generateSingleFactorItems {pcFactorStan}

Generate paired comparison data with a common factor that accounts for some proportion of the variance

Description

Imagine that there are people that play in tournaments of more than one board game. For example, the computer player AlphaZero (Silver et al. 2018) has trained to play chess, shogi, and Go. We can take the tournament match outcome data and find rankings among the players for each of these games. We may also suspect that there is a latent board game skill that accounts for some proportion of the variance in the per-board game rankings.

Usage

generateSingleFactorItems(df, prop, th = 0.5, name, ..., scale = 1, alpha = 1)

Arguments

df

a data frame with pairs of vertices given in columns pa1 and pa2, and item response data in other columns

prop

the number of items or a vector of signed proportions of variance

th

a vector of thresholds

name

a vector of item names

...

Not used. Forces remaining arguments to be specified by name.

scale

a vector of scaling constants

alpha

a vector of item discriminations

Value

The given data.frame df with additional columns for each item.

Response model

See cmp_probs for details.

Backward incompatibility

The function generateFactorItems was renamed to generateSingleFactorItems (version 1.1.0) to make space for a more flexible factor model with an arbitrary number of factors and arbitrary factor-to-item loading pattern. If you don't need this flexibility, you can call the old function generateSingleFactorItems.

References

Silver, D., Hubert, T., Schrittwieser, J., Antonoglou, I., Lai, M., Guez, A., ... & Lillicrap, T. (2018). A general reinforcement learning algorithm that masters chess, shogi, and Go through self-play. Science, 362(6419), 1140-1144.

See Also

Other item generators: generateCovItems(), generateFactorItems(), generateItem()

Examples

df <- twoLevelGraph(letters[1:10], 100)
df <- generateSingleFactorItems(df, 3)