entropies: Entropy measures of inter-item dependency

In TestGardener: Optimal Analysis of Test and Rating Scale Data

Entropy measures of inter-item dependency

Description

Entropy $I_1$ is a scalar measure of how much informationn is required to predict the outcome of a choice number 1 exactly, and consequently is a measure of item effectiveness suitable for multiple choice tests and rating scales. Joint entropy $J_1,2$ is a scalar measure of the cross-product of multinomial vectors 1 and 2. Mutual entropy $I_1,2 = I_1 + I_2 - J_1,2$ is a measure of the co-dependency of items 1 and 2, and thus the analogue of the negative log of a squared correlation $R^2$. this function computes all four types of entropies for two specificed items.

Usage

entropies(theta, m, n, U, noption)

Arguments

theta	A vector of length N containing score index values for each test taker.
m	The index of the first choice.
n	The index of the second choice.
U	The data matrix containing the indices of choisen options for each test taker.
noption	A vector containing the number of options for all items.

Value

A named list object containing objects produced from analyzing the simulations, one set for each simulation:

I_m:

The entropy of item m.

I_n:

The entropy of item n.

J_nm:

The joint entropy of items m and n.

I_nm:

The mutual entropy of items m and n.

Author(s)

Juan Li and James Ramsay

References

Ramsay, J. O., Li J. and Wiberg, M. (2020) Full information optimal scoring. Journal of Educational and Behavioral Statistics, 45, 297-315.

Ramsay, J. O., Li J. and Wiberg, M. (2020) Better rating scale scores with information-based psychometrics. Psych, 2, 347-360.

http://testgardener.azurewebsites.net

See Also

Entropy.plot

Examples

#  Load needed objects
U       <- Quantshort_dataList$U
theta   <- Quantshort_parList$theta
noption <- matrix(5,24,1)
#  compute mutual entropies for all pairs of the first 6 items
Mvec    <- 1:6
Mlen    <- length(Mvec)
Hmutual <- matrix(0,Mlen,Mlen)
for (i1 in 1:Mlen) {
  for (i2 in 1:i1) {
    Result <- entropies(theta, Mvec[i1], Mvec[i2], U, noption)
    Hmutual[i1,i2] = Result$Hmutual
    Hmutual[i2,i1] = Result$Hmutual
  }
}
print("Matrix of mutual entries (off-digagonal) and self-entropies (diagonal)")
print(round(Hmutual,3))

TestGardener documentation built on Jan. 16, 2023, 1:06 a.m.