Using Nonlinear Quantile Regression for the Estimation of Software Cost

Estimation of effort costs is an important task for the management of software development projects. Researchers have followed two approaches –namely, statistical/machine-learning and theory-based– which explicitly rely on mean/median regression lines in order to model the relationship between software size and effort. Those approaches share a common drawback deriving from their inability to properly incorporate risk attitudes in the presence of heteroskedasticity. We propose a more flexible quantile regression approach that enables risk aversion to be incorporated in a systematic way, with the higher order conditional quantiles of the relationship between project size and effort being used to represent more risk adverse decision makers. A cubic quantile regression model allows consideration of economies/diseconomies of scale. The method is illustrated with an empirical application to a database of real projects. Results suggest that the shapes of higher order regression quantiles may sharply differ from that of the conditional median, revealing that the naive expedient of translating or multiplying some average norm (adding a safety margin to median estimates or including a multiplicative correction factor) is a potentially biased way to consider risk aversion. The proposed approach enables a more realistic analysis, adapted to the specificities of software development databases.