---
title: "QAIG: Automatic Item Generator for Quantitative Multiple-Choice Items"
author: "Subhabrata"
date: "2020-05-19"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{QAIG Introduction}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

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

Automatic item generation (AIG) is an old concept which was first introduced by John R. Bormuth (1969). This process has not been advanced that much in past few decades. Due to recent demand of test items and high costs in item development, this process has become in light of many educators and psychometricians again.

**QAIG** is an effort to provide tool by means of R function for generating group of dissimilar sibling items from  **Quantitative Multiple-Choice** type parent item model. When we think about generating sibling items from a parent item, main focus becomes to have:

- generated items that look dissimilar to each other as much as possible.
- effective distractors in each of the items.

**QAIG** package enables users to generate large number of items from a parent item:

- by applying possible dissimilarities within the sibling items.
- by taking care of effectiveness of the distractors for each sibling item.



## Usage of `itemgen()` function and its arguments.
**QAIG** package includes a function called `itemgen`:

`itemgen(stem_text = stem_text, formulae = formulae, N = N, C, ans_key, options_affix, save.csv)`

The usage of this function is illustrated here.

### 1: Formation of the parent item.
**For `stem_text`:** User of this package should construct a parent item model i.e. a *stem text* along with desired number of *response choices*. All the changeable elements (variables) in the stem of an item should be replaced by specific notations enclosed by `[]`. Character variable should be written as `[C1], [C2], [C3] … etc.`. Number variables should be written as `[N1], [N2], [N3] … etc.`.

**For `N` and `C`:** For each of the number variables (`[N1], [N2], [N3], …`) in the *stem text*, user has to decide a set of numbers that should be declared as vectors `n1, n2, n3, …` respectively. Vectors of characters `c1, c2, c3, …` for each character variable should also be declared similar way. All the *input number vectors* and *input character vectors* should be wrapped within `list` separately as the inputs for `N` and `C` in `itemgen()` function.

**For `formulae`:** A generic *formula* for each of the response choices should be provided using the names (`n1, n2, n3, …`) of *input number vectors*. All the *formulae* need to be written in new line separately and should be wrapped as a raw text as an input for `formulae` in `itemgen()`  function. The correct response choice should be marked by "~" and distractors should be marked by "?" in the *formulae*.

**Note:** User must have *stem text*, *formulae* and the `list` of *input number vector(s)* to work with `itemgen()` function, as `stem_text`, `formulae` and `N` are the three default arguments in this function.


### Example I
```{R include = TRUE}
library(QAIG)
```
```{R echo = TRUE}
stem_text <- "What is the sum of first [N1] [C1] ?"

n1 <- c(5, 8, 11, 14, 17)
c1 <- c("natural numbers", "non-zero positive integers")

N <- list(n1 = n1)
C <- list(c1 = c1)

formulae <- "Option_A ? 2*n1-1
Option_B ? 3*n1-2
Option_C ~ n1*(n1+1)/2
Option_D ? n1*(n1-1)/2
"

## itemgen() function can be used as:
newitems <- QAIG::itemgen(stem_text = stem_text, formulae = formulae, N = N, C = C)

newitems
```

### 2: Using `options_affix` argument.
Suffix or prefix or both can be attached with the numeric values in the response choices by using `options_affix` argument of `itemgen()` function. Response choice names in `formulae` and in `options_affix` must be same. If user wants to declare difficulty level of the item, that also can be added within `options_affix`.

### Example II
```{R include = TRUE}
library(QAIG)
```
```{R echo = TRUE}
stem_text <- "[C1] has $ [N1] and [C2] has $ [N2] . If [C2] takes $ [N3] from [C1] later, then how much more amount than [C1] does [C3] have now?"

c1 <- c('Sam', 'Sean')
c2 <- c('Max', 'Martha', 'Mandy')
c3 <- c('he', 'she', 'she')

n1 <- c(4, 5, 6, 7)
n2 <- c(8, 9, 10)
n3 <- c(2, 3)

C <- list(c1 = c1, c2 = c2, c3 = c3)
N <- list(n1 = n1, n2 = n2, n3 = n3)

formulae <- "Option_A ? (n1 + n2)
Option_B ~ (n2 + 2*n3 - n1)
Option_C ? (n1 + n2 + 1)
Option_D ? (n1 + n2 - 2)
Option_E ? (n2 + n3 - n1)
"
options_affix <- list(Option_A = c('$ ', ''), Option_B = c('$ ', ''), Option_C = c('$ ', ''), Option_D = c('$ ', ''), Option_E = c('$ ', ''), Difficulty = 'EASY')

## itemgen() function can be used as:
newitems <- QAIG::itemgen(stem_text = stem_text, formulae = formulae, N = N, C = C, options_affix = options_affix)

newitems[, c(1, 4, 21, 24)]
```

### User can include a response choice with only text using `options_affix`.
### Example III
```{R include = TRUE}
library(QAIG)
```
```{R echo = TRUE}
stem_text <- "[C1] bought a [C2] at $ [N1] . [C3] spent $ [N2] for repairing it and then sold it at $ [N3] . What was [C4] percentage of profit or loss?"

c1 <- c('Samuel', 'April')
c2 <- c('motorcycle', 'moped')
c3 <- c('He', 'She')
c4 <- c('his', 'her')

n1 <- c(925, 862, 784)
n2 <- c(92, 102)
n3 <- 1030

C <- list(c1 = c1, c2 = c2, c3 = c3, c4 = c4)
N <- list(n1 = n1, n2 = n2, n3 = n3)

formulae <- "Option_A ? round((n2/n1)*100, 2)
Option_B ? round(((n3-n2-n1)/n3)*100, 1)
Option_C ? round(((n3-n2-n1+0)/n3)*100, 1)
Option_D ~ round((((n3-n2-n1)/(n1+n2))*100), 2)
"
options_affix <- list(Option_A = c('', '% loss'), Option_B = c('', '% profit'), Option_C = c('', '% loss'), Option_D = c('', '% profit'), Option_E = 'No profit no loss')

## itemgen() function can be used as:
newitems <- QAIG::itemgen(stem_text = stem_text, formulae = formulae, C = C, N = N, options_affix = options_affix)

newitems[, c(1, 2, 3, 6)]
```

### 3: Using `ans_key` argument.

Answer key of the items can be declared using `ans_key` argument also. In case of any text response choice becomes the answer key, user should declare the answer key using `ans_key` argument. In this case all the response choices in `formulae` must be marked by “?” only.

### Example IV
```{R include = TRUE}
library(QAIG)
```
```{R echo = TRUE}
stem_text <- "A [C1] was delayed somewhere for [N1] minutes but made up for the delay on a section of [N2] km travelling at a speed of [N3] km per hour higher than that which accorded the schedule. What was the speed of the [C1] that accorded the schedule?"

c1 <- c('car', 'bus', 'truck', 'train')

n1 <- c(16, 18, 20, 22, 24)
n2 <- c(80, 90, 100, 110)
n3 <- c(10, 12, 15, 18)

C <- list(c1 = c1)
N <- list(n1 = n1, n2 = n2, n3 = n3)

formulae <- "p <- 1
Option_A ? round((-n3 + sqrt(n3^2 - 4*p*(-60*n2*n3/n1)))/2,2)
Option_B ? round((-n3 - sqrt(n3^2 - 4*p*(-60*n2*n3/n1)))*(-1)/2-20,2)
Option_C ? round((-n3 - sqrt(n3^2 - 4*p*(-60*n2*n3/n1)))*(-1)/2,2)
Option_D ? round((-n3 + sqrt(n3^2 - 4*p*(-60*n2*n3/n1)))/2+30,2)
"
options_affix <- list(Option_A = c('', ' km/hr'), Option_B = c('', ' km/hr'), Option_C = c('', ' km/hr'), Option_D = c('', ' km/hr'), Option_E = 'Cannot be determined', Difficulty = 'HARD')

## itemgen() function can be used as:
newitems <- QAIG::itemgen(stem_text = stem_text, formulae = formulae, N = N, C = C, ans_key = 'Option_A', options_affix = options_affix)

newitems[, c(1, 2, 79, 80)]
```

### 4: Using supporting values and function(s) within `formulae`.

User may want to provide supporting values or a self-defined function to use during formulation of the response choice models. Those can be supplied within `formulae` by writing in separate lines.

**Note:** Formulation of each response choice model (formula) in `formulae` must produce a single numeric value.

### Example V
```{R include = TRUE}
library(QAIG)
```
```{R echo = TRUE}
stem_text <- "Sum of present ages of [C1] and [C2] [C3] is [N1] . After [N2] years [C2] [C3] will be thrice as old as [C1] . The present age of [C2] [C3] is"

n1 <- c(74, 80, 72, 68)
n2 <- c(8, 10)

c1 <- c('Sophia', 'Viktor', 'Julia', 'Andy')
c2 <- c('her', 'his')
c3 <- c('father', 'mother')

N <- list(n1 = n1, n2 = n2)
C <- list(c1 = c1, c2 = c2, c3 = c3)

formulae <- "a <- 5
sol <- function(x, y){
  A <- matrix(c(1, 1, 1, -3), nrow=2)
  B <- matrix(c(x, 2*y), nrow=2)
  return((as.matrix(solve(A)%*%B)))
}

Option_A ? round(sol(n1, n2)[1,]+a, 2)
Option_B ? round(sol(n1, n2)[2,]+a, 2)
Option_C ~ round(sol(n1, n2)[1,], 2)
Option_D ? round(sol(n1, n2)[2,], 2)
Option_E ? round(sol(n1, n2)[1,]-a, 2)
"
options_affix <- list(Option_A = c('', ' years'), Option_B = c('', ' years'), Option_C = c('', ' years'), Option_D = c('', ' years'), Option_E = c('', ' years'), Difficulty = 'MEDIUM')

## itemgen() function can be used as:
newitems <- QAIG::itemgen(stem_text = stem_text, formulae = formulae, N = N, C = C, options_affix = options_affix)
newitems[, c(1, 2, 7, 8)]
```

### 5: Using `save.csv` argument

Generated items can be saved in a `.csv` file by using the `save.csv` argument. If a name of the file is passed to this argument, all the generated items will be saved automatically in `.csv` format in the working directory.

As example:

`itemgen(stem_text, formulae, N, C = C, options_affix = options_affix, save.csv = 'New Items')`



[Reference: AIG for Developing Mathematics Achievement Items](https://onlinelibrary.wiley.com/doi/epdf/10.1111/jedm.12166)
