Should Regularization Replace Simple Structure Rotation in Exploratory Factor Analysis?

Scharf, Florian; Nestler, Steffen

doi:10.1080/10705511.2018.1558060

Cited by 39 publications

(56 citation statements)

References 58 publications

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“…Primary loadings estimates were unbiased but secondary loadings were consistently underestimated. This result aligns with Scharf and Nestler's (2019) finding that lasso underestimates smaller loadings when items load on multiple factors. Intercepts were moderately underestimated across replications.…”

Section: An Incomplete Bifactor Patternsupporting

confidence: 91%

“…First, secondary loadings were underestimated in the incomplete bifactor simulation study and intercept estimates were moderately biased in both simulation studies. The secondary loadings estimate bias is likely due to the lasso penalty's tendency to over-shrink smaller loadings when items load on multiple factors (Scharf & Nestler, 2019) and may be alleviated by using a different regularization penalty (e.g., Yamamoto et al, 2017). It is unclear to what extent the intercept estimate bias is due to (1) inaccurate loadings estimates due to the lasso penalty, (2) insufficient sample size, or (3) the approximate nature of the ELBO.…”

Section: Discussionmentioning

confidence: 99%

“…We now show how to conduct exploratory IFA with our VAE for fitting the GRM. While traditional approaches to exploratory factor analysis (EFA) rely on an additional factor rotation step after fitting (Browne, 2001), our approach relies on developments in regularized EFA that produce interpretable models by penalizing factor loadings directly during fitting (Scharf & Nestler, 2019;Trendafilov, 2014;Yamamoto, Hirose, & Nagata, 2017).…”

Section: Regularized Exploratory Ifamentioning

confidence: 99%

“…We therefore compared loadings matrices across starting values by selecting a reference loadings matrix and finding the column permutation of each comparison matrix that minimized the element-wise MSE. Factors were inverted before being compared if the sum of their loadings was negative (Scharf & Nestler, 2019). Across 100 sets of random starting values, mean column-permuted RMSE for loadings was 0.03 (SD = 0.02) and mean RMSE for intercepts was 0.07 (SD = 0.02), which are small relative to primary loadings and intercept magnitudes and would not meaningfully change the conclusions of the analysis.…”

Section: A Big-five Personality Factors Data Setmentioning

confidence: 99%

“…Mean bias was calculated separately for primary loadings, cross loadings, and intercepts to measure parameter recovery. Following previous studies (e.g., Asparouhov & Muthén, 2009;Scharf & Nestler, 2019), we defined mean bias as the average deviation of the estimated parameters from the data generating parameters. Table 4 contains Monte Carlo averages and standard deviations of all summary statistics.…”

Section: A Simple Factor Patternmentioning

confidence: 99%

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A Deep Learning Algorithm for High-Dimensional Exploratory Item Factor Analysis

Urban

Bauer

2020

Preprint

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Deep learning methods are the gold standard for non-linear statistical modeling in computer vision and in natural language processing but are rarely used in psychometrics. To bridge this gap, we present a novel deep learning algorithm for exploratory item factor analysis (IFA). Our approach combines a deep artificial neural network (ANN) model called a variational autoencoder (VAE) with recent work that uses regularization for exploratory factor analysis. We first provide overviews of ANNs and VAEs. We then describe how to conduct exploratory IFA with a VAE and demonstrate our approach in two empirical examples and in two simulated examples. Our empirical results were consistent with existing psychological theory across random starting values. Our simulations suggest that the VAE consistently recovers the data generating factor pattern with moderate-sized samples. Secondary loadings were underestimated with a complex factor structure and intercept parameter estimates were moderately biased with both simple and complex factor structures. All models converged in minutes, even with hundreds of thousands of observations, hundreds of items, and tens of factors. We conclude that the VAE offers a powerful new approach to fitting complex statistical models in psychological and educational measurement.

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Section: An Incomplete Bifactor Patternsupporting

confidence: 91%

Section: Discussionmentioning

confidence: 99%

Section: Regularized Exploratory Ifamentioning

confidence: 99%

Section: A Big-five Personality Factors Data Setmentioning

confidence: 99%

Section: A Simple Factor Patternmentioning

confidence: 99%

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A Deep Learning Algorithm for High-Dimensional Exploratory Item Factor Analysis

Urban

Bauer

2020

Preprint

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A generalized expectation model selection algorithm for latent variable selection in multidimensional item response theory models

Shang,

Zheng,

et al. 2023

Stat Comput

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A Lasso and a Regression Tree Mixed-Effect Model with Random Effects for the Level, the Residual Variance, and the Autocorrelation

Nestler

Humberg

2021

Psychometrika

Self Cite

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Research in psychology is experiencing a rapid increase in the availability of intensive longitudinal data. To use such data for predicting feelings, beliefs, and behavior, recent methodological work suggested combinations of the longitudinal mixed-effect model with Lasso regression or with regression trees. The present article adds to this literature by suggesting an extension of these models that—in addition to a random effect for the mean level—also includes a random effect for the within-subject variance and a random effect for the autocorrelation. After introducing the extended mixed-effect location scale (E-MELS), the extended mixed-effect location-scale Lasso model (Lasso E-MELS), and the extended mixed-effect location-scale tree model (E-MELS trees), we show how its parameters can be estimated using a marginal maximum likelihood approach. Using real and simulated example data, we illustrate how to use E-MELS, Lasso E-MELS, and E-MELS trees for building prediction models to forecast individuals’ daily nervousness. The article is accompanied by an R package (called ) and functions that support users in the application of the suggested models.

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Should Regularization Replace Simple Structure Rotation in Exploratory Factor Analysis?

Cited by 39 publications

References 58 publications

A Deep Learning Algorithm for High-Dimensional Exploratory Item Factor Analysis

A Deep Learning Algorithm for High-Dimensional Exploratory Item Factor Analysis

A generalized expectation model selection algorithm for latent variable selection in multidimensional item response theory models

A Lasso and a Regression Tree Mixed-Effect Model with Random Effects for the Level, the Residual Variance, and the Autocorrelation

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