Package 'robcat' reference manual

Title:	Robust Categorical Data Analysis
Description:	Robust categorical data analysis based on the theory of C-estimation developed in Welz (2024) <doi:10.48550/arXiv.2403.11954>. For now, the package only implements robust estimation of polychoric correlation as proposed in Welz, Mair and Alfons (2026) <doi:10.1017/psy.2025.10066> and robust estimation of polyserial correlation (Welz, 2026 <doi:10.1017/psy.2026.10091>) with methods for printing and plotting. We will implement further models in future releases. In addition, the package is still experimental, so input arguments and class structure may change in future releases.
Authors:	Max Welz [aut, cre] (ORCID: <https://orcid.org/0000-0003-2945-1860>), Andreas Alfons [aut] (ORCID: <https://orcid.org/0000-0002-2513-3788>), Patrick Mair [aut] (ORCID: <https://orcid.org/0000-0003-0100-6511>)
Maintainer:	Max Welz <[email protected]>
License:	GPL (>= 2)
Version:	0.2
Built:	2026-05-11 08:58:51 UTC
Source:	https://github.com/mwelz/robcat

Neutral initialization of starting values for polychoric correlation

Description

Initializes starting values for numerical optimization in a neutral way. The optimization problem itself is convex, so the initialization should not matter much.

Usage

initialize_param(x, y)
initialize_param(x, y)

Arguments

x

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

y

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

Value

A vector of initial values for the polychoric correlation coefficient, the X-threshold parameters, and the Y-threshold parameters

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)
initialize_param(x, y)

## 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)
initialize_param(x, y)

Plot method for classes `"robpolycor"` and `"polycor"`.

Description

Plot method for classes "robpolycor" and "polycor".

Usage

## S3 method for class 'robpolycor'
plot(x, cutoff = 3, ...)
## S3 method for class 'robpolycor'
plot(x, cutoff = 3, ...)

Arguments

x

Object of class "robpolycor" or "polycor".

cutoff

Cutoff beyond which the color scale for Pearson residuals is truncated.

...

Additional parameters to be passed down.

Value

An object of class "ggplot".

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)

fit <- polycor(x,y) 
plot(fit)

## 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)

fit <- polycor(x,y) 
plot(fit)

Robust estimation of polychoric correlation

Description

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

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.

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.

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

## 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

Maximum likelihood estimation of polychoric correlation coefficient

Description

Implements the maximum likelihood estimator of Olsson (1979, Psychometrika, doi:10.1007/BF02296207) for the polychoric correlation model.

Usage

polycor_mle(
  x,
  y = NULL,
  variance = TRUE,
  constrained = "ifneeded",
  twostep = FALSE,
  method = NULL,
  maxcor = 0.999,
  tol_thresholds = 0.01,
  init = initialize_param(x, y)
)
polycor_mle(
  x,
  y = NULL,
  variance = TRUE,
  constrained = "ifneeded",
  twostep = FALSE,
  method = NULL,
  maxcor = 0.999,
  tol_thresholds = 0.01,
  init = initialize_param(x, y)
)

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.

variance

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

constrained

twostep

Shall two-step estimation of Olsson (1979) <doi:10.1007/BF02296207> be performed? Default is FALSE.

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.

Value

An object of class "robpolycor". See polycor() for details.

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

## 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

Robust estimation of polychoric correlation matrix

Description

A useful wrapper of polycor to robustly estimate a polychoric correlation matrix by calculating all unique pairwise polychoric correlation coefficients.

Usage

polycormat(
  data,
  c = 0.6,
  parallel = FALSE,
  num_cores = 1L,
  return_polycor = TRUE,
  variance = TRUE,
  constrained = "ifneeded",
  method = NULL,
  maxcor = 0.999,
  tol_thresholds = 0.01
)
polycormat(
  data,
  c = 0.6,
  parallel = FALSE,
  num_cores = 1L,
  return_polycor = TRUE,
  variance = TRUE,
  constrained = "ifneeded",
  method = NULL,
  maxcor = 0.999,
  tol_thresholds = 0.01
)

Arguments

data

Data matrix or data.frame of integer-valued responses, individual respondents are in rows and responses to the items in the columns.

c

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

parallel

Logical. Shall parallelization be used? Default is FALSE.

num_cores

Number of cores to be used, only relevant if parallel = TRUE. Defaults to the number of system cores.

return_polycor

Logical. Shall the individual "polycor" objects for each item pair estimate be returned? Default is TRUE.

variance

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

constrained

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.

Value

If return_polycor = TRUE, returns a list with a polychoric correlation matrix and list of "polycor" objects. If return_polycor = FALSE, then only a correlation matrix is returned.

Examples

## example data
set.seed(123)
data <- matrix(sample(c(1,2,3), size = 3*100, replace = TRUE), nrow = 100)
polycormat(data)     # robust 
polycormat_mle(data) # non-robust MLE

## example data
set.seed(123)
data <- matrix(sample(c(1,2,3), size = 3*100, replace = TRUE), nrow = 100)
polycormat(data)     # robust 
polycormat_mle(data) # non-robust MLE

Maximum likelihood estimation of polychoric correlation matrix

Description

A useful wrapper of polycor_mle to estimate a polychoric correlation matrix via maximum likelihood by calculating all unique pairwise polychoric correlation coefficients.

Usage

polycormat_mle(
  data,
  parallel = FALSE,
  num_cores = 1L,
  return_polycor = TRUE,
  variance = TRUE,
  constrained = "ifneeded",
  method = NULL,
  maxcor = 0.999,
  tol_thresholds = 0.01
)
polycormat_mle(
  data,
  parallel = FALSE,
  num_cores = 1L,
  return_polycor = TRUE,
  variance = TRUE,
  constrained = "ifneeded",
  method = NULL,
  maxcor = 0.999,
  tol_thresholds = 0.01
)

Arguments

data

Data matrix or data.frame of integer-valued responses, individual respondents are in rows and responses to the items in the columns.

parallel

Logical. Shall parallelization be used? Default is FALSE.

num_cores

Number of cores to be used, only relevant if parallel = TRUE. Defaults to the number of system cores.

return_polycor

Logical. Shall the individual "polycor" objects for each item pair estimate be returned? Default is TRUE.

variance

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

constrained

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.

Value

If return_polycor = TRUE, returns a list with a polychoric correlation matrix and list of "polycor" objects. If return_polycor = FALSE, then only a correlation matrix is returned.

Examples

## example data
set.seed(123)
data <- matrix(sample(c(1,2,3), size = 3*100, replace = TRUE), nrow = 100)
polycormat(data)     # robust 
polycormat_mle(data) # non-robust MLE

## example data
set.seed(123)
data <- matrix(sample(c(1,2,3), size = 3*100, replace = TRUE), nrow = 100)
polycormat(data)     # robust 
polycormat_mle(data) # non-robust MLE

Robust estimation of polyserial correlation

Description

Implements the robust estimator of Welz (2025, doi:10.48550/arXiv.2510.15632) for the polyserial correlation model.

Usage

polyserial(
  x,
  y,
  alpha = 0.5,
  num_y = max(y),
  constrained = "ifneeded",
  method = NULL,
  variance = TRUE,
  weights = TRUE,
  init = polyserial_initialize_param(x = x, num_y = num_y, robust = TRUE),
  maxcor = 0.999,
  tol_thresholds = 0.01,
  tol_sigma2 = 0.01
)
polyserial(
  x,
  y,
  alpha = 0.5,
  num_y = max(y),
  constrained = "ifneeded",
  method = NULL,
  variance = TRUE,
  weights = TRUE,
  init = polyserial_initialize_param(x = x, num_y = num_y, robust = TRUE),
  maxcor = 0.999,
  tol_thresholds = 0.01,
  tol_sigma2 = 0.01
)

Arguments

x

Vector of numeric values.

y

Vector of integer-valued ordinal values.

alpha

Tuning constant that governs robustness-efficiency tradeoff; must be in [0, Inf]. Defaults to 0.5.

num_y

Number of response categories in y; defaults to max(y)

constrained

Shall parameter restructions be 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 "BFGS" in case of unconstrained optimization and "Nelder-Mead" in case of constrained optimization.

variance

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

weights

Shall weights be returned? Default is TRUE.

init

Initialization of numerical optimization. Default is neutral.

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.

tol_sigma2

Minimum value of sigma2 parameter (population variance of X); only relevant in case of constrained optimization. Default is 0.01.

Value

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

thetahat: A vector of estimates for the polyserial correlation coefficient (rho), population mean of X (mu), population variance of Y (sigma2), as well as thresholds for y (named tau1,tau2,...,tau_{r-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.
pointpolyserial: Estimated polyserial correlation coefficient, calculated with provided scoring of Y
weights: List of rescaled and raw outlyingness weights for each observation as well as maximum possible raw weight that was used for rescaling (sup).
objective: Value of minimized loss function.
optim: Object of class optim.
inputs: List of provided inputs.

Examples

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

polyserial(x,y)

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

polyserial(x,y)

Efficiency of minimum DPD estimators of polyserial model

Description

Calculate population asymptotic variance-covariance matrix associated with a parameter vector theta, assuming that the polyserial model is correctly specified and that theta is the true model parameter. May take a few moments to compute because a relatively large number of integrals need to be numerically solved.

Usage

polyserial_efficiency(theta, alpha)
polyserial_efficiency(theta, alpha)

Arguments

theta

Parameter vector of polyserial model; assumed to be the true one. First element is polyserial correlatio coefficient, second is the population mean of X, third is population variance of X, and the remaining elements are the thresholds associated with the ordnal Y (must be in increasing order)

alpha

Tuning constant governing robustness-efficiency tradeoff. Set to 0 for maximum likelihood.

Value

A numeric matrix that is the population asymptotic variance-covariance matrix associated with a parameter vector theta and tuning constant alpha.

Examples

theta <- c(rho = 0, mu = 0, sigma2 = 1, tau1 = 0) # true parameter vector
polyserial_efficiency(theta, alpha = 0.5)

theta <- c(rho = 0, mu = 0, sigma2 = 1, tau1 = 0) # true parameter vector
polyserial_efficiency(theta, alpha = 0.5)

Neutral initialization of starting values for polyserial correlation

Description

Initializes starting values for numerical optimization in a neutral way.

Usage

polyserial_initialize_param(x, num_y, robust = FALSE)
polyserial_initialize_param(x, num_y, robust = FALSE)

Arguments

x

Vector of numeric values

num_y

Number of response options of ordinal variable

robust

Should values of mu and sigma2 be initialized in robust way (that is, median and squared MAD)? If FALSE (default), then nonrobust sample mean and variance are used.

Value

A vector of initial values for the polyserial correlation coefficient, mu, sigma2, and Y-threshold parameters

Examples

## example data
set.seed(123)
x <- rnorm(100)
polyserial_initialize_param(x = x, num_y = 3)

## example data
set.seed(123)
x <- rnorm(100)
polyserial_initialize_param(x = x, num_y = 3)

Maximum likelihood estimation of polyserial correlation

Description

Implements maximum likelihood estimation of the polyserial correlation model.

Usage

polyserial_mle(
  x,
  y,
  num_y = max(y),
  constrained = "ifneeded",
  method = NULL,
  variance = TRUE,
  init = polyserial_initialize_param(x = x, num_y = num_y, robust = FALSE),
  maxcor = 0.999,
  tol_thresholds = 0.01,
  tol_sigma2 = 0.01
)
polyserial_mle(
  x,
  y,
  num_y = max(y),
  constrained = "ifneeded",
  method = NULL,
  variance = TRUE,
  init = polyserial_initialize_param(x = x, num_y = num_y, robust = FALSE),
  maxcor = 0.999,
  tol_thresholds = 0.01,
  tol_sigma2 = 0.01
)

Arguments

x

Vector of numeric values.

y

Vector of integer-valued ordinal values.

num_y

Number of response categories in y; defaults to max(y)

constrained

method

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

variance

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

init

Initialization of numerical optimization. Default is neutral.

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.

tol_sigma2

Minimum value of sigma2 parameter (population variance of X); only relevant in case of constrained optimization. Default is 0.01.

Value

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

thetahat: A vector of estimates for the polyserial correlation coefficient (rho), population mean of X (mu), population variance of Y (sigma2), as well as thresholds for y (named tau1,tau2,...,tau_{r-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.
pointpolyserial: Estimated polyserial correlation coefficient, calculated with provided scoring of Y
objective: Value of minimized loss function.
optim: Object of class optim.
inputs: List of provided inputs.

Examples

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

polyserial_mle(x,y)

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

polyserial_mle(x,y)

Print method for classes `"robpolycor"` and `"polycor"`.

Description

Print method for classes "robpolycor" and "polycor".

Usage

## S3 method for class 'robpolycor'
print(x, digits = max(3L, getOption("digits") - 3L), ...)
## S3 method for class 'robpolycor'
print(x, digits = max(3L, getOption("digits") - 3L), ...)

Arguments

x

Object of class "robpolycor" or "polycor".

digits

Number of digits to be printed.

...

Additional parameters to be passed down.

Value

A print to the console.

Examples

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

print(fit)
fit # equivalent

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

print(fit)
fit # equivalent

Print method for classes `"robpolyserial"` and `"polyserial"`.

Description

Print method for classes "robpolyserial" and "polyserial".

Usage

## S3 method for class 'robpolyserial'
print(x, digits = max(3L, getOption("digits") - 3L), ...)
## S3 method for class 'robpolyserial'
print(x, digits = max(3L, getOption("digits") - 3L), ...)

Arguments

x

Object of class "robpolyserial" or "polyserial".

digits

Number of digits to be printed.

...

Additional parameters to be passed down.

Value

A print to the console.

Examples

set.seed(123)
x <- rnorm(100)
y <- sample(c(1,2), size = 100, replace = TRUE)
fit <- polyserial(x,y) 

print(fit)
fit # equivalent

set.seed(123)
x <- rnorm(100)
y <- sample(c(1,2), size = 100, replace = TRUE)
fit <- polyserial(x,y) 

print(fit)
fit # equivalent

Obtain estimated asymptotic variance-covariance matrix

Description

Estimate asymptotic variance-covariance matrix of polychoric model.

Usage

## S3 method for class 'robpolycor'
vcov(object, ...)
## S3 method for class 'robpolycor'
vcov(object, ...)

Arguments

object

Object of class "robpolycor" or "polycor".

...

Additional parameters to be passed down.

Details

Method for classes "robpolycor" and "polycor". Returns the estimated asymptotic variance-covariance matrix of a point estimate thetahat. The matrix $\Sigma$ in the paper (asymptotic variance-covariance matrix of $\sqrt{N} \hat{\theta}$ ) can be obtained via multiplying the returned matrix by the sample size.

Value

A numeric matrix, being the estimated asymptotic covariance matrix for the model parameters

Examples

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

vcov(fit)

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

vcov(fit)

Obtain estimated asymptotic variance-covariance matrix

Description

Estimate asymptotic variance-covariance matrix of polyserial model.

Usage

## S3 method for class 'robpolyserial'
vcov(object, ...)
## S3 method for class 'robpolyserial'
vcov(object, ...)

Arguments

object

Object of class "robpolyserial" or "polyserial".

...

Additional parameters to be passed down.

Details

Method for classes "robpolyserial" and "polyserial". Returns the estimated asymptotic variance-covariance matrix of a point estimate thetahat. The matrix $\Sigma$ in the paper (asymptotic variance-covariance matrix of $\sqrt{N} \hat{\theta}$ ) can be obtained via multiplying the returned matrix by the sample size.

Value

A numeric matrix, being the estimated asymptotic covariance matrix for the model parameters

Examples

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

fit <- polyserial(x,y)
vcov(fit)

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

fit <- polyserial(x,y)
vcov(fit)

Package 'robcat'

Help Index

Neutral initialization of starting values for polychoric correlation

Description

Usage

Arguments

Value

Examples

Plot method for classes "robpolycor" and "polycor".

Description

Usage

Arguments

Value

Examples

Robust estimation of polychoric correlation

Description

Usage

Arguments

Value

Examples

Maximum likelihood estimation of polychoric correlation coefficient

Description

Usage

Arguments

Value

Examples

Robust estimation of polychoric correlation matrix

Description

Usage

Arguments

Value

Examples

Maximum likelihood estimation of polychoric correlation matrix

Description

Usage

Arguments

Value

Examples

Robust estimation of polyserial correlation

Description

Usage

Arguments

Value

Examples

Efficiency of minimum DPD estimators of polyserial model

Description

Usage

Arguments

Value

Examples

Neutral initialization of starting values for polyserial correlation

Description

Usage

Arguments

Value

Examples

Maximum likelihood estimation of polyserial correlation

Description

Usage

Arguments

Value

Examples

Print method for classes "robpolycor" and "polycor".

Description

Usage

Arguments

Value

Examples

Print method for classes "robpolyserial" and "polyserial".

Description

Usage

Arguments

Value

Examples

Obtain estimated asymptotic variance-covariance matrix

Description

Usage

Arguments

Details

Value

Plot method for classes `"robpolycor"` and `"polycor"`.

Print method for classes `"robpolycor"` and `"polycor"`.

Print method for classes `"robpolyserial"` and `"polyserial"`.