---
title: "Comparability of translated exam forms"
output: markdown::html_format
vignette: >
  %\VignetteIndexEntry{Comparability of translated exam forms}
  %\VignetteEngine{knitr::knitr}
  %\VignetteEncoding{UTF-8}
---

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

When an exam is offered in a second language, the question is whether a score
means the same thing in both. Standard DIF tools struggle when the translated
group is small, differs in ability, and many items shift in the same
direction. transDIF is built for that situation.

## Data

A source-language group of 2,000 and a translated-language group of 150 who
are 0.5 logits lower on average. Items with idioms, cultural referents,
measurement units or heavy vocabulary tend to shift in translation.

```{r}
library(transDIF)
sim <- td_simulate(n_ref = 2000, n_focal = 150, n_items = 40, seed = 5)
colSums(sim$features[-1])
```

## Calibrate each group, then link and detect DIF together

```{r}
cal <- td_calibrate(sim$responses, sim$group)
dif <- td_dif(cal)
dif
```

The linking shift (the ability difference) is the center of the densest
cluster of items, not the mean of all items, so it does not assume that DIF
cancels out. Compare with linking on
all items:

```{r}
c(true = -sim$truth$focal_mean, robust = dif$link[["c"]], all_items = dif$c_mean)
```

## Does DIF change pass rates?

```{r}
td_impact(dif, cut = 24, n_draws = 100, seed = 1)
```

## What should translators look at?

```{r}
td_features(dif, sim$features)
```

## A report to start from

```{r}
cat(td_report(dif, languages = c("English", "French")))
```

With focal groups of 100 or fewer, treat flags as candidates for expert
review: in the package's validation the false discovery rate exceeded its
target at those sizes.