robcat (version 0.2)

polycor: Robust estimation of polychoric correlation

Description

Implements to robust estimator of Welz, Mair and Alfons (2024, tools:::Rd_expr_doi("10.48550/arXiv.2407.18835")) for the polychoric correlation model, based on the general theory of C-estimation proposed by Welz (2024, tools:::Rd_expr_doi("10.48550/arXiv.2403.11954")).

Usage

polycor(
  x,
  y = NULL,
  c = 0.6,
  variance = TRUE,
  constrained = "ifneeded",
  method = NULL,
  maxcor = 0.999,
  tol_thresholds = 0.01,
  init = initialize_param(x, y)
)

Value

An object of class "robpolycor", which is a list with the following components.

thetahat

A vector of estimates for the polychoric correlation coefficient (rho) as well as thresholds for x (named a1,a2,...,a_{Kx-1}) and y (named b1,b2,...,b_{Ky-1}).

stderr

A vector of standard errors for each estimate in thetahat.

vcov

Estimated asymptotic covariance matrix of thetahat. The matrix \(\Sigma\) in the paper (asymptotic covariance matrix of \(\sqrt{N} \hat{\theta}\)) can be obtained via vcov * N, where N is the sample size.

chisq,pval,df

Currently NULL, will in a future release be the test statistic, p-value, and degrees of freedom of a test for bivariate normality.

objective

Value of minimized loss function.

optim

Object of class optim.

Arguments

x

Vector of integer-valued responses to first item, or contingency table (a "table" object).

y

Vector of integer-valued responses to second item; only required if x is not a contingency table.

c

Tuning constant that governs robustness; must be in [0, Inf]. Defaults to 0.6.

variance

Shall an estimated asymptotic covariance matrix be returned? Default is TRUE.

constrained

Shall strict monotonicity of thresholds be explicitly enforced by linear constraints? This can be a logical (TRUE or FALSE), or "ifneeded" to first try unconstrained optimization and in case of an error perform constrained optimization. Default is "ifneeded".

method

Numerical optimization method, see optim() and constrOptim(). Default is to use "L-BFGS-B" in case of unconstrained optimization and "Nelder-Mead" in case of constrained optimization.

maxcor

Maximum absolute correlation (to ensure numerical stability). Default is 0.999.

tol_thresholds

Minimum distance between consecutive thresholds (to enforce strict monotonicity); only relevant in case of constrained optimization. Default is 0.01.

init

Initialization of numerical optimization. Default is neutral.

Examples

## example data
set.seed(123)
x <- sample(c(1,2,3), size = 100, replace = TRUE)
y <- sample(c(1,2,3), size = 100, replace = TRUE)

polycor(x,y)     # robust
polycor_mle(x,y) # non-robust MLE