autoFC (version 0.2.0.1002)

cal_block_energy_with_iia: Calculation of Item Block "Energy" with IIAs Included

Description

Calculates the total "energy" of one or multiple paired item blocks, which is a linear combination of different functions applied to different item characteristics of interest.

This function extends cal_block_energy function with consideration of inter item agreement (IIA) metrics.

Usage

cal_block_energy_with_iia(block, item_chars, weights,
                                 FUN, rater_chars,
                                 iia_weights = c(BPlin = 1, BPquad = 1,
                                 AClin = 1, ACquad = 1), verbose = FALSE)

Value

A numeric value indicating the total energy for the given item block(s).

Arguments

block, item_chars, weights, FUN

See ?cal_block_energy for details.

rater_chars

A p by m numeric matrix with scores of each of the p participants for the m items.

iia_weights

A vector of length 4 indicating weights given to each IIA metric:

Linearly weighted AC (Gwet, 2008; 2014);

Quadratic weighted AC;

Linearly weighted Brennan-Prediger (BP) Index(Brennan & Prediger, 1981; Gwet, 2014);

Quadratic weighted BP.

verbose

Logical. Should IIAs be printed when this function is called?

Author

Mengtong Li

Details

This energy calculation function serves as the core for determining the acceptance or rejection of a newly built block over the previous one. Higher energy is considered more preferable in this case.

Items in the same block can be paired based on characteristics such as: Mean score, Item Factor, Factor loading, Item IRT Parameters, Reverse Coding, etc.

In addition, IIAs can be adopted to further estimate rater agreements between different items, if such information is available for the researchers.

Pairings of different characteristics can be optimized in different way, by determining the customized function vector FUN and the corresponding weights. Currently only linear weighted combination for IIAs can be used in optimization.

References

Brennan, R. L., & Prediger, D. J. (1981). Coefficient kappa: Some uses, misuses, and alternatives. Educational and Psychological Measurement, 41(3), 687-699. https://doi.org/10.1177/001316448104100307

Gwet, K. L. (2008). Computing inter rater reliability and its variance in the presence of high agreement. British Journal of Mathematical and Statistical Psychology, 61(1), 29-48. https://doi.org/10.1348/000711006X126600

Gwet, K. L. (2014). Handbook of inter-rater reliability (4th ed.): The definitive guide to measuring the extent of agreement among raters. Gaithersburg, MD: Advanced Analytics Press.

See Also

cal_block_energy

Examples

## Simulate 60 items loading on different Big Five dimensions,
## with different mean and item difficulty

item_dims <- sample(c("Openness","Conscientiousness","Neuroticism",
                     "Extraversion","Agreeableness"), 60, replace = TRUE)
item_mean <- rnorm(60, 5, 2)
item_difficulty <- runif(60, -1, 1)

## Construct data frame for item characteristics and produce
## 20 random triplet blocks with these 60 items

item_df <- data.frame(Dimensions = item_dims, Mean = item_mean,
                     Difficulty = item_difficulty)
solution <- make_random_block(60, 60, 3)


## Simple simulation of responses from 600 participants on the 60 items.
## In practice, should use real world data or simluation based on IRT parameters.

item_responses <- matrix(sample(seq(1:5), 600*60, replace = TRUE), ncol = 60, byrow = TRUE)


cal_block_energy_with_iia(solution, item_chars = item_df, weights = c(1,1,1),
                          FUN = c("facfun", "var", "var"),
                          rater_chars = item_responses, iia_weights = c(1,1,1,1))