Autoencoder for the study of nonlinear relationships in latent variable models
Are you already subscribed?
Login to check
whether this content is already included on your personal or institutional subscription.
Abstract
The study, through psychometric testing, of latent variables and their relationships with observed variables is of great importance in psychology. Traditionally, to investigate these relationships, linear methods belonging to an explanatory approach, such as Principal Component Analysis (PCA), have been used. Although useful in some contexts, linear methods can be limiting when it comes to exploring more complex relationships between variables. Indeed, relying solely on linear methods narrows the range of hypotheses that can be tested and may lead to incorrect conclusions. For example, treating a non-linear relationship as linear could lead to rejecting factorial invariance or erroneously attributing non-linear effects to interaction effects between latent variables. Moreover, explanatory models can be improved by integrating predictive modeling techniques. Predictive models, which do not make a priori assumptions about the causal structure of data and can be generalized to new observations, can be used to develop and refine explanatory models. In this article, we propose the use of artificial neural networks – specifically autoencoders – which are predictive methods of dimensionality reduction, as an alternative to PCA. We have tested autoencoders and PCA under various conditions, including linear and non-linear relationships between items and factors, and have evaluated their performance in terms of mean squared error of item response reconstruction and the relationship between item and factor. The results show that the autoencoder, unlike PCA, is capable of capturing the shape of the relationship between items and factors. These findings suggest that the autoencoder could be a useful tool for improving the validation processes of psychometric tests by providing a representation of the relationship between item and factor that is closer to the real one.
Keywords
- artificial neural networks
- autoencoders
- dimensionality reduction
- nonlinear relationships
- latent variable models