itemValuesConstraint: Constrain the sum of item values per form.

In eatATA: Create Constraints for Small Test Assembly Problems

Constrain the sum of item values per form.

Description

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Create constraints related to an item parameter/value. That is, the created constraints assure that the sum of the item values (itemValues) per test form is either (a) smaller than or equal to (operator = "<="), (b) equal to (operator = "="), or (c) greater than or equal to (operator = ">=") the chosen targetValue.

Usage

itemValuesConstraint(
  nForms,
  itemValues,
  operator = c("<=", "=", ">="),
  targetValue,
  whichForms = seq_len(nForms),
  info_text = NULL,
  itemIDs = names(itemValues)
)

Arguments

nForms	Number of forms to be created.
itemValues	Item parameter/values for which the sum per test form should be constrained.
operator	A character indicating which operator should be used in the constraints, with three possible values: "<=", "=", or ">=". See details for more information.
targetValue	the target test form value.
whichForms	An integer vector indicating which test forms should be constrained. Defaults to all the test forms.
info_text	a character string of length 1, to be used in the "info"-attribute of the resulting constraint-object.
itemIDs	a character vector of item IDs in correct ordering, or NULL.

Details

When operator is "<=", the constraint can be mathematically formulated as: \mjsdeqn\sum_i=1^I v_i \times x_if \leq t , \; \; \; for \: f \in G, where \mjseqnI refers to the number of items in the item pool, \mjseqnv_i is the itemValue for item \mjseqni and \mjseqnt is the targetValue. Further, \mjseqnG corresponds to whichForms, so that the above inequality constraint is repeated for every test form \mjseqnf in \mjseqnG. In addition, let \mjseqn\boldsymbolx be a vector of binary decision variables with length \mjseqnI \times F, where \mjseqnF is nForms. The binary decision variables \mjseqnx_if are defined as:

\mjseqn\;\;\;\;\;\;\;\;	\mjseqnx_if = 1,\mjseqn\;\;\;\;	if item \mjseqni is assigned to form \mjseqnf, and
\mjseqn\;\;\;\;\;\;\;\;	\mjseqnx_if = 0,\mjseqn\;\;\;\;	otherwise.

Value

An object of class "constraint".

Examples

## constraints to make sure that the sum of the item values (1:10) is between
## 4 and 6
combineConstraints(
  itemValuesConstraint(2, 1:10, operator = ">=", targetValue = 4),
  itemValuesConstraint(2, 1:10, operator = "<=", targetValue = 6)
)

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