eatATA (version 1.1.2)

computeTargetValues: Compute target values based on the item pool.

Description

Compute target values for item values/categories based on the number of items in the item pool, the number of test forms to assemble and the number of items in each test form (i.e., test length).

Usage

computeTargetValues(
  itemValues,
  nForms,
  testLength = NULL,
  allowedDeviation = NULL,
  relative = FALSE
)
# S3 method for default
computeTargetValues(
  itemValues,
  nForms,
  testLength = NULL,
  allowedDeviation = NULL,
  relative = FALSE
)
# S3 method for factor
computeTargetValues(
  itemValues,
  nForms,
  testLength = NULL,
  allowedDeviation = NULL,
  relative = FALSE
)

Value

a vector or a matrix with target values (see details)

Arguments

itemValues

Item parameter/values for which the sum per test form should be constrained.

nForms

Number of forms to be created.

testLength

to be documented.

allowedDeviation

Numeric value of length 1. How much deviance is allowed from target values?

relative

Is the allowedDeviation expressed as a proportion?

Methods (by class)

• computeTargetValues(default): compute target values

• computeTargetValues(factor): compute target frequencies for item categories

Details

Both for numerical and categorical item values, the target values are the item pool average scaled by the ratio of items in the forms and items in the item pool. The behavior of the function changes depending on the class of itemValues.

When itemValues is a numerical vector, an when allowedDeviation is NULL (the default), only one target value is computed. This value could be used in the targetConstraint-function. Otherwise (i.e., allowedDeviation is a numerical value), the target is computed, but a minimal and a maximal (target)value are returned, based on the allowed deviation. When relative == TRUE the allowed deviation should be expressed as a proportion. In that case the minimal and maximal values are a computed proportionally.

When itemValues is a factor, it is assumed that the item values are item categories, and hence only whole valued frequencies are returned. To be more precise, a matrix with the minimal and maximal target frequencies for every level of the factor are returned. When allowedDeviation is NULL, the difference between the minimal and maximal value is one (or zero). As a consequence, dummy-item values are best specified as a factor (see examples).

Examples

## Assume an item pool with 50 items with random item information values (iif) for
## a given ability value.
set.seed(50)
itemInformations <- runif(50, 0.5, 3)

## The target value for the test information value (i.e., sum of the item
## informations) when three test forms of 10 items are assembled is:
computeTargetValues(itemInformations, nForms = 3, testLength = 10)

## The minimum and maximum test iformation values for an allowed deviation of
## 10 percent are:
computeTargetValues(itemInformations, nForms = 3, allowedDeviation = .10,
   relative = TRUE, testLength = 10)


## items_vera$MC is dummy variable indication which items in the pool are multiple choise
str(items_vera$MC)

## when used as a numerical vector, the dummy is not treated as a categorical
## indicator, but rather as a numerical value.
computeTargetValues(items_vera$MC, nForms = 14)
computeTargetValues(items_vera$MC, nForms = 14, allowedDeviation = 1)

## Therefore, it is best to convert dummy variables into a factor, so that
## automatically freqyencies are returned
MC_factor <- factor(items_vera$MC, labels = c("not MC", "MC"))
computeTargetValues(MC_factor, nForms = 14)
computeTargetValues(MC_factor, nForms = 3)

## The computed minimum and maximum frequencies can be used to create contstraints.
MC_ranges <- computeTargetValues(MC_factor, nForms = 3)
itemCategoryRangeConstraint(3, MC_factor, range = MC_ranges)

## When desired, the automatically computed range can be adjusted by hand. This
##  can be of use when only a limited set of the categories should be constrained.
##  For instance, when only the multiple-choice items should be constrained, and
##  the non-multiple-choice items should not be constrained, the minimum and
##  maximum value can be set to a very small and a very high value, respectively.
##  Or to other sensible values.
MC_ranges["not MC", ] <- c(0, 40)
MC_ranges
itemCategoryRangeConstraint(3, MC_factor, range = MC_ranges)