Autoencoders as a Tool to Detect Nonlinear Relationships in Latent Variables Models

Understanding data dimensionality and the relationships between observed variables and data dimensions is a crucial task in psychology. Principal Component Analysis (PCA) is a traditional method used for dimensionality reduction, but it assumes that relationships between observed variables and factors are linear. Linear methods can be limiting when exploring more complex relationships between variables, and they may restrict the range of hypotheses that can be tested, potentially leading to misleading conclusions. To overcome these limitations, we propose using an artificial neural network called autoencoder as an alternative to PCA. Autoencoders are multi-layer perceptrons with as many inputs as outputs and a smaller number of hidden nodes. Since they can use non-linear activations at different layers and require mild assumptions on input data, they are a valuable tool to perform nonlinear dimensionality reduction. We compared the performance of autoencoders and PCA under different conditions, including linear and non-linear relationships between items and factors, and evaluated them in terms of mean squared error of reconstruction of item responses and the relationship between items and factors. Our results demonstrate that autoencoders can capture the shape of the relationship between items and factors, unlike PCA. We conclude that autoencoders could be a valuable tool for enhancing psychometric test validation processes by providing a representation of the relationship between items and factors that is closer to the actual one.