exametrika (version 1.6.0)

CSR: Conditional Selection Rate

Description

Calculate the Conditional Selection Rate (CSR) for polytomous data. CSR measures the proportion of respondents who selected a specific category in item K, given that they selected a particular category in item J.

Usage

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

Value

A list of Joint Selection Rate matrices for each item pair.

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.

Details

The function returns a nested list structure CSR, where CSR[[j]][[k]] contains a matrix of conditional probabilities. In this matrix, the element at row l and column m represents P(K=m|J=l), which is the probability of selecting category m for item K, given that category l was selected for item J.

Mathematically, for each cell (l,m) in the CSR[[j]][[k]] matrix: CSR[[j]][[k]][l,m] = P(Item K = category m | Item J = category l)

This is calculated as the number of respondents who selected both category l for item J and category m for item K, divided by the total number of respondents who selected category l for item J.

Examples

# example code
# Calculate CSR using sample dataset J5S1000
CSR(J5S1000)

# Extract the conditional selection rates from item 1 to item 2
csr_1_2 <- CSR(J5S1000)[[1]][[2]]
# This shows the probability of selecting each category in item 2
# given that a specific category was selected in item 1