Estimating the Minimum Sample Size for Neural Network Model Fitting-A Monte Carlo Simulation Study

In the era of machine learning, many psychological studies use machine learning methods. Specifically, neural networks, a set of machine learning methods that exhibit exceptional performance in various tasks, have been used on psychometric datasets for supervised model fitting. From the computer scientist's perspective, psychometric independent variables are typically ordinal and low-dimensional-characteristics that can significantly impact model performance. To our knowledge, there is no guidance about the sample planning suggestion for this task. Therefore, we conducted a simulation study to test the performance of an NN with different sample sizes and the simulation of both linear and nonlinear relationships. We proposed the minimum sample size for the neural network model fitting with two criteria: the performance of 95% of the models is close to the theoretical maximum, and 80% of the models can outperform the linear model. The findings of this simulation study show that the performance of neural networks can be unstable with ordinal variables as independent variables, and we suggested that neural networks should not be used on ordinal independent variables with at least common nonlinear relationships in psychology. Further suggestions and research directions are also provided.