Longitudinal models for project expenditure plans

Abstract

The ability of project managers to generate accurate budget predictions for capital investments is critical for successful project completion and the management of the Australian Department of Defence budget. Accordingly, this paper discusses non-linear regression models to analyse planned time-phasing of expenditures for projects in an Australian Defence capital investment program. Earlier research on time-phasing primarily focuses on the theoretical foundation for applying the cumulative distribution function, usually of functional forms such as Rayleigh and Weibull curves, to model the distribution of project expenditures. Previous approaches have also relied on elementary regression techniques to estimate the parameters of the curves. However, these analyses have generally ignored the longitudinal, repeated measures nature of the data for each project, potentially compromising results because the data within projects is correlated. Here, a non-linear mixed-effects model is used to estimate the parameters of the time-phasing distributions for a large number of major capital investment projects. Unlike ordinary linear or non-linear regression, this has the advantage of accounting for within project correlation and unequal variance. The model can be thought of as a hierarchical model involving both fixed-effects associated with the population of projects and random-effects accounting for unexplained inter- and intra-project variability. The fixed part of the model incorporates military domain effects and project epochs, and random effects account for heteroscedasticity and correlations between the repeated measures. Analysis reveals significant differences between project’s time-phasing due to their domain and epoch. The model may be used by project and portfolio planners to estimate required spending plans against project schedule and total planned expenditure; it therefore provides a tool to measure project and financial risk.