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hbamr

Hierarchical Bayesian Aldrich-McKelvey Scaling

This R package implements hierarchical Bayesian Aldrich-McKelvey (HBAM) scaling using Hamiltonian Monte Carlo via Stan. Aldrich-McKelvey (AM) scaling is a method for estimating the latent positions of survey respondents and external objects on a common scale using positional survey data (Aldrich & McKelvey 1977). The hierarchical versions of the AM model included in this package outperform other versions both in terms of yielding meaningful posterior distributions for respondent positions and in terms of recovering true respondent positions in simulations (Bølstad 2024). The package provides functions for preparing data, fitting models, extracting estimates, plotting key results, and comparing models using cross-validation.

Installation

The package is available from CRAN and can be installed using the standard method:

This is the easiest way to install the package, as the binaries on CRAN include pre-compiled models that are ready for use.

Usage

Load the package:

Load and recode example data:

data(LC1980)
LC1980[LC1980 == 0 | LC1980 == 8 | LC1980 == 9] <- NA 
self <- LC1980[, 1]
stimuli <- LC1980[, -1]

Fit the standard HBAM model:

fit_hbam <- hbam(self, stimuli)

Fit the HBAM_MINI model:

fit_hbam_mini <- hbam(self, stimuli, model = "HBAM_MINI")

Plot estimated stimuli positions:

plot_stimuli(fit_hbam)

Plot the distribution of estimated respondent positions:

Plot estimated scale-stretching over respondents’ self-placements:

plot_over_self(list(fit_hbam, fit_hbam_mini), "abs_beta")

References

  • Aldrich, John H, and Richard D McKelvey. 1977. “A Method of Scaling with Applications to the 1968 and 1972 Presidential Elections.” American Political Science Review 71(1): 111-130.
  • Bølstad, Jørgen. 2020. “Capturing Rationalization Bias and Differential Item Functioning: A Unified Bayesian Scaling Approach.” Political Analysis 28(3): 340-355.
  • Bølstad, Jørgen. 2024. “Hierarchical Bayesian Aldrich-McKelvey Scaling.” Political Analysis 32(1): 50-64.
  • Hare, Christopher et al. 2015. “Using Bayesian Aldrich-McKelvey Scaling to Study Citizens’ Ideological Preferences and Perceptions.” American Journal of Political Science 59(3): 759-774.