entropies | R Documentation |

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.

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

`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. |

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.

Juan Li and James Ramsay

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

`Entropy.plot`

# 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))

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