Bootstrap Confidence Intervals for Ordinary Least Squares Factor Loadings and Correlations in Exploratory Factor Analysis
@article{Zhang2010BootstrapCI,
title={Bootstrap Confidence Intervals for Ordinary Least Squares Factor Loadings and Correlations in Exploratory Factor Analysis},
author={Guangjian Zhang and Kristopher J Preacher and Shanhong Luo},
journal={Multivariate Behavioral Research},
year={2010},
volume={45},
pages={104 - 134}
}This article is concerned with using the bootstrap to assign confidence intervals for rotated factor loadings and factor correlations in ordinary least squares exploratory factor analysis. Coverage performances of SE-based intervals, percentile intervals, bias-corrected percentile intervals, bias-corrected accelerated percentile intervals, and hybrid intervals are explored using simulation studies involving different sample sizes, perfect and imperfect models, and normal and elliptical data…
24 Citations
Ordinary Least Squares Estimation of Parameters in Exploratory Factor Analysis With Ordinal Data
- Mathematics, PsychologyMultivariate behavioral research
- 2012
The empirical illustration and the Monte Carlo study showed that ordinary least squares (OLS) estimation of parameters in EFA is feasible with large models, and point estimates of rotated factor loadings are unbiased, and standard error estimates and confidence intervals perform satisfactorily at moderately large samples.
Estimating Standard Errors in Exploratory Factor Analysis
- PsychologyMultivariate behavioral research
- 2014
6 issues influencing standard errors in exploratory factor analysis are described and 7 methods of computing standard errors for rotated factor loadings and factor correlations are reviewed.
Bootstrap Standard Error Estimates in Dynamic Factor Analysis
- PsychologyMultivariate behavioral research
- 2010
Two bootstrap procedures that are appropriate for dynamic factor analysis are described and are demonstrated using 103 days of affective mood self-ratings from a pregnant woman, 90 days of personality self-rats from a psychology freshman, and a simulation study.
A comparison of three confidence intervals of composite reliability of a unidimensional test.
- Engineering
- 2012
The widely used coefficient α may underestimate or overestimate reliability when its premise assumption is violated and therefore is not a good index to evaluate reliability.Composite reliability can…
The Infinitesimal Jackknife with Exploratory Factor Analysis
- Mathematics
- 2012
The infinitesimal jackknife, a nonparametric method for estimating standard errors, has been used to obtain standard error estimates in covariance structure analysis. In this article, we adapt it for…
R-squared change in structural equation models with latent variables and missing data.
- PsychologyBehavior research methods
- 2021
Four approaches to calculating ΔR2 in SEMs with latent variables and missing data are described, their performance via simulation is compared, a set of extensions to the methods are described and provided, and an set of R functions are provided for calculating the change in R-squared.
Analytic Standard Errors for Exploratory Process Factor Analysis
- PsychologyPsychometrika
- 2014
The analytic standard errors for EPFA take into account the time dependency in time series data and factor rotation is treated as the imposition of equality constraints on model parameters.
Standard error estimates for rotated estimates of canonical correlation analysis: an implementation of the infinitesimal jackknife method
- Mathematics
- 2021
In applications of canonical correlation analysis (CCA), rotation of the canonical loadings is recommended to facilitate the interpretation of canonical variates. Based on the COSAN modeling approach…
Recovering Substantive Factor Loadings in the Presence of Acquiescence Bias: A Comparison of Three Approaches
- PsychologyMultivariate behavioral research
- 2014
The main findings are that the CFA method performs best overall and that it is robust to the violation of its assumptions, the EFA and the CB approaches work well when their assumptions are strictly met, and the “do nothing” approach can be surprisingly robust when the ACQ factor is not very strong.
Spatial Dependence and Heterogeneity in Bayesian Factor Analysis: A Cross-National Investigation of Schwartz Values
- EconomicsMultivariate behavioral research
- 2012
This article presents a Bayesian spatial factor analysis model that applies to Schwartz value priority data obtained from 5 European countries and shows that the Schwartz motivational types of values, such as Conformity, Tradition, Benevolence, and Hedonism, possess high spatial autocorrelation.
References
SHOWING 1-10 OF 51 REFERENCES
Application of the bootstrap methods in factor analysis
- Mathematics
- 1995
A Monte Carlo experiment is conducted to investigate the performance of the bootstrap methods in normal theory maximum likelihood factor analysis both when the distributional assumption is satisfied…
Applications of standard error estimates in unrestricted factor analysis: significance tests for factor loadings and correlations.
- MathematicsPsychological bulletin
- 1994
Estimates of standard errors of factor loadings and factor correlations in the unrestricted factor analysis model can be computed for oblique or orthogonal solutions under maximum likelihood, and a Bonferroni correction for the critical point of the individual test statistics is recommended to control the probability of a Type I error.
Constructing second-order accurate confidence intervals for communalities in factor analysis.
- MathematicsThe British journal of mathematical and statistical psychology
- 2008
This paper compares four methods of generating second-order accurate confidence intervals for non-standardized and standardized communalities in exploratory factor analysis under the normality assumption and finds accurate alternatives to the usual confidence intervals.
Approximating Confidence Intervals for Factor Loadings.
- MathematicsMultivariate behavioral research
- 1991
A method is presented for exploiting information in the empirical data, collected for a study's primary goals, to approximate confidence intervals for factor loadings, which appears generalizable across factor methods, numbers of extracted factors, and rotation criteria.
Variance estimation in factor analysis: An application of the bootstrap
- Economics
- 1984
Sampling variability of the estimates of factor loadings is neglected in modern factor analysis. Such investigations are generally normal theory based and asymptotic in nature. The bootstrap, a…
Standard errors in covariance structure models: asymptotics versus bootstrap.
- Mathematics, EconomicsThe British journal of mathematical and statistical psychology
- 2006
This paper studies the relationship between the bootstrap estimates of SEs and those based on asymptotic variance-covariance matrices and their validity.
Estimating the standard errors of rotated factor loadings by jackknifing
- Mathematics
- 1979
The jackknife by groups and modifications of the jackknife by groups are used to estimate standard errors of rotated factor loadings for selected populations in common factor model maximum likelihood…
The effect of sampling error on convergence, improper solutions, and goodness-of-fit indices for maximum likelihood confirmatory factor analysis
- Mathematics
- 1984
A Monte Carlo study assessed the effect of sampling error and model characteristics on the occurrence of nonconvergent solutions, improper solutions and the distribution of goodness-of-fit indices in…
A unified approach to exploratory factor analysis with missing data, nonnormal data, and in the presence of outliers
- Mathematics
- 2002
Factor analysis is regularly used for analyzing survey data. Missing data, data with outliers and consequently nonnormal data are very common for data obtained through questionnaires. Based on…
Standard errors for obliquely rotated factor loadings
- Mathematics
- 1973
In a manner similar to that used in the orthogonal case, formulas for the aymptotic standard errors of analytically rotated oblique factor loading estimates are obtained. This is done by finding…