yy=if_else(yy==-Inf,0,yy),yy=yy+1) %>% group_by(Var1,ndrow) %>% mutate(rand=runif(1)) %>% filter(cdf<rand) %>% slice_tail(n=1) %>% ungroup()
ggplot(data=y_rep2, aes(x=yy, group=Var1)) +
geom_density(col="lightblue") +
geom_density(data=data.frame(yval=y2), aes(x=yval),color="blue", inherit.aes = FALSE)
```
```{r}
# posterior predictive check (betancourt)?
c_light <- c("#DCBCBC")
c_light_highlight <- c("#C79999")
c_mid <- c("#B97C7C")
c_mid_highlight <- c("#A25050")
c_dark <- c("#8F2727")
c_dark_highlight <- c("#7C0000")
B <- 15
idx <- rep(1:B, each=2)
x <- sapply(1:length(idx), function(b) if(b %% 2 == 0) idx[b] + 0.5 else idx[b] - 0.5)
obs_counts <- hist(dat4$y_num, breaks=(1:(B + 1)) - 0.5, plot=FALSE)$counts
pad_obs_counts <- sapply(idx, function(n) obs_counts[n])
pc0<-lapply(paste0(LETTERS,1:50), function(n) y_rep2 %>% filter(Var1==n) %>% select("yy") %>% pull())
pred_counts <-sapply(pc0, function(x) hist(x,breaks=(1:(B + 1)) - 0.5, plot=FALSE)$counts)
probs = c(0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9)
cred <- sapply(1:B, function(b) quantile(pred_counts[b,], probs=probs))
pad_cred <- do.call(cbind, lapply(idx, function(n) cred[1:9,n]))
plot(1, type="n", main="Posterior Predictive Distribution",
xlim=c(0.5, B + 0.5), xlab="y",
ylim=c(0, max(c(obs_counts, cred[9,]))), ylab="")
polygon(c(x, rev(x)), c(pad_cred[1,], rev(pad_cred[9,])),
col = c_light, border = NA)
polygon(c(x, rev(x)), c(pad_cred[2,], rev(pad_cred[8,])),
col = c_light_highlight, border = NA)
polygon(c(x, rev(x)), c(pad_cred[3,], rev(pad_cred[7,])),
col = c_mid, border = NA)
polygon(c(x, rev(x)), c(pad_cred[4,], rev(pad_cred[6,])),
col = c_mid_highlight, border = NA)
lines(x, pad_cred[5,], col=c_dark, lwd=2)
lines(x, pad_obs_counts, col="white", lty=1, lw=2.5)
lines(x, pad_obs_counts, col="black", lty=1, lw=2)
```
```{r}
#misspecified model (dropped x2 & x3, wrong link)
mod_data5 <- mkStanDat(dat4, outcome="y", preds = c("x1"), link=3)
bg3 <- bayes_cpm(mod_data5, seed=2782,
iter=2500, warmup=2000, chains=4,
control = list(adapt_delta = 0.85))
summary(bg3,par="b")$summary
cdf_dat3 <- getCDF(bg3, mod_data5, newdata=data.frame(x1=x1), summ=FALSE)
```
```{r}
# prob scale residuals
cdf_dat_tst3 <- cdf_dat3 %>% filter(Var1 %in% paste0(LETTERS,1:20))
# prob scale residuals
# check Liu_orm_code.r for presid.orm()
# pr(y>Y) - pr(y<Y) = - pr(y<Y) + pr(y>Y)
cdf_mrg3 <- merge(dat4, cdf_dat_tst3, by=c("x1")) %>% mutate(y_chk=as.numeric(as.character(y)), flg=(y_chk==yval),
surv=1-cdf, psr=surv-cdf) %>%
filter(flg==TRUE)
cdf_mrg3 %>% ggplot(aes(sample=psr,group=Var1)) +
# geom_qq(distribution = stats::qunif,
# dparams=list(min=-1,max=1),
# alpha=0.2) +
geom_qq(distribution = stats::qunif,
dparams=list(min=-1,max=1),
geom="path", alpha=0.2) +
geom_qq_line(aes(sample=psr),
distribution = stats::qunif,
dparams=list(min=-1,max=1),line.p=c(0.01,0.99),
inherit.aes=FALSE)
cdf_mrg3 %>% ggplot(aes(x=x1,y=psr,group=Var1))+geom_point()+geom_smooth(se=FALSE)
```
```{r}
# posterior predictive check?
# --> is procedure more like bootstrap draws from outcome?
# is it a useful ppc??
#!! ---> redo this procedure (correct & misspecified mod) with rstanarm and look at ppcs <--- !!#
y_rep3 <- cdf_dat3 %>% filter(Var1 %in% paste0(LETTERS,1:50)) %>%
mutate(yy=yval,yy=if_else(yy==-Inf,0,yy),yy=yy+1) %>% group_by(Var1,ndrow) %>% mutate(rand=runif(1)) %>% filter(cdf<rand) %>% slice_tail(n=1) %>% ungroup()
ggplot(data=y_rep3, aes(x=yy, group=Var1)) +
geom_density(col="lightblue") +
geom_density(data=data.frame(yval=y2), aes(x=yval),color="blue", inherit.aes = FALSE)
```
```{r}
#ppc (betancourt)
obs_counts <- hist(dat4$y_num, breaks=(1:(B + 1)) - 0.5, plot=FALSE)$counts
pad_obs_counts <- sapply(idx, function(n) obs_counts[n])
pc0<-lapply(paste0(LETTERS,1:50), function(n) y_rep3 %>% filter(Var1==n) %>% select("yy") %>% pull())
pred_counts <-sapply(pc0, function(x) hist(x,breaks=(1:(B + 1)) - 0.5, plot=FALSE)$counts)
probs = c(0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9)
cred <- sapply(1:B, function(b) quantile(pred_counts[b,], probs=probs))
pad_cred <- do.call(cbind, lapply(idx, function(n) cred[1:9,n]))
plot(1, type="n", main="Posterior Predictive Distribution",
xlim=c(0.5, B + 0.5), xlab="y",
ylim=c(0, max(c(obs_counts, cred[9,]))), ylab="")
polygon(c(x, rev(x)), c(pad_cred[1,], rev(pad_cred[9,])),
col = c_light, border = NA)
polygon(c(x, rev(x)), c(pad_cred[2,], rev(pad_cred[8,])),
col = c_light_highlight, border = NA)
polygon(c(x, rev(x)), c(pad_cred[3,], rev(pad_cred[7,])),
col = c_mid, border = NA)
polygon(c(x, rev(x)), c(pad_cred[4,], rev(pad_cred[6,])),
col = c_mid_highlight, border = NA)
lines(x, pad_cred[5,], col=c_dark, lwd=2)
lines(x, pad_obs_counts, col="white", lty=1, lw=2.5)
lines(x, pad_obs_counts, col="black", lty=1, lw=2)
```