This function calculates statistics for each item, with different metrics available depending on the data type (binary, ordinal, or rated).
ItemStatistics(U, na = NULL, Z = NULL, w = NULL)# S3 method for default
ItemStatistics(U, na = NULL, Z = NULL, w = NULL)
# S3 method for binary
ItemStatistics(U, na = NULL, Z = NULL, w = NULL)
# S3 method for ordinal
ItemStatistics(U, na = NULL, Z = NULL, w = NULL)
For binary data:
Label identifying each item
Number of Respondents for each item
Correct Response Rate denoted as $p_j$.
Item Odds is the ratio of the correct response rate to the incorrect response rate. Defined as \(o_j = \frac{p_j}{1-p_j}\)
Item Threshold is a measure of difficulty based on a standard normal distribution.
Item Entropy is an indicator of the variability or randomness of the responses. Defined as \(e_j=-p_j \log_2 p_j - (1-p_j)\log_2(1-p_j)\)
Item-total Correlation is a Pearson's correlation of an item with the Number-Right score.
For ordinal polytomous data:
Label identifying each item
Number of Respondents for each item
Matrix of threshold values for each item's category boundaries, based on a standard normal distribution. For an item with K categories, there are K-1 thresholds.
Item Entropy calculated using the category probabilities. Unlike binary data, this is calculated using the formula \(e_j = -\sum_{k=1}^{K_j} p_{jk} \log_{K_j} p_{jk}\), where \(K_j\) is the number of categories for item j.
Item-total Correlation calculated using polyserial correlation, which accounts for the ordinal nature of the item responses and the continuous total score.
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(binary)
ItemStatistics(J15S500)
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