基于长短期记忆网络的探索性因子分析因子保留方法

doi:10.3724/SP.J.1041.2026.0558

摘要/Abstract

摘要：

心理学研究中, 确定心理特质的维度及其特征极为重要。探索性因子分析(EFA)是识别潜在维度的一种重要统计方法。准确识别因子数量是EFA的关键技术之一, 低估或者高估因子数量都会带来不良后果。为准确识别因子数量, 本研究将特征根视作序列数据, 采用长短期记忆(LSTM)网络构建的深度神经网络的各项评估指标(准确率、精确率、召回率、F1、Kappa)均在83%以上。通过大规模的模拟实验及实证研究, 验证了LSTM在不同数据条件中的性能。结果表明: LSTM比CDF、EKC和PA方法具有更高的准确率, 平均提升率为48.50%, 最大提升率高达171.09%。而且, LSTM比CDF、EKC和PA方法具有更小偏差, 表现出更好稳健性。研究者可使用R包LSTMfactors调用本研究所训练的LSTM分析实证数据。

关键词: 探索性因子分析, 长短期记忆, 因子保留, 深度学习

Abstract:

Psychological research focuses on the latent traits of individuals, necessitating clear operational definitions to delineate the constructs of interest. Following this, the exploration and description of the dimensions and characteristics of these traits are essential. Exploratory Factor Analysis (EFA) is a pivotal statistical method for identifying these latent dimensions, widely utilized, especially in the development of psychological scales and instruments.

A critical aspect of employing EFA is the accurate determination of the number of factors. Underestimating the number of factors may result in the omission of theoretically significant psychological structures or sub-dimensions, leading to the loss of critical information, increased estimation errors in factor loadings, and diminished accuracy of factor scores. Conversely, overestimating the number of factors may lead to factors splitting, where the primary loadings of manifest variables are dispersed across multiple factors, thereby weakening the association between the manifest variables and the intended factor. Moreover, this may result in a model characterized by undue complexity and structures of limited practical or theoretical utility. To address these challenges, researchers have proposed various methods, including the Kaiser criterion (i.e., eigenvalues greater than one), the empirical Kaiser criterion, Parallel Analysis, the Hull method, Comparison Data, Factor Forest, and Comparison Data Forest. With the rapid advancement of machine learning, its application in EFA has begun to attract attention. This study introduces an innovative approach by treating eigenvalues as sequential data and leveraging Long Short-Term Memory (LSTM) networks to construct a predictive model. The performance of the LSTM-based method was subsequently evaluated through extensive simulations and empirical studies under diverse data conditions, demonstrating its robustness and applicability.

The findings of the study indicate that: (1) After hyperparameter tuning, an optimal combination was identified, enabling the LSTM model to achieve excellent performance across accuracy, precision, and other evaluation metrics, demonstrating high classification capability. (2) In the simulation study, the LSTM model significantly outperformed Comparison Data Forest, the Empirical Kaiser Criterion, and Parallel Analysis under nearly all data conditions, with an average improvement in estimation accuracy of 48.50% and a maximum improvement of 171.09%.

Furthermore, an empirical study was conducted using data from a parental psychological control scale administered to a cohort of 987 high school students in a city in 2022. Both traditional methods and the LSTM approach were employed to assess ecological validity. The results demonstrated that the LSTM provided the most accurate estimation of the number of factors, while the CDF method exhibited a significant tendency to overestimate. Overall, the LSTM proposed in this study demonstrates strong practical value and is worthy of broader adoption. Researchers can use the R package LSTMfactors to call the LSTM trained in this study to analyze empirical data.

Key words: exploratory factor analysis, LSTM, factor retention, deep learning

中图分类号:

B841

郭磊, 秦海江. (2026). 基于长短期记忆网络的探索性因子分析因子保留方法. 心理学报, 58(3), 558-568.

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

图/表 11

参考文献 42

[1]	Auerswald M., & Moshagen M. (2019). How to determine the number of factors to retain in exploratory factor analysis: A comparison of extraction methods under realistic conditions. Psychological Methods, 24(4), 468-491. doi: 10.1037/met0000200 pmid: 30667242
[2]	Bergstra J., & Bengio Y. (2012). Random search for hyper- arameter optimization. Journal of Machine Learning Research, 13, 281-305.
[3]	Braeken J., & van Assen M. A. (2017). An empirical Kaiser criterion. Psychological Methods, 22(3), 450-466. doi: 10.1037/met0000074 pmid: 27031883
[4]	Brownlee J. (2018). Deep Learning for Time Series Forecasting: Predict the Future with MLPs, CNNs and LSTMs in Python. Machine Learning Mastery.
[5]	Chen S., Abhinav S., Saurabh S., & Abhinav G. (2017). Revisiting unreasonable effectiveness of data in deep learning era. arXiv preprint:1707.02968.
[6]	DeepSeek-AI , Liu A., Feng B., Xue B., Wang B., Wu B.,... Pan Z.,(2024). DeepSeek-V3 technical report. arXiv preprint: 2412.19437.
[7]	Deng Y., Gao X., Xu C., Sun Z., Yue Y., & Liu X. (2019). Reliability and validity test of Dependency-Oriented and Achievement-Oriented Psychological Control Scale in Chinese adolescents. Chinese Journal of Clinical Psychology, 27(2), 253-257.
	[邓衍鹤, 高芯芸, 徐陈晰, 孙治英, 岳艳春, 刘翔平. (2019). 依赖导向与成就导向心理控制量表修订版在我国青少年中的信效度检验. 中国临床心理学杂志, 27(2), 253-257.]
[8]	de Winter J. C., & Dodou D. (2012). Factor recovery by principal axis factoring and maximum likelihood factor analysis as a function of factor pattern and sample size. Journal of Applied Statistics, 39(4), 695-710.
[9]	Dinno A. (2009). Exploring the sensitivity of Horn’s parallel analysis to the distributional form of random data. Multivariate Behavioral Research, 44(3), 362-388. doi: 10.1080/00273170902938969 URL
[10]	Fava J. L., & Velicer W. F. (1996). The effects of underextraction in factor and component analyses. Educational and Psychological Measurement, 56(6), 907-929. doi: 10.1177/0013164496056006001 URL
[11]	Goodfellow I., Bengio Y., & Courville A. (2016). Deep learning. MIT Press.
[12]	Goretzko D. (2025). How many factors to retain in exploratory factor analysis? A critical overview of factor retention methods. Psychological Methods, https://doi.org/0.1037/met0000733.
[13]	Goretzko D., & Bühner M. (2020). One model to rule them all? Using machine learning algorithms to determine the number of factors in exploratory factor analysis. Psychological Methods, 25(6), 776-786. doi: 10.1037/met0000262 URL
[14]	Goretzko D., & Bühner M. (2022). Factor retention using machine learning with ordinal data. Applied Psychological Measurement, 46(5), 406-421. doi: 10.1177/01466216221089345 pmid: 35812814
[15]	Goretzko D., & Ruscio J. (2024). The comparison data forest: A new comparison data approach to determine the number of factors in exploratory factor analysis. Behavior Research Methods, 56(3), 1838-1851. doi: 10.3758/s13428-023-02122-4
[16]	Heaton J. (2008). Introduction to neural networks with Java (2nd ed., pp. 143-172). Heaton Research, Inc.
[17]	Hochreiter S., & Schmidhuber J. (1997). Long short-term memory. Neural Computation, 9(8), 1735-1780. doi: 10.1162/neco.1997.9.8.1735 pmid: 9377276
[18]	Horn J. L. (1965). A rationale and test for the number of factors in factor analysis. Psychometrika, 30(2), 179-185. doi: 10.1007/BF02289447 URL
[19]	Humphreys L. G., & Montanelli R. G. (1975). An investigation of the parallel analysis criterion for determining the number of common factors. Multivariate Behavioral Research, 10(2), 193-205. doi: 10.1207/s15327906mbr1002_5 URL
[20]	Ioffe S., & Szegedy C. (2015). Batch normalization: Accelerating deep network training by reducing internal covariate shift. arXiv preprint:1502.03167.
[21]	Kaiser H. F. (1960). The application of electronic computers to factor analysis. Educational and Psychological Measurement, 20, 141-151. doi: 10.1177/001316446002000116 URL
[22]	Kalinowski T., Ushey K., Allaire J. J., RStudio, Tang Y., Eddelbuettel D.,... Geelnard M. (2025). reticulate: Interface to Python. R package version 1. 42.0. https://ran.r-project.org/web/packages/reticulate/index.html
[23]	Kingma D. P., & Ba J. (2014). Adam: A method for stochastic optimization. arXiv preprint: 1412.6980.
[24]	Lange S., Helfrich K., & Ye Q. (2022). Batch normalization preconditioning for neural network training. Journal of Machine Learning Research, 23(1), 3118-3158.
[25]	LeCun Y., Bengio Y., & Hinton G. (2015). Deep learning. Nature, 521, 436-444.
[26]	Li Y., Wen Z., Hau K.-T., Yuan K.-H., & Peng Y. (2020). Effects of cross-loadings on determining the number of factors to retain. Structural Equation Modeling: A Multidisciplinary Journal, 27(6), 841-863. doi: 10.1080/10705511.2020.1745075 URL
[27]	Lorenzo-Seva U., Timmerman M. E., & Kiers H. A. (2011). The Hull method for selecting the number of common factors. Multivariate Behavioral Research, 46(2), 340-364. doi: 10.1080/00273171.2011.564527 pmid: 26741331
[28]	Marčenko V. A., & Pastur L. A. (1967). Distribution of eigenvalues for some sets of random matrices. Mathematics of the USSR-Sbornik, 1, 457-483. doi: 10.1070/SM1967v001n04ABEH001994 URL
[29]	Nair V., & Hinton G. E. (2010). Rectified linear units improve restricted Boltzmann machines. In Proceedings of the 27th International Conference on Machine Learning (ICML-10) (pp. 807-814). Omnipress.
[30]	Peres-Neto P. R., Jackson D. A., & Somers K. M. (2005). How many principal components? Stopping rules for determining the number of non-trivial axes revisited. Computational Statistics & Data Analysis, 49(4), 974-997.
[31]	Qin H., & Guo L. (2024). Using machine learning to improve Q-matrix validation. Behavior Research Methods, 56(3), 1916-1935. doi: 10.3758/s13428-023-02126-0
[32]	Qin H., & Guo L. (2025a). EFAfactors: Determining the number of factors in exploratory factor analysis. R package version 1.2.1.
[33]	Qin H., & Guo L. (2025b). LSTMfactors: Determining the number of factors in exploratory factor analysis by LSTM. R package version 1.0.0.
[34]	Paszke A., Gross S., Massa F., Lerer A., Bradbury J., Chanan G.,... Chintala S. (2019). PyTorch: An imperative style, high-performance deep learning library. In Proceedings of the 33rd International Conference on Neural Information Processing Systems (pp. Article 721). Curran Associates Inc.
[35]	Pedregosa F., Varoquaux G., Gramfort A., Michel V., Thirion B., Grisel O.,... Duchesnay É. (2011). Scikit-learn: Machine learning in Python. Journal of Machine Learning Research, 12, 2825-2830.
[36]	R Core Team. (2025). R: A language and environment for statistical computing. R Foun dation for Statistical Computing, Vienna, Austria. https://www.R-project.org
[37]	Ruscio J., & Kaczetow W. (2008). Simulating multivariate nonnormal data using an iterative algorithm. Multivariate Behavioral Research, 43(3), 355-381. doi: 10.1080/00273170802285693 pmid: 26741201
[38]	Ruscio J., & Roche B. (2012). Determining the number of factors to retain in an exploratory factor analysis using comparison data of known factorial structure. Psychological Assessment, 24(2), 282-292. doi: 10.1037/a0025697 pmid: 21966933
[39]	Soenens B., & Vansteenkiste M. (2010). A theoretical upgrade of the concept of parental psychological control: Proposing new insights on the basis of self-determination theory. Developmental Review, 30(1), 74-99. doi: 10.1016/j.dr.2009.11.001 URL
[40]	Velicer W. F. (1976). Determining the number of components from the matrix of partial correlations. Psychometrika, 41(3), 321-327. doi: 10.1007/BF02293557 URL
[41]	Wood J. M., Tataryn D. J., & Gorsuch R. L. (1996). Effects of under- and overextraction on principal axis factor analysis with varimax rotation. Psychological Methods, 1(4), 354-365. doi: 10.1037/1082-989X.1.4.354 URL
[42]	Zwick W. R., & Velicer W. F. (1986). Comparison of five rules for determining the number of components to retain. Psychological Bulletin, 99(3), 432-442. doi: 10.1037/0033-2909.99.3.432 URL

最优的超参数组合		最优模型评价指标
超参数	值	指标	值
学习率	0.01	Accuracy	0.847
LSTM层数	2	Precision	0.847
LSTM每层节点数	32, 38	Recall	0.847
全连接网络层数	5	F1-Score	0.847
全连接层每层节点数	38, 39, 34, 31, 27	Kappa	0.831
激活函数	Tanh

最优的超参数组合		最优模型评价指标
超参数	值	指标	值
学习率	0.01	Accuracy	0.847
LSTM层数	2	Precision	0.847
LSTM每层节点数	32, 38	Recall	0.847
全连接网络层数	5	F1-Score	0.847
全连接层每层节点数	38, 39, 34, 31, 27	Kappa	0.831
激活函数	Tanh

数据条件	水平	准确率acc
数据条件	水平	CDF	EKC	PA	LSTM	提升率
因子数量	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%
因子间相关	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%
每因子题目数量	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%
主要载荷	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%
交叉载荷	L	0.486	0.519	0.508	0.750	44.59%
交叉载荷	H	0.545	0.565	0.532	0.785	38.99%
样本量	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%

数据条件	水平	准确率acc
数据条件	水平	CDF	EKC	PA	LSTM	提升率
因子数量	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%
因子间相关	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%
每因子题目数量	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%
主要载荷	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%
交叉载荷	L	0.486	0.519	0.508	0.750	44.59%
交叉载荷	H	0.545	0.565	0.532	0.785	38.99%
样本量	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%

数据条件	水平	偏差bias
数据条件	水平	CDF	EKC	PA	LSTM
因子数量	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
因子间相关	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
每因子题目数量	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
主要载荷	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
交叉载荷	L	−1.838	−1.889	−1.963	0.176
交叉载荷	H	−1.222	−1.037	−1.605	0.155
样本量	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