thrstThrsh {conquestr}  R Documentation 
thrstThrsh
Description
Generates Thurstonian Thresholds (sometimes called gammas) to an item. 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
thrstThrsh(myItem, threshP = 0.5, minTheta = 20, maxTheta = 20, convC = 1e05)
Arguments
myItem 
A matrix of parameters for a single item of the structure used in 
threshP 
The probability at which the threshold is calculated (defaults to the usual value of 0.5) 
minTheta 
The lowerbound starting value of the splithalf search used to find the threshold for the category. 
maxTheta 
The upperbound starting value of the splithalf 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

Value
A k1 by 1 matrix with Thurstonian thresholds for this item. Values are NA when the threshold cannot be calculated.
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
)
thrstThrsh(myItem)