Create item category constraints with minimum and maximum. — itemCategoryRangeConstraint • eatATA

itemCategoriesRange, itemCategoriesMin, and itemCategoriesMax create constraints related to item categories/groupings (as represented by itemCategories). That is, the created constraints assure that the number of items of each category per test form is either smaller or equal than the specified max, greater than or equal to min or both range.

Usage

itemCategoryRangeConstraint(
  nForms,
  itemCategories,
  range,
  whichForms = seq_len(nForms),
  info_text = NULL,
  itemIDs = names(itemCategories)
)

itemCategoryMinConstraint(
  nForms,
  itemCategories,
  min,
  whichForms = seq_len(nForms),
  info_text = NULL,
  itemIDs = names(itemCategories)
)

itemCategoryMaxConstraint(
  nForms,
  itemCategories,
  max,
  whichForms = seq_len(nForms),
  info_text = NULL,
  itemIDs = names(itemCategories)
)

itemCategoryDeviationConstraint(
  nForms,
  itemCategories,
  targetValues,
  allowedDeviation,
  relative = FALSE,
  whichForms = seq_len(nForms),
  info_text = NULL,
  itemIDs = names(itemCategories)
)

Arguments

nForms: Number of forms to be created.
itemCategories: a factor representing the categories/grouping of the items
range: a matrix with two columns representing the the minimal and the maximum frequency of the items from each level/category itemCategories
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.
min: the minimal sum of the itemValues per test form
max: the minimal sum of the itemValues per test form
targetValues: an integer vector representing the target number per category. The order of the target values should correspond with the order of the levels of the factor in itemCategory.
allowedDeviation: the maximum allowed deviation from the targetValue
relative: a logical expressing whether or not the allowedDeviation should be interpreted as a proportion of the targetValue

Value

A sparse matrix.

Details

itemCategoriesDeviation also constrains the minimal and the maximal value of the number of items of each category per test form, but based on chosen targetValues, and maximal allowed deviations (i.e., allowedDeviation) from those targetValues.

Functions

itemCategoryMinConstraint(): constrain minimum value
itemCategoryMaxConstraint(): constrain maximum value
itemCategoryDeviationConstraint(): constrain the distance form the targetValues

Examples

## constraints to make sure that there are at least 2 and maximally 4
##  items of each item type in each test form
nItems <- 30
item_type <- factor(sample(1:3, size = nItems, replace = TRUE))
itemCategoryRangeConstraint(2, item_type, range = cbind(min = rep(2, 3), max = rep(4, 3)))
#> Warning: Argument 'itemIDs' is missing. 'itemIDs' will be generated automatically.
#> Warning: Argument 'itemIDs' is missing. 'itemIDs' will be generated automatically.
#> Warning: Argument 'itemIDs' is missing. 'itemIDs' will be generated automatically.
#> Warning: Argument 'itemIDs' is missing. 'itemIDs' will be generated automatically.
#> Warning: Argument 'itemIDs' is missing. 'itemIDs' will be generated automatically.
#> Warning: Argument 'itemIDs' is missing. 'itemIDs' will be generated automatically.
#> $A_binary
#> 12 x 60 sparse Matrix of class "dgCMatrix"
#>                                                                                
#>  [1,] 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 1 0 1 0 0 0 0 . . . . . . .
#>  [2,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 0 0 0 0 0 0
#>  [3,] 1 1 1 0 0 0 1 1 0 1 0 1 1 0 1 1 0 1 0 0 0 0 1 0 0 0 1 1 0 0 . . . . . . .
#>  [4,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 1 0 0 0 1
#>  [5,] 0 0 0 1 1 1 0 0 1 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 1 1 . . . . . . .
#>  [6,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 0 0 1 1 1 0
#>  [7,] 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 1 0 1 0 0 0 0 . . . . . . .
#>  [8,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 0 0 0 0 0 0
#>  [9,] 1 1 1 0 0 0 1 1 0 1 0 1 1 0 1 1 0 1 0 0 0 0 1 0 0 0 1 1 0 0 . . . . . . .
#> [10,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 1 0 0 0 1
#> [11,] 0 0 0 1 1 1 0 0 1 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 1 1 . . . . . . .
#> [12,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 0 0 1 1 1 0
#>                                                    
#>  [1,] . . . . . . . . . . . . . . . . . . . . . . .
#>  [2,] 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 1 0 1 0 0 0 0
#>  [3,] . . . . . . . . . . . . . . . . . . . . . . .
#>  [4,] 1 0 1 0 1 1 0 1 1 0 1 0 0 0 0 1 0 0 0 1 1 0 0
#>  [5,] . . . . . . . . . . . . . . . . . . . . . . .
#>  [6,] 0 1 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 1 1
#>  [7,] . . . . . . . . . . . . . . . . . . . . . . .
#>  [8,] 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 1 0 1 0 0 0 0
#>  [9,] . . . . . . . . . . . . . . . . . . . . . . .
#> [10,] 1 0 1 0 1 1 0 1 1 0 1 0 0 0 0 1 0 0 0 1 1 0 0
#> [11,] . . . . . . . . . . . . . . . . . . . . . . .
#> [12,] 0 1 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 1 1
#> 
#> $A_real
#> NULL
#> 
#> $operators
#>  [1] ">=" ">=" ">=" ">=" ">=" ">=" "<=" "<=" "<=" "<=" "<=" "<="
#> 
#> $d
#>  [1] 2 2 2 2 2 2 4 4 4 4 4 4
#> 
#> $c_binary
#> NULL
#> 
#> $c_real
#> NULL
#> 
#> attr(,"class")
#> [1] "constraint"
#> attr(,"nForms")
#> [1] 2
#> attr(,"nItems")
#> [1] 30
#> attr(,"info")
#>    rowNr formNr itemNr   constraint
#> 1      1      1     NA item_type>=2
#> 2      2      2     NA item_type>=2
#> 3      3      1     NA item_type>=2
#> 4      4      2     NA item_type>=2
#> 5      5      1     NA item_type>=2
#> 6      6      2     NA item_type>=2
#> 7      7      1     NA item_type<=4
#> 8      8      2     NA item_type<=4
#> 9      9      1     NA item_type<=4
#> 10    10      2     NA item_type<=4
#> 11    11      1     NA item_type<=4
#> 12    12      2     NA item_type<=4
#> attr(,"itemIDs")
#>  [1] "it01" "it02" "it03" "it04" "it05" "it06" "it07" "it08" "it09" "it10"
#> [11] "it11" "it12" "it13" "it14" "it15" "it16" "it17" "it18" "it19" "it20"
#> [21] "it21" "it22" "it23" "it24" "it25" "it26" "it27" "it28" "it29" "it30"

## or alternatively
itemCategoryDeviationConstraint(2, item_type,
targetValues = rep(3, 3),
allowedDeviation = rep(4, 3))
#> Warning: Argument 'itemIDs' is missing. 'itemIDs' will be generated automatically.
#> Warning: Argument 'itemIDs' is missing. 'itemIDs' will be generated automatically.
#> Warning: Argument 'itemIDs' is missing. 'itemIDs' will be generated automatically.
#> Warning: Argument 'itemIDs' is missing. 'itemIDs' will be generated automatically.
#> Error in itemValuesConstraint(nForms, 1 * (itemCategories == levels[levelNr]),     operator, targetValues[levelNr], whichForms, info_text[levelNr],     itemIDs): The 'targetValue' should be smaller than the sum of the 'itemValues'.