itemListToThresholds {conquestr}

itemListToThresholds

Description

Taskes a list of item parameter matricies and returns a data frame containing Thurstonian Thresholds (gammas) for all items. Thurstonian thresholds are the location on the trait/scale at which the cumulative probability of being in category k, or any higher category equals some probability (usually 0.5, the default). Thurstonian thresholds are considered a way of describing the difficulty of polytomously scored items and are usually the value used in visualisations like Wright maps. Thurstonian thresholds can only be calculated for items where response categories are scored such that each category can be placed in an order increasing scores (e.g., no ties as per the Ordered Partition model)

Usage

itemListToThresholds(
  myItems,
  threshP = 0.5,
  minTheta = -20,
  maxTheta = 20,
  convC = 1e-05
)

Arguments

myItems

A list of item parameter matricies of the structure used in simplef (a matrix of k categories by four (category score, delta dot, tau, discrimination)).

threshP

The probability at which the thresholds are calculated (defaults to the usual value of 0.5)

minTheta

The lower-bound starting value of the split-half search used to find the threshold for the category.

maxTheta

The upper-bound starting value of the split-half search used to find the threshold for the category.

convC

The convergence criteria used to determine when the threshold has been found. The difference between threshP and the cumulative probability of the category and any higher category at the current value of theta (the current proposed value of threshold being tested).

Value

A data frame including 4 columns:

• id, an integer index reflecting which item this is, in the same order as myItems

• itemid, a string with the names from the items in myItems (NA if item list is not named)

• step, which step does this threshold belong?

• location, the value of the threshold

Examples

myItem <- matrix(
  c(
    0, -0.58    ,  0     , 1,  # delta+tau   thurst thresh (gamma)
    1, -0.58    ,  0.776 , 1,  # 0.196       -1.14
    2, -0.58    , -0.697 , 1,  # -1.277      -0.93
    3, -0.58    , -0.629 , 1,  # -1.209      -0.64
    4, -0.58    ,  0.55  , 1   # -0.03        0.25
    ), ncol =4, byrow=TRUE
 )
itemListToThresholds(list(myItem))