In the paper, we explore the behaviour of neural network software quality models. We select a multiple regression quality model from the principal components of software complexity metrics collected from a large commercial software system. We train two neural networks; one with the complete set of principal components and one with the set of components selected by multiple regression model selection. Comparisons of the three models, for two quality measures gathered from five related software systems, lead to a better understanding of neural network software quality models, and the relationship between software complexity metrics and software quality metrics.