# Rotational Uniqueness Conditions Under Oblique Factor Correlation Metric

@article{Peeters2012RotationalUC, title={Rotational Uniqueness Conditions Under Oblique Factor Correlation Metric}, author={Carel F. W. Peeters}, journal={Psychometrika}, year={2012}, volume={77}, pages={288-292} }

In an addendum to his seminal 1969 article Jöreskog stated two sets of conditions for rotational identification of the oblique factor solution under utilization of fixed zero elements in the factor loadings matrix (Jöreskog in Advances in factor analysis and structural equation models, pp. 40–43, 1979). These condition sets, formulated under factor correlation and factor covariance metrics, respectively, were claimed to be equivalent and to lead to global rotational uniqueness of the factor… Expand

#### 15 Citations

A note on identification constraints and information criteria in Bayesian latent variable models.

- Medicine
- Behavior research methods
- 2021

It is shown that Bayesian model comparison metrics can systematically change depending on constraints used, and principled methods for setting the scale of the latent variable that stabilize the model comparison metric are studied. Expand

Rotation Invariant Householder Parameterization for Bayesian PCA

- Mathematics, Computer Science
- ICML
- 2019

A parameterization based on Householder transformations, which remove the rotational symmetry of the posterior of probabilistic PCA by relying on results from random matrix theory and avoiding the need to compute the Jacobian determinant of the parameter transformation is proposed. Expand

Improving Bi-Factor Exploratory Modeling

- Computer Science
- Methodology
- 2019

Bi-factor exploratory modeling has recently emerged as a promising approach to multidimensional psychological measurement, but state-of-the-art methods relying on target rotation requirements for this work are still in their infancy. Expand

Bayesian Constrained-Model Selection for Factor Analytic Modeling

- Mathematics
- 2016

My dissertation revolves around Bayesian approaches towards constrained statistical inference in the factor analysis (FA) model. Two interconnected types of restricted-model selection are considered.… Expand

Efficient Bayesian Structural Equation Modeling in Stan

- Computer Science, Mathematics
- 2020

A general, efficient approach to Bayesian SEM estimation in Stan is described, contrasting it with previous implementations in R package blavaan (Merkle & Rosseel, 2018); a practical comparison shows that the new approach is clearly better. Expand

Latent Variable Models of Categorical Responses in the Bayesian and Frequentist Frameworks

- Mathematics
- 2014

The thesis consists of two self-contained manuscripts. The first manuscript presents a Bayesian multilevel formulation of a cross-classified latent variable model for categorical responses. In the… Expand

Beating the average forecast: Regularization based on forecaster attributes

- Computer Science
- 2020

A model inspired by Cultural Consensus Theory is developed that allows us to jointly estimate both forecaster characteristics and environmental characteristics and contains the unweighted average as a special case and allows the model to apply existing results on optimal forecaster weighting to real data. Expand

A Comparison of Bayesian and Frequentist Model Selection Methods for Factor Analysis Models

- Mathematics, Medicine
- Psychological methods
- 2017

Simulation results indicate that of the Bayesian measures considered, the BF and the BIC showed the best balance between true positive rates and false positive rates, followed closely by the SSP, while the LRTs are still the preferred frequentist model comparison tool, except for their higher false positive detection rates. Expand

Bayesian latent variable models for the analysis of experimental psychology data

- Psychology, Medicine
- Psychonomic bulletin & review
- 2018

The use of Bayesian factor analysis and structural equation models to draw inferences from experimental psychology data is addressed, and the models are used to re-analyze experimental data on risky choice, compared to simpler, alternative methods. Expand

Minimum Distance Estimation of Multidimensional Diffusion-Based Item Response Theory Models

- Medicine, Mathematics
- Multivariate behavioral research
- 2020

This work proposes an alternative estimator that is more efficient than the least squares estimator and less demanding than the maximum likelihood estimator, which is based on minimum distance estimation and consists in modeling the sample quantiles and sample covariances. Expand

#### References

SHOWING 1-10 OF 18 REFERENCES

Rotational equivalence of factor loading matrices with specified values

- Mathematics
- 1978

Under mild assumptions, when appropriate elements of a factor loading matrix are specified to be zero, all orthogonally equivalent matrices differ at most by column sign changes. Here a variety of… Expand

Exploratory Structural Equation Modeling

- Psychology
- 2009

Exploratory factor analysis (EFA) is a frequently used multivariate analysis technique in statistics. Jennrich and Sampson (1966) solved a significant EFA factor loading matrix rotation problem by… Expand

Uniqueness does not Imply Identification

- Mathematics
- 1985

Many authors suggest that conditions originally presented by Howe (1955) and later by Jöreskog (1979) are sufficient to identify confirmatory factor analysis models. In this note we show that these… Expand

Foundations of Factor Analysis

- Mathematics
- 2009

Introduction Factor Analysis and Structural Theories Brief History of Factor Analysis as a Linear Model Example of Factor Analysis Mathematical Foundations for Factor Analysis Introduction Scalar… Expand

A general approach to confirmatory maximum likelihood factor analysis

- Mathematics
- 1969

We describe a general procedure by which any number of parameters of the factor analytic model can be held fixed at any values and the remaining free parameters estimated by the maximum likelihood… Expand

A comparison of four methods of calculating standard errors of maximum likelihood estimates in the analysis of covariance structure.

- Mathematics
- 1991

Compares 4 models of calculating standard errors (SEs) in the analysis of covariance (ANCOVA) structure using normal theory maximum-likelihood estimation, namely LISREL SEs, SEs derived from the… Expand

A note on a sufficiency condition for uniqueness of a restricted factor matrix

- Mathematics
- 1973

A counterexample is produced to a conjecture by K. G. Jöreskog concerning sufficiency conditions for uniqueness of a restricted factor matrix. A substitute condition is stated and proved for the most… Expand

Advances in factor analysis and structural equation models

- Computer Science
- 1979

The methods in this book do not provide final answers to the question of model specification but offer the researcher the flexibility to formulate and test a variety of causal models and to guide the analysis toward more adequate explanations of the relationships embedded in data. Expand

The Sage handbook of quantitative methodology for the social sciences

- Psychology
- 2004

Preface Acknowledgments Section I: Scaling Chapter 1: Dual Scaling - Shizuhiko Nishisato Chapter 2: Multidimensional Scaling and Unfolding of Symmetric and Asymmetric Proximity Relations - Willem J.… Expand

Measuring the pricing error of the arbitrage pricing theory

- Mathematics, Economics
- 1995

This paper provides an exact Bayesian framework for analyzing the arbitrage pricing theory (APT). Based on the Gibbs sampler, we show how to obtain the exact posterior distributions for functions of… Expand