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)# S3 method for binary
ItemThreshold(U, na = NULL, Z = NULL, w = NULL)
# S3 method for ordinal
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
Either an object of class "exametrika" or raw data. When raw data is given,
it is converted to the exametrika class with the dataFormat function.
Values to be treated as missing values.
Missing indicator matrix of type matrix or data.frame. Values of 1 indicate observed responses, while 0 indicates missing data.
Item weight vector specifying the relative importance of each item.
# using sample dataset
ItemThreshold(J5S10)
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