Minimax Constraint.

Create minimax-constraints related to an item parameter/value. That is, the created constraints can be used to minimize the maximum distance between the sum of the item values (itemValues) per test form and the chosen targetValue.

Usage

minimaxObjective(
  nForms,
  itemValues,
  targetValue,
  weight = 1,
  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.

targetValue

the target test form value.

weight

a weight for the real-valued variable(s). Useful when multiple constraints are combined. Should only be used if the implications are well understood.

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".

Examples

# constraint that minimizes the maximum difference per test form value and a
#   target value of 0
minimaxObjective(nForms = 2,
                 itemValues = rep(-2:2, 2),
                 targetValue = 0)
#> $A_binary
#> 4 x 20 sparse Matrix of class "dgCMatrix"
#>                                                     
#> [1,] -2 -1 0 1 2 -2 -1 0 1 2  .  . . . .  .  . . . .
#> [2,]  .  . . . .  .  . . . . -2 -1 0 1 2 -2 -1 0 1 2
#> [3,] -2 -1 0 1 2 -2 -1 0 1 2  .  . . . .  .  . . . .
#> [4,]  .  . . . .  .  . . . . -2 -1 0 1 2 -2 -1 0 1 2
#> 
#> $A_real
#>      [,1]
#> [1,]   -1
#> [2,]   -1
#> [3,]    1
#> [4,]    1
#> 
#> $operators
#> [1] "<=" "<=" ">=" ">="
#> 
#> $d
#> [1] 0 0 0 0
#> 
#> $c_binary
#> NULL
#> 
#> $c_real
#> [1] 1
#> 
#> attr(,"class")
#> [1] "constraint"
#> attr(,"nForms")
#> [1] 2
#> attr(,"nItems")
#> [1] 10
#> attr(,"sense")
#> [1] "min"
#> attr(,"info")
#>   rowNr formNr itemNr         constraint
#> 1     1      1     NA minimax_lowerBound
#> 2     2      2     NA minimax_lowerBound
#> 3     3      1     NA minimax_upperBound
#> 4     4      2     NA minimax_upperBound
#> attr(,"itemIDs")
#>  [1] "it01" "it02" "it03" "it04" "it05" "it06" "it07" "it08" "it09" "it10"