Bliss points from preference ratings

External unfolding with the PREFMAP ideal-point model: per rater, least squares of ratings on (1, z_j, ||z_j||^2) gives the ideal point -c / (2 c2) and salience -c2 (anti-ideal points flagged when c2 >= 0); optionally a Nadaraya-Watson (Gaussian kernel) smooth of each rater's ratings over a grid.

Usage

BlissPoints(ratings, stimuli, grid = NULL, bandwidth = NULL)

Arguments

ratings

Raters by stimuli matrix.

stimuli

Stimulus positions (vector or matrix rows).

grid

Optional evaluation points for the utility surface.

bandwidth

Kernel bandwidth (default: median inter-stimulus distance).

Value

list(ideal, salience, anti_ideal, r2, surface, bandwidth).

References

Carroll, J. D. (1972). Individual differences and multidimensional scaling. In Multidimensional Scaling: Theory and Applications in the Behavioral Sciences, vol. 1, 105-155.

Examples

z <- 0:3
BlissPoints(matrix(10 - (z - 1.2)^2, 1), z)$ideal
#> [[1]]
#> [1] 1.2
#>