rotate: S3 Methods: rotate

In ForceChoice: Forced-Choice Modeling Based on Item Response Theory and Cognitive Diagnostic Models

S3 Methods: rotate

Description

Applies factor rotation to the posterior mean parameter estimates of fitted exploratory multidimensional models from the ForceChoice package. Rotation reparameterises the latent space to improve interpretability of factor loadings while preserving the model-implied covariance structure. Standard errors and other posterior uncertainty summaries are carried over from the original fit object without recomputation. No per-iteration rotation or cross-iteration alignment is performed.

For GPArotation methods, theta is re-standardized to a standard normal scale after rotation. For Promax rotation, no post-rotation standardization is applied. Loadings and the factor correlation matrix are updated accordingly to preserve model-implied covariances.

Rotation is not permitted when the fitted Q.matrix contains zeros because that confirmatory structure would not generally be preserved under rotation.

Usage

## S3 method for class 'MGPCM'
rotate(
  object,
  method,
  vis = TRUE,
  target.a = NULL,
  target.theta = NULL,
  pst.W = NULL,
  lp.p = 1,
  lp.gpaiter = 5,
  promax_m = 4,
  ...
)

## S3 method for class 'MIRT'
rotate(
  object,
  method,
  vis = TRUE,
  target.a = NULL,
  target.theta = NULL,
  pst.W = NULL,
  lp.p = 1,
  lp.gpaiter = 5,
  promax_m = 4,
  ...
)

Arguments

object	A fitted model object of class "MIRT" (returned by fit.MIRT) or "MGPCM" (returned by fit.MGPCM).
method	Character string specifying the rotation method. Supported methods include "promax", "Varimax", "quartimax", "oblimin", "quartimin", "geominT", "geominQ", "targetT", "targetQ", "pstT", "pstQ", and others provided by the GPArotation package.
vis	Logical; if TRUE (default), displays informational messages during rotation.
target.a	Numeric matrix of target loadings for target rotations ("targetT", "targetQ", "pstT", "pstQ").
target.theta	Numeric matrix of target latent traits for target rotations ("targetT", "targetQ" only).
pst.W	Numeric weight matrix for PST rotations ("pstT", "pstQ").
lp.p	Numeric; p parameter for Lp rotation (default = 1).
lp.gpaiter	Integer; max GPA iterations for Lp rotation (default = 5).
promax_m	Numeric; power parameter for Promax rotation (default = 4).
...	Additional arguments passed to the GPArotation rotation function.

Details

Only posterior means are rotated. For MGPCM objects, the first D columns of object$par$est are treated as discrimination parameters; all category intercepts are unchanged.

Value

rotate.MIRT

An object of class "RotateMIRT" containing the rotated "MIRT" fit object (object), the matched call (call), and the rotation arguments (arguments). Standard errors in the fitted object are preserved without recomputation.

rotate.MGPCM

An object of class "RotateMGPCM" containing the rotated "MGPCM" fit object (object), the matched call (call), and the rotation arguments (arguments). Category intercepts are retained from the original fit.

Methods (by class)

• rotate(MGPCM): Applies a factor rotation to the posterior mean discrimination parameters of MGPCM objects. The latent trait estimates and factor correlation matrix are transformed consistently. Category intercepts and posterior uncertainty summaries are retained from the original fit without recomputation.

• rotate(MIRT): Applies rotation to the posterior mean of loadings only from MIRT objects. Loadings (a) and factor correlation matrix (Corr) are updated to preserve model-implied covariances. For GPArotation methods, theta is re-standardized to a standard normal scale after rotation; for Promax, no post-rotation standardization is applied.

See Also

fit.MIRT, fit.MGPCM

ForceChoice documentation built on Sept. 13, 2026, 1:06 a.m.