Principal Component Analysis (PCA) is a statistical technique used to reduce the dimensionality of a dataset while preserving as much variability as possible. By transforming the original variables into a new set of uncorrelated variables called principal components, PCA helps in identifying patterns and simplifying the complexity of high-dimensional data. The 'RankPCA' package provides a streamlined workflow for performing PCA on datasets containing both categorical and continuous variables. It facilitates data preprocessing, encoding of categorical variables, and computes PCA to determine the optimal number of principal components based on a specified variance threshold. The package also computes composite indices for ranking observations, which can be useful for various analytical purposes. Garai, S., & Paul, R. K. (2023) <doi:10.1016/j.iswa.2023.200202>.

For a given suit, if you add up the number of cards that you hold, plus the number that has been played so far, you can easily determine the number that remains in the combined hands of your three opponents. You can also determine the ("special") card of highest rank of the remaining cards for that suit. At some point, you notice that a certain opponent discards that special card. What can you infer about his holding in that suit? A series of simulation studies are reported here that allows a quantitative inference based on the conditional probability, given that the opponent has the special card. The same procedure is also used for the conditional probability, given that the opponent does not have the special card.

Statistical tools for the Mallows-Binomial model, the first joint statistical model for preference learning for rankings and ratings. This project was supported by the National Science Foundation under Grant No. 2019901.

Methods for ranking responses of a single response question or a 
  multiple response question are described in the two papers: 
  1. Wang, H. (2008). Ranking Responses in Multiple-Choice Questions. Journal of 
  Applied Statistics, 35, 465-474. <DOI:10.1080/02664760801924533> 
  2. Wang, H. and Huang, W. H. (2014). Bayesian Ranking Responses in Multiple 
  Response Questions. Journal of the Royal Statistical Society: Series A 
  (Statistics in Society), 177, 191-208. <DOI:10.1111/rssa.12009>.