TestGardener (version 3.3.6)

entropies: Entropy measures of inter-item dependency

Description

Entropy \(I_1\) is a scalar measure of how much information 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(index, m, n, chcemat, noption)

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.

Arguments

index

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.

chcemat

The data matrix containing the indices of choisen options for each test taker.

noption

A vector containing the number of options for all items.

Author

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.

See Also

Entropy_plot

Examples

#  Load needed objects
chcemat <- Quant_13B_problem_dataList$chcemat
index   <- Quant_13B_problem_parmList$index
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(index, Mvec[i1], Mvec[i2], chcemat, 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))