Factor retention in exploratory factor analysis based on LSTM

doi:10.3724/SP.J.1041.2026.0558

Abstract

Abstract:

In psychological research, determining the dimensional structure and characteristics of psychological traits is of paramount importance. Exploratory Factor Analysis (EFA) serves as a critical statistical methodology for identifying latent dimensions. Accurately determining the number of factors constitutes a pivotal technical challenge in EFA; under- or over-extraction of factors invariably yields detrimental consequences. To address this challenge, the present study conceptualizes eigenvalues as sequential data and employs a deep neural network architecture based on Long Short-Term Memory (LSTM) networks. Comprehensive evaluation metrics (including accuracy, precision, recall, F1-score, and Kappa) all exceeded 83%. Rigorous validation through extensive simulation studies and empirical analyses confirmed the robust performance of LSTM across diverse data conditions. Results demonstrate that LSTM achieves substantially higher accuracy than Comparison Data Fit (CDF), Empirical Kaiser Criterion (EKC), and Parallel Analysis (PA) methods, with a mean improvement rate of 48.50% and a peak improvement of 171.09%. Furthermore, LSTM exhibits smaller bias and superior robustness relative to CDF, EKC, and PA. Researchers may utilize the R package LSTMfactors to apply the LSTM model trained in this study to empirical data analysis.

Key words: Exploratory Factor Analysis, Long Short-Term Memory, Factor Retention, Deep Learning

GUO Lei, QIN Haijiang. (2026). Factor retention in exploratory factor analysis based on LSTM. Acta Psychologica Sinica, 58(3), 558-568.

Figures/Tables 11

References 42

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Optimal Hyperparameter Configuration		Optimal Metric
Hyperparameter	Value	Metric	Value
Learning rate	0.01	Accuracy	0.847
Number of LSTM layers	2	Precision	0.847
Units per LSTM layer	32, 38	Recall	0.847
Number of fully connected layers	5	F1-Score	0.847
Units per FC layer	38, 39, 34, 31, 27	Kappa	0.831
Activation function	Tanh

Optimal Hyperparameter Configuration		Optimal Metric
Hyperparameter	Value	Metric	Value
Learning rate	0.01	Accuracy	0.847
Number of LSTM layers	2	Precision	0.847
Units per LSTM layer	32, 38	Recall	0.847
Number of fully connected layers	5	F1-Score	0.847
Units per FC layer	38, 39, 34, 31, 27	Kappa	0.831
Activation function	Tanh

Conditions	Level	acc
Conditions	Level	CDF	EKC	PA	LSTM	Improvement Rate
Number of factors	1	0.677	0.922	0.944	0.969	2.58%
	2	0.722	0.715	0.677	0.879	21.69%
	4	0.558	0.516	0.493	0.732	31.08%
	6	0.450	0.419	0.394	0.523	16.17%
	8	0.373	0.358	0.330	0.636	70.62%
	10	0.313	0.319	0.280	0.865	171.09%
Factor correlations	0.00	0.686	0.724	0.761	0.901	18.29%
	0.25	0.619	0.650	0.662	0.867	31.00%
	0.50	0.485	0.495	0.450	0.775	56.44%
	0.75	0.273	0.298	0.206	0.527	76.96%
Indicators per factor	4	0.370	0.416	0.381	0.772	85.47%
	7	0.547	0.568	0.547	0.765	34.51%
	10	0.630	0.640	0.631	0.765	19.54%
Primary loadings	L	0.332	0.347	0.376	0.687	82.60%
	M	0.525	0.564	0.540	0.784	39.14%
	H	0.690	0.714	0.643	0.831	16.25%
Cross- loadings	L	0.486	0.519	0.508	0.750	44.59%
Cross- loadings	H	0.545	0.565	0.532	0.785	38.99%
Sample size	100	0.286	0.299	0.309	0.637	106.58%
	200	0.429	0.461	0.454	0.755	63.70%
	500	0.617	0.657	0.614	0.823	25.26%
	1000	0.731	0.750	0.703	0.854	13.94%

Conditions	Level	acc
Conditions	Level	CDF	EKC	PA	LSTM	Improvement Rate
Number of factors	1	0.677	0.922	0.944	0.969	2.58%
	2	0.722	0.715	0.677	0.879	21.69%
	4	0.558	0.516	0.493	0.732	31.08%
	6	0.450	0.419	0.394	0.523	16.17%
	8	0.373	0.358	0.330	0.636	70.62%
	10	0.313	0.319	0.280	0.865	171.09%
Factor correlations	0.00	0.686	0.724	0.761	0.901	18.29%
	0.25	0.619	0.650	0.662	0.867	31.00%
	0.50	0.485	0.495	0.450	0.775	56.44%
	0.75	0.273	0.298	0.206	0.527	76.96%
Indicators per factor	4	0.370	0.416	0.381	0.772	85.47%
	7	0.547	0.568	0.547	0.765	34.51%
	10	0.630	0.640	0.631	0.765	19.54%
Primary loadings	L	0.332	0.347	0.376	0.687	82.60%
	M	0.525	0.564	0.540	0.784	39.14%
	H	0.690	0.714	0.643	0.831	16.25%
Cross- loadings	L	0.486	0.519	0.508	0.750	44.59%
Cross- loadings	H	0.545	0.565	0.532	0.785	38.99%
Sample size	100	0.286	0.299	0.309	0.637	106.58%
	200	0.429	0.461	0.454	0.755	63.70%
	500	0.617	0.657	0.614	0.823	25.26%
	1000	0.731	0.750	0.703	0.854	13.94%

Conditions	Level	bias
Conditions	Level	CDF	EKC	PA	LSTM
Number of factors	1	0.363	-0.063	-0.038	0.031
	2	-0.053	-0.290	-0.326	0.010
	4	-0.892	-0.936	-1.131	0.524
	6	-1.826	-1.689	-2.061	0.669
	8	-2.851	-2.489	-3.055	0.164
	10	-3.919	-3.309	-4.095	-0.406
Factor correlations	0.00	-0.616	-0.824	-0.476	0.088
	0.25	-0.893	-1.049	-0.858	0.117
	0.50	-1.596	-1.555	-2.005	0.242
	0.75	-3.014	-2.422	-3.798	0.215
Indicators per factor	4	-1.853	-2.133	-2.371	-0.269
	7	-1.476	-1.334	-1.671	0.208
	10	-1.261	-0.921	-1.311	0.558
Primary loadings	L	-2.466	-2.462	-2.279	0.464
	M	-1.447	-1.365	-1.727	0.151
	H	-0.676	-0.561	-1.347	-0.118
Cross-loadings	L	-1.838	-1.889	-1.963	0.176
Cross-loadings	H	-1.222	-1.037	-1.605	0.155
Sample size	100	-2.609	-2.722	-2.695	0.270
	200	-1.856	-1.899	-2.022	0.129
	500	-1.036	-0.908	-1.383	0.150
	1000	-0.618	-0.321	-1.037	0.113