Item threshold is a measure of difficulty based on a standard normal distribution. This function is applicable only to binary response data.
The threshold is calculated as: $$\tau_j = \Phi^{-1}(1-p_j)$$ where \(\Phi^{-1}\) is the inverse standard normal distribution function and \(p_j\) is the correct response rate for item j.
Higher threshold values indicate more difficult items, as they represent the point on the standard normal scale above which examinees tend to answer incorrectly.
ItemThreshold(U, na = NULL, Z = NULL, w = NULL, ...)A numeric vector of threshold values for each item on the standard normal scale. Typical values range from about -3 to 3, where:
Positive values indicate difficult items
Zero indicates items of medium difficulty (50% correct)
Negative values indicate easy items
U is a data matrix of the type matrix or data.frame.
na argument specifies the numbers or characters to be treated as missing values.
Z is a missing indicator matrix of the type matrix or data.frame
w is item weight vector
Internal parameters for maintaining compatibility with the binary data processing system. Not intended for direct use.
# using sample dataset
ItemThreshold(J5S10)
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