---
title: "An Application to HB Twofold Normal Model On sampel dataset"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{An Application to HB Twofold Normal Model}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
```

## FIRST STEPS: Load package and load the data
```{r setup}
library(saeHB.twofold)
data("dataTwofold")
```

## STEPS 2: Fitting HB Model
```{r}
model=NormalTF(y~x1+x2,vardir="vardir",area = "codearea",weight = "w",iter.mcmc = 100000,thin=50,burn.in = 1000,data=dataTwofold)
```

## STEP 3 Extract mean estimation

### Subarea Estimation
```{r}
model$Est_sub
```
### Area Estimatio
```{r}
model$Est_area
```
### Coefficient Estimation
```{r}
model$coefficient
```
### Random effect variance estimation
```{r}
model$refVar
```

## STEP 3 : Extract CV and MSE Subarea
* CV $CV(\theta \hat)=\frac{SD(\theta \hat)}{(\theta \hat)} \times 100$
* MSE $MSE= V(\theta\hat)$
```{r}
CV=(model$Est_sub$SD)/(model$Est_sub$Mean)*100
MSE=model$Est_sub$SD^2
summary(cbind(CV,MSE))
```
## STEP 4 Extract CV and MSE of Area
```{r}
CV2=(model$Est_area$SD)/(model$Est_area$Mean)*100
MSE2=model$Est_area$SD^2
summary(cbind(CV2,MSE2))
```

## STEP 5 : You can also compare the CV between subarea direct estimator and HB Twofold estimator
```{r}
dirCV=sqrt(dataTwofold$vardir)/(dataTwofold$y)*100
summary(cbind(dirCV,CV))
```

* Look that! ,CV on our model is less than CV on direct estimator.
```{r}
boxplot(cbind(dirCV,CV),ylim=c(0,50))
```

```{r}
model$refVar
```