ItemStatistics {exametrika} | R Documentation |
Simple Item Statistics
Description
This function calculates statistics for each item, with different metrics available depending on the data type (binary, ordinal, or rated).
Usage
ItemStatistics(U, na = NULL, Z = NULL, w = NULL)
## Default S3 method:
ItemStatistics(U, na = NULL, Z = NULL, w = NULL)
## S3 method for class 'binary'
ItemStatistics(U, na = NULL, Z = NULL, w = NULL)
## S3 method for class 'ordinal'
ItemStatistics(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 |
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
For binary data:
- ItemLabel
Label identifying each item
- NR
Number of Respondents for each item
- CRR
Correct Response Rate denoted as $p_j$.
- ODDs
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}
- Threshold
Item Threshold is a measure of difficulty based on a standard normal distribution.
- Entropy
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)
- ITCrr
Item-total Correlation is a Pearson's correlation of an item with the Number-Right score.
For ordinal polytomous data:
- ItemLabel
Label identifying each item
- NR
Number of Respondents for each item
- Threshold
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.
- Entropy
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}
, whereK_j
is the number of categories for item j.- ITCrr
Item-total Correlation calculated using polyserial correlation, which accounts for the ordinal nature of the item responses and the continuous total score.
Note
For rated data, the function processes the data as binary, with each response being compared to the correct answer to determine correctness.
Examples
# using sample dataset(binary)
ItemStatistics(J15S500)