Typical Use of `eatATA`: a Minimal Example"

In eatATA: Create Constraints for Small Test Assembly Problems

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
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eatATA efficiently translates test design requirements for Automated Test Assembly (ATA) into constraints for a Mixed Integer Linear Programming Model (MILP). A number of efficient and user-friendly functions are available that translate conceptual test assembly constraints to constraint objects for MILP solvers, like the GLPK solver. In the remainder of this vignette we will illustrate the use of eatATA using a minimal example. A general overview over eatATA can be found in the vignette Overview of eatATA Functionality.

Setup

The eatATA package can be installed from CRAN.

install.packages("eatATA")

Item Pool

First, eatATA is loaded into your R session. In this vignette we use a small simulated item pool, items_mini. The goal will be to assemble a single test form consisting of ten items, an average test time of eight minutes and maximum TIF at medium ability. We therefore calculate the IIF at medium ability and append it to the item pool using the calculateIFF() function.

# loading eatATA
library(eatATA)

# item pool structure
str(items_mini)

# calculate and append IIF
items_mini[, "IIF_0"] <- calculateIIF(B = items_mini$difficulty, theta = 0)

In Table 1 you can see the first five items of the item pool.

# create content bounderies in advance
knitr::kable(items_mini[1:5,], digits = 3, caption = "Table 1. First 5 Items of the Item Pool")

Objective Function

Next, the objective function is defined: The TIF should be maximized at medium ability. For this, we use the maxObjective() function.

testInfo <- maxObjective(nForms = 1, itemValues = items_mini$IIF,
                          itemIDs = items_mini$item)

Constraints

Our further, fixed constraints are defined as additional constraint objects.

itemNumber <- itemsPerFormConstraint(nForms = 1, operator = "=", 
                                     targetValue = 10, 
                                     itemIDs = items_mini$item)

itemUsage <- itemUsageConstraint(nForms = 1, operator = "<=", 
                                 targetValue = 1, 
                                 itemIDs = items_mini$item)

testTime <- itemValuesDeviationConstraint(nForms = 1, 
                                itemValues = items_mini$time,
                                targetValue = 8 * 60, 
                                allowedDeviation = 5,
                                relative = FALSE, 
                                itemIDs = items_mini$item)

Alternatively, we could determine the appropriate test time based on the item pool using the autoItemValuesMinMax() function.

testTime2 <- autoItemValuesMinMaxConstraint(nForms = 1, 
                                itemValues = items_mini$time,
                                testLength = 10, 
                                allowedDeviation = 5,
                                relative = FALSE, 
                                itemIDs = items_mini$item)

Solver usage

To automatically assemble the test form based on our constraints, we call the useSolver() function. In this function we define which solver should be used as back end. As a default solver, we recommend GLPK, which is automatically installed alongside this package.

solver_out <- useSolver(list(itemNumber, itemUsage, testTime, testInfo),
                        solver = "GLPK")

Inspect solution

The solution can be inspected directly via inspectSolution() or appended to the item pool via appendSolution(). Using the inspectSolution() function an additional row is created that calculates the column sums for all numeric variables.

inspectSolution(solver_out, items = items_mini, idCol = "item")

appendSolution(solver_out, items = items_mini, idCol = "item")

eatATA documentation built on Nov. 28, 2022, 5:14 p.m.