Item Odds

Item Odds are defined as the ratio of Correct Response Rate to Incorrect Response Rate: $$O_j = \frac{p_j}{1-p_j}$$ where \(p_j\) is the correct response rate for item j. This function is applicable only to binary response data.

The odds value represents how many times more likely a correct response is compared to an incorrect response. For example, an odds of 2 means students are twice as likely to answer correctly as incorrectly.

Usage

ItemOdds(U, na = NULL, Z = NULL, w = NULL)

# Default S3 method
ItemOdds(U, na = NULL, Z = NULL, w = NULL)

# S3 method for class 'binary'
ItemOdds(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 dataFormat function.

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 odds values for each item. Values range from 0 to infinity, where:

• odds > 1: correct response more likely than incorrect

• odds = 1: equally likely

• odds < 1: incorrect response more likely than correct

Note

This function is implemented using a binary data compatibility wrapper and will raise an error if used with polytomous data.

Examples

# using sample dataset
ItemOdds(J5S10)
#>             [,1]
#> Item01 1.5000000
#> Item02 0.6666667
#> Item03 9.0000000
#> Item04 0.4285714
#> Item05 0.6666667