Constrain the sum of item values per form.

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.

Value

An object of class "constraint".

Details

When operator is "<=", the constraint can be mathematically formulated as: _i=1^I v_i x_if t , \; \; \; for \: f G, where I refers to the number of items in the item pool, v_i is the itemValue for item i and t is the targetValue. Further, G corresponds to whichForms, so that the above inequality constraint is repeated for every test form f in G. In addition, let x be a vector of binary decision variables with length I F, where F is nForms. The binary decision variables x_if are defined as:

\;\;\;\;\;\;\;\;	x_if = 1,\;\;\;\;	if item i is assigned to form f, and
\;\;\;\;\;\;\;\;	x_if = 0,\;\;\;\;	otherwise.

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)
)
#> Warning: Argument 'itemIDs' is missing. 'itemIDs' will be generated automatically.
#> Warning: Argument 'itemIDs' is missing. 'itemIDs' will be generated automatically.
#> $A_binary
#> 4 x 20 sparse Matrix of class "dgCMatrix"
#>                                               
#> [1,] 1 2 3 4 5 6 7 8 9 10 . . . . . . . . .  .
#> [2,] . . . . . . . . .  . 1 2 3 4 5 6 7 8 9 10
#> [3,] 1 2 3 4 5 6 7 8 9 10 . . . . . . . . .  .
#> [4,] . . . . . . . . .  . 1 2 3 4 5 6 7 8 9 10
#> 
#> $A_real
#> NULL
#> 
#> $operators
#> [1] ">=" ">=" "<=" "<="
#> 
#> $d
#> [1] 4 4 6 6
#> 
#> $c_binary
#> NULL
#> 
#> $c_real
#> NULL
#> 
#> attr(,"class")
#> [1] "constraint"
#> attr(,"nForms")
#> [1] 2
#> attr(,"nItems")
#> [1] 10
#> attr(,"info")
#>   rowNr formNr itemNr constraint
#> 1     1      1     NA    1:10>=4
#> 2     2      2     NA    1:10>=4
#> 3     3      1     NA    1:10<=6
#> 4     4      2     NA    1:10<=6
#> attr(,"itemIDs")
#>  [1] "it01" "it02" "it03" "it04" "it05" "it06" "it07" "it08" "it09" "it10"