Desarrollo del Músculo Piriforme

The indicators are combined in an index by assigning a weight to each indicator and applying an aggregation method. In literature, several weighting and aggregation methods exist, none of them being the best technique to use in all circumstances. First, we determine weighting methods most often used in the construction of an index and valuable for the road safety context. Section 4.5.2 discusses the options related to aggregation.

4.5.1 Weighting methods

By studying other indexes we obtain an idea about the most popular weighting methods. The e-business index 2003 (Nardo et al., 2004) explored three weighting schemes, namely equal weighting, budget allocation (qualitative method) and factor analysis (quantitative method). Al Haji (2005) used simple equal average, a principal components analysis, an assessment technique from experts’ opinions and an assessment technique from literature and theory review. Other examples can be found in Saisana and Tarantola (2002). In fact, it is common practice to experiment with various weighting techniques and compare the results. Nevertheless, the reasoning behind the choice of a particular weighting technique is often lacking in a study and simpler methods are more commonly

applied than complex ones. In Booysen (2002) it is concluded that no weighting system is above criticism. Therefore, a thorough evaluation of the most relevant weighting methods for the topic under study is essential. In general, weights can be chosen to be equal, can be determined statistically, can involve the opinion of persons (e.g. experts) or can be optimized. Below, five common weighting methods – equal weighting, weights based on factor analysis, budget allocation, analytic hierarchy process and data envelopment analysis – are briefly explained.

- equal weighting: assigning the same weight to each indicator is the most simple method. This is the main reason why it is commonly used in indexes. Salzman (2003) states that this method reduces the subjectivity of weights, has an interpretive meaning and is transparent. On the other hand, the importance of an indicator is not reflected by its weight and there is a risk of double counting (Nardo et al., 2005b).

- weights based on factor analysis: factor analysis is a technique which can also be used to determine weights. More specifically, weights consist of the factor loadings of each indicator (after rotation) and the variance explained. Indicators with a strong capacity of explaining the variation in the data are expected to receive a relatively high weight (Pennoni et al., 2005).

- budget allocation: a group of experts is asked to allocate a budget of N points over the set of indicators, where more important indicators should receive a higher share of the budget. The share of the budget assigned to an indicator equals its weight. To obtain good results, a team of qualified experts needs to be found. The weights resulting from a particular expert could be considered for the analysis as well as a set of weights representing the opinion of all experts.

- analytic hierarchy process: this method uses experts’ opinions as well. Each indicator is compared to another indicator and the expert decides which of the two is more contributing to the overall goal and indicates the intensity of the strength (Saaty, 1980). In case two indicators are considered to have the same contribution to road safety, a score of one is given whereas an extreme difference in contribution results in a score of nine. All scores are then transformed in weights, summing up to one.

- data envelopment analysis: in this case, the weights are endogenously determined from the data set as to obtain the best possible index score for a country. This means that higher weights are attached to the domains on which a country performs relatively well (Cherchye and Kuosmanen, 2004). Moreover, restrictions regarding the share of each indicator in the overall index score can be incorporated in the optimization problem to obtain more realistic weights. This method can result in optimal country-specific weights as well as one set of indicator weights that is the same for each country (like other weighting methods do).

For the road safety index, the advantages and disadvantages of the five previously described methods are worthwhile investigating. Each technique requires a profound examination.

4.5.2 Aggregation methods

As is the case for weighting, aggregation is a potential area of methodological controversy in the field of composite indicator construction (Yale Center for Environmental Law and Policy and Center for International Earth Science Information Network, 2006). Various types of aggregators exist of which the selection should fit the purpose of the study and the subject being measured. In the handbook on constructing composite indicators (Nardo et al., 2005b) three aggregation methods are mentioned. Additive or linear aggregation sums the weighted indicators. Secondly, the non- compensatory multi-criteria approach guarantees the interpretation of weights as importance coefficients. This aggregation involves the creation of an outranking matrix.

Thirdly, geometric aggregation implies that the index is the product of its indicators to the power of their weights. Linear aggregation is the best-known way of aggregating. However, the suitability of this type of aggregation has been questioned (see e.g. Munda and Nardo, 2005).

Apart from the three aggregation types suggested for creating an index, aggregation is a very extensive research domain in which numerous types of operators exist. They are all characterized by certain mathematical properties and aggregate in a different manner. In general, aggregation operators can be roughly divided into three classes (Grabisch et al., 1999): conjunctive operators (AND), disjunctive operators (OR) and averaging operators. The third class possesses interesting properties and consists of mean operators, ordered weighted averaging (OWA) operators, fuzzy integrals, etc. Of these operators, OWA is an often used and comprehensible class of operators that is worthwhile testing. The attitude of decision makers in terms of the allowed degree of compensation between good and bad values can be reflected (Yager, 1996). That way, road safety professionals can express their aggregation policy in natural language (e.g. in case a country scores badly on more than a few indicators, its final road safety index score should be small). This guideline is then translated mathematically and index scores respecting the statements can be computed. By changing the parameters OWA can generate a wide spectrum of policy scenarios.