InterItemAnalysis {exametrika}R Documentation

Inter-Item Analysis for Psychometric Data

Description

Calculates various relationship metrics between pairs of items in test data. This analysis helps identify item interdependencies, content overlaps, and potential local dependence. For binary data, metrics include joint response rates, conditional probabilities, and several correlation measures. For ordinal/rated data, appropriate correlation measures are calculated.

The following metrics are calculated for binary data:

For ordinal/rated data, the function calculates:

Usage

InterItemAnalysis(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.

Details

This function automatically detects the data type and applies appropriate analysis methods:

Inter-item analysis is useful for:

Value

For binary data, an object of class "exametrika" and "IIAnalysis" containing:

JSS

Joint Sample Size matrix - N(i,j) shows number of examinees who responded to both items i and j

JCRR

Joint Correct Response Rate matrix - P(Xi=1, Xj=1) shows probability of correct responses to both items

CCRR

Conditional Correct Response Rate matrix - P(Xi=1|Xj=1) shows probability of correct response to item i given correct response to item j

IL

Item Lift matrix - P(Xi=1, Xj=1)/(P(Xi=1)*P(Xj=1)) measures association strength

MI

Mutual Information matrix - measures information shared between items

Phi

Phi Coefficient matrix - correlation coefficient between binary variables

Tetrachoric

Tetrachoric Correlation matrix - correlation between underlying continuous variables

For ordinal/rated data, an object of class "exametrika" and "IIAnalysis.ordinal" containing:

JSS

Joint Sample Size matrix

JSR

Joint Selection Rate matrix - frequencies of joint category selections

CSR

Conditional Selection Rate matrix - probabilities of response categories conditional on other items

MI

Mutual Information matrix

Polychoric

Polychoric Correlation matrix - correlations between underlying continuous variables

See Also

dataFormat for data preparation, CTT for Classical Test Theory analysis

Examples


# Basic usage with binary data
ii_analysis <- InterItemAnalysis(J15S500)

# View joint sample sizes
head(ii_analysis$JSS)

# View tetrachoric correlations
head(ii_analysis$Tetrachoric)

# Find pairs of items with high mutual information (potential local dependence)
high_MI <- which(ii_analysis$MI > 0.2 & upper.tri(ii_analysis$MI), arr.ind = TRUE)
if (nrow(high_MI) > 0) {
  print("Item pairs with high mutual information:")
  print(high_MI)
}

# Example with ordinal data
ordinal_analysis <- InterItemAnalysis(J15S3810)

# View polychoric correlations for ordinal data
head(ordinal_analysis$Polychoric)



[Package exametrika version 1.5.1 Index]