Item Lift

The lift is a commonly used index in a POS data analysis. The item lift of Item k to Item j is defined as follow: \( l_{jk} = \frac{p_{k\mid j}}{p_k} \) This function is applicable only to binary response data.

Usage

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

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

# S3 method for class 'binary'
ItemLift(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 matrix of item lift values with exametrika class. Each element (j,k) represents the lift value of item k given item j, which indicates how much more likely item k is to be correct given that item j was answered correctly.

Note

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

References

Brin, S., Motwani, R., Ullman, J., & Tsur, S. (1997). Dynamic itemset counting and implication rules for market basket data. In Proceedings of ACM SIGMOD International Conference on Management of Data (pp. 255–264). https://dl.acm.org/doi/10.1145/253262.253325

Examples

# example code
# Calculate ItemLift using sample dataset J5S10
ItemLift(J5S10)
#>        Item01 Item02 Item03 Item04 Item05
#> Item01  1.667   1.25   1.11   1.67  0.833
#> Item02  1.250   2.50   1.11   1.67  1.250
#> Item03  1.111   1.11   1.11   1.11  1.111
#> Item04  1.667   1.67   1.11   3.33  1.667
#> Item05  0.833   1.25   1.11   1.67  2.500