Package 'conogive'

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

data	A data frame of observations or a named list with elements lambda, sigma, and cuts. See the details.
use	Passed to stats::cov; defaults to "complete.obs".
...	Passed to psych::fa, where fm = "ml" by default.

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)
}

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Massage Cuts to the Desired Shape

Description

Massage Cuts to the Desired Shape

Usage

massage_cuts(cuts, k)

Arguments

cuts	A matrix, list, or vector of cuts
k	Optional k saying how many times the vector of cuts should be repeated. Only matters when cuts is a vector.

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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

object	An object of class "conogive".
newdata	An optional data frame with variables to predict with. The fitted values are used if omitted.
weights	Weights to use; choose between optimal weights and equal weights.
...	Ignored.

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.
 }

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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

object	An object of class conogive.
xi	How to calculate the Xi matrix. Option "theoretical" calculates the theoretical Xi matrix from rho, while "sample" calculates the sample Xi matrix.
weights	The weights used to calculate the ordinal reliability. Option "optimal" uses the optimal weights and "equal" the equal weights.

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
}

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