---
title: "Example for simulating and running the iCARH model"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Example of simulating and running the iCARH model}
  %\VignetteEngine{knitr::rmarkdown}
  \usepackage[utf8]{inputenc}
---

```{r setup}
library(iCARH)
library(abind)

Tp=4L # timepoints
N=10L # number of samples
J=14L # number of metabolites
K=2L # number of bacteria species
P=8L  # number of pathways

set.seed(12473)
```

 For real data
 Build pathway matrices using iCARH.getPathwaysMat. Elements in KEGG id list may contain multiple KEGG ids per metabolite. If KEGG id unknown use : "Unk[number]".

```{r real data, eval=F}
keggid = list("Unk1", "C03299","Unk2","Unk3",
 c("C08363", "C00712")  # allowing multiple ids per metabolite
 )
 pathways = iCARH.getPathwaysMat(keggid, "rno")
```

To simulate data use iCARH.simulate. Use path.names to manually choose pathways or simply specify the expected proportion of metabolites per pathway via path.probs.


```{r pathways}
# Example of manually picked pathways
# path.names = c("path:map00564","path:map00590","path:map00061","path:map00591",
#               "path:map00592","path:map00600","path:map01040","path:map00563")
# Specify expected proportion of metabolites per pathway
path.probs = 0.8
data.sim = iCARH.simulate(Tp, N, J, P, K, path.probs = 0.8, Zgroupeff=c(0,4),
                          beta.val=c(1,-1,0.5, -0.5))

XX = data.sim$XX
Y = data.sim$Y
Z = data.sim$Z
pathways = data.sim$pathways
XX[2,2,2] = NA #missing value example
```

Check inaccuracies between covariance and design matrices

```{r}
pathways.bin = lapply(pathways, function(x) { y=1/(x+1); diag(y)=0; y})
adjmat = rowSums(abind::abind(pathways.bin, along = 3), dims=2)
cor.thresh = 0.7
# check number of metabolites in same pathway but not correlated
for(i in 1:Tp) print(sum(abs(cor(XX[i,,])[which(adjmat>0)])<cor.thresh))
```

Run iCARH model.

```{r}
rstan::rstan_options(auto_write = TRUE)
options(mc.cores = 2)
# For testing, does not converge
fit.sim = iCARH.model(XX, Y, Z, groups=rep(c(0,1), each=5), pathways = pathways, control = list(max_treedepth=8),
                     iter = 4, chains = 1)
# Not run
# fit.sim = iCARH.model(XX, Y, Z, pathways, control = list(adapt_delta = 0.99, max_treedepth=10),
#                      iter = 2000, chains = 2, pars=c("YY","Xmis","Ymis"), include=F)
```

Check convergence

```{r}
if(!is.null(fit.sim$icarh)){
  rhats = iCARH.checkRhats(fit.sim)
}
```

Processing results.
Bacteria effects.

```{r}
if(!is.null(fit.sim$icarh)){
  gplot = iCARH.plotBeta(fit.sim)
  gplot
}
```
Treatments effects

```{r}
if(!is.null(fit.sim$icarh)){
  gplot = iCARH.plotTreatmentEffect(fit.sim)
  gplot
}
```

Pathway analysis

```{r}
if(!is.null(fit.sim$icarh)){
  gplot = iCARH.plotPathwayPerturbation(fit.sim, path.names=names(data.sim$pathways))
  gplot
}
```
Normality assumptions

```{r}
if(!is.null(fit.sim$icarh)){
  par(mfrow=c(1,2))
  iCARH.checkNormality(fit.sim)
}
```

WAIC

```{r}
if(!is.null(fit.sim$icarh)){
  waic = iCARH.waic(fit.sim)
  waic
}
```

Posterior predictive checks
MAD : mean absolute deviation between covariance matrices

```{r}
if(!is.null(fit.sim$icarh)){
  mad = iCARH.mad(fit.sim)
  quantile(mad)
}
```

Get missing data

```{r}
if(!is.null(fit.sim$icarh)){
  imp = iCARH.getDataImputation(fit.sim)
}
```