Interactive statistics with ILLMO

Progress in empirical research relies on adequate statistical analysis and reporting. This article proposes an alternative approach to statistical modeling that is based on an old but mostly forgotten idea, namely Thurstone modeling. Traditional statistical methods assume that either the measured data, in the case of parametric statistics, or the rank-order transformed data, in the case of nonparametric statistics, are samples from a specific (usually Gaussian) distribution with unknown parameters. Consequently, such methods should not be applied when this assumption is not valid. Thurstone modeling similarly assumes the existence of an underlying process that obeys an a priori assumed distribution with unknown parameters, but combines this underlying process with a flexible response mechanism that can be either continuous or discrete and either linear or nonlinear. One important advantage of Thurstone modeling is that traditional statistical methods can still be applied on the underlying process, irrespective of the nature of the measured data itself. Another advantage is that Thurstone models can be graphically represented, which helps to communicate them to a broad audience. A new interactive statistical package, Interactive Log Likelihood MOdeling (Illmo), was specifically designed for estimating and rendering Thurstone models and is intended to bring Thurstone modeling within the reach of persons who are not experts in statistics. Illmo is unique in the sense that it provides not only extensive graphical renderings of the data analysis results but also an interface for navigating between different model options. In this way, users can interactively explore different models and decide on an adequate balance between model complexity and agreement with the experimental data. Hypothesis testing on model parameters is also made intuitive and is supported by both textual and graphical feedback. The flexibility and ease of use of Illmo means that it is also potentially useful as a didactic tool for teaching statistics.