---
title: "Introduction to samplingin"
# author: "Choerul Afifanto"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Introduction to samplingin}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(collapse = T, comment = "#>")
options(tibble.print_min = 4L, tibble.print_max = 4L)
library(samplingin)
library(dplyr)
library(magrittr)
set.seed(114)
```

## Population DataFrame

We'll use the dataset `pop_dt`. The dataset contains tabulation of Indonesia's population based on the results of the 2020 population census by regency/city and gender from BPS-Statistics Indonesia <https://sensus.bps.go.id/main/index/sp2020>.

```{r}
dim(pop_dt)

pop_dt %>% head()
```

## Allocation DataFrame

The dataset used is `alokasi_dt` which is a dataset consisting of sample allocations for each province for sampling purposes.

```{r}
dim(alokasi_dt)

alokasi_dt
```

## Simple Random Sampling (SRS)

A simple random sample is a randomly selected subset of a population. In this sampling method, each member of the population has an exactly equal chance of being selected.

The following is the syntax for simple random sampling. Use parameter `method = 'srs'`

```{r}
dtSampling_srs = doSampling(
  pop     = pop_dt,
  alloc   = alokasi_dt,
  nsample = "n_primary",
  seed    = 7891,
  method  = "srs",
  ident   = c("kdprov"),
  type    = "U"
)
```

Displaying the primary sampling result

#### Population Sampled

```{r}
head(dtSampling_srs$pop)
```

#### Units Sampled

```{r}
head(dtSampling_srs$sampledf)

dtSampling_srs$sampledf %>% nrow
```

#### Sampling Details

```{r}
head(dtSampling_srs$details)
```

## Systematic Random Sampling

Systematic random sampling is a method to select samples at a particular preset interval. Using population and allocation data that has been provided previously, we will carry out systematic random sampling by utilizing the `doSampling` function from `samplingin` package. Use parameter `method = 'systematic'`

### Primary Units Sampling

The following is the syntax for sampling the primary units

```{r}
dtSampling_u = doSampling(
  pop     = pop_dt,
  alloc   = alokasi_dt,
  nsample = "n_primary",
  seed    = 2,
  method  = "systematic",
  ident   = c("kdprov"),
  type    = "U"
)
```

Displaying the primary sampling result

#### Population Sampled

```{r}
head(dtSampling_u$pop)
```

#### Units Sampled

```{r}
head(dtSampling_u$sampledf)

dtSampling_u$sampledf %>% nrow
```

#### Sampling Details

```{r}
head(dtSampling_u$details)
```

### Secondary Units Sampling

To perform sampling for secondary units, we utilize the population results from prior sampling, which have been marked for the selected primary units. Parameters in `doSampling` are added with `is_secondary=TRUE`.

```{r}
alokasi_dt_p = alokasi_dt %>% 
  mutate(n_secondary = 2*n_primary)

dtSampling_p = doSampling(
  pop     = dtSampling_u$pop,
  alloc   = alokasi_dt_p,
  nsample = "n_secondary",
  seed    = 243,
  method  = "systematic",
  ident   = c("kdprov"),
  type    = "P",
  is_secondary = TRUE
)
```

It can be seen that there are still 2 units that have not been selected as samples. To view the allocation that has not yet been selected as samples, it is as follows:

```{r}
dtSampling_p$details %>% 
  filter(n_deficit>0)
```

Displaying the secondary sampling result

#### Population Sampled

```{r}
head(dtSampling_p$pop)
```

Flags for primary and secondary units

```{r}
dtSampling_p$pop %>% count(flags)
```

#### Units Sampled

```{r}
head(dtSampling_p$sampledf)

dtSampling_p$sampledf %>% nrow
```

#### Sampling Details

```{r}
head(dtSampling_p$details)
```

## PPS Systematic Sampling

PPS systematic sampling is a method of sampling from a finite population in which a size measure is available for each population unit before sampling and where the probability of selecting a unit is proportional to its size. Units with larger sizes have more chance to be selected. We will use `doSampling` function with parameter `method = 'pps'` and `auxVar = 'Total'` for its auxiliary variable.

```{r}
dtSampling_pps = doSampling(
  pop     = pop_dt,
  alloc   = alokasi_dt,
  nsample = "n_primary",
  seed    = 321,
  method  = "pps",
  auxVar  = "Total",
  ident   = c("kdprov"),
  type    = "U"
)
```

Displaying the PPS sampling result

#### Population Sampled

```{r}
head(dtSampling_pps$pop)
```

#### Units Sampled

```{r}
head(dtSampling_pps$sampledf)

dtSampling_pps$sampledf %>% nrow
```

#### Sampling Details

```{r}
head(dtSampling_pps$details)
```

## Sampling using Stratification

For sampling that utilizes stratification, the `doSampling` function includes additional parameter called `strata`. The strata variable must be available in the population and the allocation being used. For example, in the `pop_dt` data, information about `strata` is added, namely `strata_kabkot`, which indicates information about districts (strata_kabkot = 1) and cities (strata_kabkot = 2).

```{r}
pop_dt_strata = pop_dt %>% 
  mutate(
    strata_kabkot = ifelse(substr(kdkab,1,1)=='7', 2, 1)
  )

alokasi_dt_strata = pop_dt_strata %>% 
  group_by(kdprov,strata_kabkot) %>% 
  summarise(
    jml_kabkota = n()
  ) %>% 
  ungroup %>% 
  left_join(
    alokasi_dt %>% 
      select(kdprov,n_primary) %>% 
      rename(n_alloc = n_primary)
  )
  
alokasi_dt_strata = alokasi_dt_strata %>%
  get_allocation(n_alloc = "n_alloc", group = c("kdprov"), pop_var = "jml_kabkota")

dtSampling_strata = doSampling(
  pop     = pop_dt_strata,
  alloc   = alokasi_dt_strata,
  nsample = "n_primary",
  seed    = 3512,
  method  = "systematic",
  strata  = "strata_kabkot",
  ident   = c("kdprov"),
  type    = "U"
)
```

Displaying the sampling result with stratification

#### Population Sampled

```{r}
head(dtSampling_strata$pop)
```

#### Units Sampled

```{r}
head(dtSampling_strata$sampledf)

dtSampling_strata$sampledf %>% nrow

dtSampling_strata$sampledf %>% count(strata_kabkot)

```

#### Sampling Details

```{r}
head(dtSampling_strata$details)
```

## Sampling with Implicit Stratification

So that the characteristics of the selected sample are distributed according to certain variables, sampling sometimes employs **implicit stratification**. For instance, if you aim to obtain samples distributed according to the total population, you can add the parameter `implicitby = 'Total'` when conducting sampling.

```{r}
dtSampling_implicit = doSampling(
  pop        = pop_dt_strata,
  alloc      = alokasi_dt_strata,
  nsample    = "n_primary",
  seed       = 3512,
  method     = "systematic",
  strata     = "strata_kabkot",
  implicitby = "Total",
  ident      = c("kdprov"),
  type       = "U"
)
```

Displaying the sampling result with implicit stratification

#### Population Sampled

```{r}
head(dtSampling_implicit$pop)
```

#### Units Sampled

```{r}
head(dtSampling_implicit$sampledf)

dtSampling_implicit$sampledf %>% nrow

dtSampling_implicit$sampledf %>% count(strata_kabkot)

```

#### Sampling Details

```{r}
head(dtSampling_implicit$details)
```

## Sampling with Predetermined Random Number

Sometimes, the random numbers for sampling have already been determined beforehand. Thus, for sampling using those predetermined random numbers, the `samplingin` package accommodates this by adding the parameter `predetermined_rn`, which takes the value of the variable storing the predetermined random numbers. For example, if the random numbers are stored in the allocation data frame under the variable name `arand`, thus we add `predetermined_rn = 'arand'`

```{r}
set.seed(988)
alokasi_dt_arand = alokasi_dt_strata %>%
  mutate(arand = runif(n(),0,1))

alokasi_dt_arand %>% as.data.frame %>% head(10)

dtSampling_prn = doSampling(
  pop        = pop_dt_strata,
  alloc      = alokasi_dt_arand,
  nsample    = "n_primary",
  seed       = 974,
  method     = "systematic",
  strata     = "strata_kabkot",
  predetermined_rn = "arand",
  ident      = c("kdprov"),
  type       = "U"
)
```

Displaying the sampling result with predetermined random number

#### Population Sampled

```{r}
head(dtSampling_prn$pop)
```

#### Units Sampled

```{r}
head(dtSampling_prn$sampledf)

dtSampling_prn$sampledf %>% nrow

```

#### Sampling Details

```{r}
head(dtSampling_prn$details)
```

## Allocate predetermined allocations to smaller levels

One of the supporting functions in the `samplingin` package is `get_allocation`. This function aims to allocate sample allocations to lower levels using the *proportional allocation* method based on the square root of the specified variable.

For example, sample allocations are available at the Province level, which will be allocated to lower levels such as Districts/Cities using the *proportional allocation* method based on the square root of the total population (`Total`).

```{r}
set.seed(242)
alokasi_prov = alokasi_dt %>%
  select(-jml_kabkota, -n_primary) %>%
  mutate(init_alloc = as.integer(runif(n(), 100, 200))) %>%
  as.data.frame()

alokasi_prov %>% head(10)

alokasi_prov %>% 
  summarise(sum(init_alloc))

alokasi_kab = pop_dt %>%
  left_join(alokasi_prov) %>%
  get_allocation(n_alloc = "init_alloc", group = c("kdprov"), pop_var = "Total") %>%
  as.data.frame()

alokasi_kab %>% head(10)

alokasi_kab %>% summarise(sum(n_primary))

alokasi_kab %>% 
  group_by(kdprov) %>% 
  summarise(sum(n_primary))

# check 

all.equal(
  alokasi_prov, alokasi_kab %>% 
  group_by(kdprov) %>% 
  summarise(init_alloc=sum(n_primary)) %>% 
  ungroup() %>% 
  as.data.frame()
)
```
