برآوردگر جدید برای تجزیه و تحلیل حساسیت خروجی مدل:یک برنامه کاربردی برای شاخص کامپوزیتی آمادگی کسب و کار الکترونیکی

In this paper we propose and test a generalisation of the method originally proposed by Sobol’, and recently extended by Saltelli, to estimate the first-order and total effect sensitivity indices. Exploiting the symmetries and the dualities of the formulas, we obtain additional estimates of first-order and total indices at no extra computational cost. We test the technique on a case study involving the construction of a composite indicator of e-business readiness, which is part of the initiative “e-Readiness of European enterprises” of the European Commission “e-Europe 2005” action plan. The method is used to assess the contribution of uncertainties in (a) the weights of the component indicators and (b) the imputation of missing data on the composite indicator values for several European countries.

In this paper we propose a methodology for sensitivity analysis, which is a generalisation of that proposed in [1] (a review is also offered in [2]) at no extra cost for the analysis. We then test it on a study for the construction of a composite indicator of e-business readiness. Composite indicators are aggregate measures that are calculated as weighted combinations of selected sub-indicators via underlying models of the policy domains of interest. Much discussion surrounds the legitimacy of such indicators. Composites are increasingly used by media and policy makers to communicate information on the situation of countries or regions in various policy fields such as environment, economy or technological development (reviews in [3] and [4]). Opponents lament that composites are mixes of dubious interpretation yet expensive to obtain. Nevertheless, organisations such as the UN, the OECD and the European Commission make a growing use of such measures. In particular the OECD and the joint research centre (JRC) have recently undertaken the joint preparation of a handbook of good practices of composite indicators building [5]. The e-business readiness composite indicator is aimed at measuring the progress of European enterprises towards a more extensive take up and use of digital technologies. We focus our analysis on the weighting scheme used to aggregate sub-indicators, and on the sensitivity of the composite indicator to different weighting schemes and to incomplete data. As far as weighting is concerned, JRC suggested and deployed a participatory technique, called “budget allocation”, which allows an expert to express his/her opinion upon the relative importance of sub-indicators (see Section 4). The issue of sensitivity is crucial for the assessment of composites. The communication from the European Commission on structural indicators [6] recognises the importance to assess the sensitivity of the message conveyed by composites with respect to the weights employed. Here we consider an additional source of uncertainty in the evaluation of the composite indicator, the uncertainty due to missing data. As we shall see in Section 3 we use a Multiple Imputation technique (based on Markov Chain Monte Carlo algorithms, henceforth MCMC) for the treatment of missing data. This method is appealing in that it provides confidence bounds for the imputed data [7] and [8]. Imputed data are, indeed, estimated values. Different imputed data may result in significantly different composite indicator values. Thus, the effect of the imputation on the resulting composite indicator must be acknowledged using both uncertainty and sensitivity analysis.

Media and policy-makers look with increasing interest at composite indicators as appealing tools to attract the attention of the community and to help focusing policy debates. But methodological gaps in their design and construction may invite politicians to draw simplistic conclusions or the press to communicate misleading information. That is why national and international organisations believe that it is important to focus on methodological issues in the design of composite indicators [5]. Here we illustrate a generalisation of the method proposed by Sobol’, and further developed by Saltelli, and we test it on a practical case study related to the design stage of composite indicators, where rarely robustness and sensitivity analysis are applied.