Title:	Congeneric Normal-Ogive Model
Version:	1.0.0
Description:	The congeneric normal-ogive model is a popular model for psychometric data (McDonald, R. P. (1997) <doi:10.1007/978-1-4757-2691-6_15>). This model estimates the model, calculates theoretical and concrete reliability coefficients, and predicts the latent variable of the model. This is the companion package to Moss (2020) <doi:10.31234/osf.io/nvg5d>.
License:	MIT + file LICENSE
Encoding:	UTF-8
LazyData:	true
URL:	https://github.com/JonasMoss/conogive
BugReports:	https://github.com/JonasMoss/conogive/issues
RoxygenNote:	7.1.0
Imports:	psych, mvtnorm, checkmate, assertthat
Suggests:	testthat (≥ 2.1.0), psychTools, covr
NeedsCompilation:	no
Packaged:	2020-06-30 10:02:28 UTC; jonas
Author:	Jonas Moss [aut, cre]
Maintainer:	Jonas Moss <jonas.gjertsen@gmail.com>
Repository:	CRAN
Date/Publication:	2020-06-30 10:30:02 UTC

Estimate a Congeneric Normal-Ogive Model

Description

conogive is used to estimate congeneric normal-ogive models (McDonald, R. P. (1997)).

Usage

conogive(data, use = "complete.obs", ...)

Arguments

Details

The data argument can be either a list containing the parameters of a normal-ogive model, or raw data. If actual data is passed to data, it is passed to psych::polychoric to estimate its polychoric correlation matrix and cutoffs. This is passed to psych::fa to do a barebones multivariate normal-ogive model. The ... arguments are passed to psych::fa, which is called with fm = "ml" by default.

Likert data should start with 1, not 0.

Value

An object of class conogive.

References

McDonald, R. P. (1997). Normal-ogive multidimensional model. In W. J. van der Linden & R. K. Hambleton (Eds.), Handbook of Modern Item Response Theory (pp. 257–269). Springer. https://doi.org/10.1007/978-1-4757-2691-6_15 Moss, J. (2020). Please avoid the standardized alpha and the ordinal alpha. https://psyarxiv.com/nvg5d

Examples

if(require("psychTools")) {
  extraversion = psychTools::bfi[c("E1", "E2", "E3", "E4", "E5")]
  extraversion[, "E1"] = 7 - extraversion[, "E1"] # Reverse-coded item.
  extraversion[, "E2"] = 7 - extraversion[, "E2"] # Reverse-coded item.
  fit = conogive(extraversion)
}

Massage Cuts to the Desired Shape

Description

Massage Cuts to the Desired Shape

Usage

massage_cuts(cuts, k)

Arguments

Transform y Into a Form Where Each Category is An Positive Integer

Description

Transform y Into a Form Where Each Category is An Positive Integer

Usage

ordered_y(y)

Arguments

Value

A matrix.

Predict Method for Conogive Objects

Description

Predict the latent variable in a congeneric normal-ogive model using the formula of ((arxiv ref.))

Usage

## S3 method for class 'conogive'
predict(object, newdata, weights = c("optimal", "equal"), ...)

Arguments

Examples

 if(require("psychTools")) {
   extraversion = psychTools::bfi[c("E1", "E2", "E3", "E4", "E5")]
   extraversion[, "E1"] = 7 - extraversion[, "E1"] # Reverse-coded item.
   extraversion[, "E2"] = 7 - extraversion[, "E2"] # Reverse-coded item.
   object = conogive(extraversion)
   hist(predict(object, extraversion)) # Plot distribution of predictions.
 }

Calculate the Ordinal Reliabiltiy

Description

The function ordinal_r calculates the concrete ordinal reliability. The functions theoretical_ordinal_r and theoretical_ordinal_alpha calculates the theoretical ordinal reliability and alpha based on the polychoric correlation matrix.

Usage

ordinal_r(
  object,
  xi = c("sample", "theoretical"),
  weights = c("optimal", "equal")
)

theoretical_ordinal_r(object, weights = c("optimal", "equal", "sigma"))

theoretical_ordinal_alpha(object)

Arguments

Details

The population value of theoretical ordinal alpha equals the theoretical ordinal reliability when the underlying multivariate normal is parallel. The concrete ordinal reliability is the sqaured correlation between the true latent variable and the best linear predictor of the observed Likert-type data. See ((ref)) for definitions.

Value

The concrete ordinal reliability, theoretical ordinal reliability, or theoretical ordinal alpha.

Examples

if(require("psychTools")) {
  agreeableness = psychTools::bfi[c("A1", "A2", "A3", "A4", "A5")]
  agreeableness[, "A1"] = 7 - agreeableness[, "A1"] # Reverse-coded item.
  object = conogive(agreeableness)
  ordinal_r(object, weights = "equal") # 0.6394087
  theoretical_ordinal_alpha(object) # 0.7589922
  theoretical_ordinal_r(object, weights = "equal") # 0.7689878
  ordinal_r(object, weights = "optimal") # 0.6763742
  theoretical_ordinal_r(object) # 0.8101108
}

Standardize Parameter Vectors

Description

The function standardize_lambda standardizes lambda and standardize_sigma standardizes sigma.

Usage

standardize_lambda(lambda, sigma)

standardize_sigma(lambda, sigma)

Arguments

Value

Standardized vector.

Thurstone weights

Description

Thurstone weights

Usage

thurstone(lambda, sigma)

Arguments

Value

The Thurstone weights.

Trace of matrix

Description

Trace of matrix

Usage

tr(A)

Arguments

Value

Trace of the matrix.

Remove Infinities from Vector, Append and Prepend -Inf and Inf, and Sort

Description

Remove Infinities from Vector, Append and Prepend -Inf and Inf, and Sort

Usage

trim_vector(x)

Arguments

Value

Vector with ⁠-Inf`` prepended and ⁠Inf' appended

Transform Likert data to X_hats.

Description

Transform Likert data to X_hats.

Usage

x_hat(y, cuts)

Arguments

Value

The X_hats associated with y and cuts.

Calculate Sample Xi

Description

Calculate Sample Xi

Usage

xi_sample(y, cuts, use = "complete.obs")

Arguments

Value

Sample xi matrix.

Calculate the Theoretical Xi

Description

Calculate the Theoretical Xi

Usage

xi_theoretical(cuts, rho)

Arguments

Value

Theoretical xi matrix.