constraints_lp_format: Format characteristics and constraints
In Karel-Kroeze/ShadowCAT: Multidimensional Computer Adaptive Testing with the Shadow Testing Procedure

Description Usage Arguments Value Characteristics specification Constraint specification Return object Note about length Examples

Get a list with characteristics and constraints which can be used in lp function from lpSolve package.

1 2	constraints_lp_format(max_n, number_items, characteristics = NULL, constraints = NULL)

`max_n`	Test length at which testing should stop.
`number_items`	Number of items available in the item bank.
`characteristics`	Data frame with characteristics, see `details`.
`constraints`	List of constraints, see `details`.

List containing characteristics and constraints in lp format; the maximum test length is always included as an additional constraint; see details.

characteristics should be specified as a data frame of characteristics. Each row indicates the characteristics of one item. Each column indicates how all items score on a certain characteristic. Characteristics may be categorical or numeric.

constraints should be specified as a list of constraints, each constraint is a list with three named values:

name: The column name of the characteristic this constraint applies to. For categorical characteristics the level should be specified as name/value, where name is the column name of the characteristic and value is the specific level of the characteristic this constraint applies to.
op: The logical operator to be used. Valid options are "<", "=", ">" and "><".
target: The target value, numeric. For categorical characteristics, it indicates the number of items of the relevant characteristic that should be administered ("="), or minimally (">"), maximally ("<"), or minimally and maximally ("><"; vector with two values required) administered. For numeric characteristics, it indicates the minimum and/or maximum sum allowed over all administered items, e.g., maximum time allowed.

The constraints and characteristics in lp format will be stored within a list. Setting the constraints and characteristics arguments to NULL results in a list with only the test length constraint. Constraints in Shadow Tests are implemented through linear programming, for which the package lpSolve is used. The returned constraints object is a list with two named elements; lp_constraints and lp_chars. The lp_constraints and lp_chars are set up to work with lpSolve, and should not be manually edited.

Note that the maximum test length is always included as an additional constraint.

max_n <- 30
number_items <- 50

# set up some dummy characteristics.
content <- sample(c('algebra','physics','calculus'), number_items, TRUE)
time <- runif(number_items)
exclusive <- rep(0, number_items)
exclusive[sample(number_items, 4)] <- 1

# bind them in a data.fame
characteristics <- data.frame(content, time, exclusive)

# set up the constraints
constraints <- list(
  list(name = 'content/algebra',
       op = '><',
       target = c(5,10)),
  list(name = 'content/physics',
       op = '><',
       target = c(2,5)),
  list(name = 'time',
       op = '<',
       target = 20),
  list(name = 'exclusive',
       op = '<',
       target = 2))

# get list of characteristics and constraintrs in lp format
ShadowCAT:::constraints_lp_format(max_n = max_n, 
                                  number_items = number_items, 
                                  characteristics = characteristics, 
                                  constraints = constraints)