The item entropy is an indicator of the variability or randomness of the responses. This function is applicable only to binary response data.
The entropy value represents the uncertainty or information content of the response pattern for each item, measured in bits. Maximum entropy (1 bit) occurs when correct and incorrect responses are equally likely (p = 0.5).
Usage
ItemEntropy(U, na = NULL, Z = NULL, w = NULL)
# Default S3 method
ItemEntropy(U, na = NULL, Z = NULL, w = NULL)
# S3 method for class 'binary'
ItemEntropy(U, na = NULL, Z = NULL, w = NULL)
# S3 method for class 'ordinal'
ItemEntropy(U, na = NULL, Z = NULL, w = NULL)Arguments
- U
Either an object of class "exametrika" or raw data. When raw data is given, it is converted to the exametrika class with the
dataFormatfunction.- na
Values to be treated as missing values.
- Z
Missing indicator matrix of type matrix or data.frame. Values of 1 indicate observed responses, while 0 indicates missing data.
- w
Item weight vector specifying the relative importance of each item.
Value
A numeric vector of entropy values for each item, measured in bits. Values range from 0 to 1, where:
1: maximum uncertainty (p = 0.5)
0: complete certainty (p = 0 or 1)
Values near 1 indicate items with balanced response patterns
Values near 0 indicate items with extreme response patterns
Details
The item entropy is calculated as: $$e_j = -p_j\log_2p_j-(1-p_j)\log_2(1-p_j)$$ where \(p_j\) is the correct response rate for item j.
The entropy value has the following properties:
Maximum value of 1 bit when p = 0.5 (most uncertainty)
Minimum value of 0 bits when p = 0 or 1 (no uncertainty)
Higher values indicate more balanced response patterns
Lower values indicate more predictable response patterns