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).
ItemEntropy(U, na = NULL, Z = NULL, w = NULL, ...)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
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.
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
# using sample dataset
ItemEntropy(J5S10)
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