# Step 2. Prepare Data

The second IPF step is to gather and transform raw data so that they are usable for calculating SEI and FEI project scores. A simple Excel environment can be constructed to populate a prioritization database with raw data. Because selection criteria variables may have different units of measurement (i.e., they are not all dollarized costs and benefits) but are combined in additive models, two types of data transformation are required. First, any qualitative data must be transformed into either ordinal or scalar data.<sup>9</sup> Second, observations are standardized to deal with disparate units of measure, transforming all measurements to have a transformed value between [-1] and [1], with the set having a zero mean and unit variance.<sup>10</sup>

# Step 3. Constructing Performance Indices – SEI and FEI

Indices are used to combine information from multiple variables into composite indicators. In IPF, variables are organized into two classes to construct the social-environmental index (SEI) and the financial-economic index (FEI). The FEI may be the standardized value of a single component derived from CBA (e.g., NPV or BCR) or a combination of several factors, but the SEI is typically constructed by combining a number of key social and environmental variables. This is done via an additive model, wherein each indicator’s contribution to the overall index score is determined by weights (the coefficients associated with each variable).

For example, if the SEI variables selected include (a) number of beneficiaries (BEN), (b) number of poor served (POOR), and (c) number of jobs created, the function may be expressed as

## SEI� w� ��BEN�� w� ��POOR�� w� ��JOBS�,

where weights, w�, are associated with each social-environmental indicator.

The weights used to combine variables can be set subjectively or objectively, such as using some form of Principal Component Analysis (PCA). PCA is an information reduction procedure that seeks redundancies in sets of variables. These redundancies can be expressed as linear combinations or ‘principal components’ of the variables comprising the set. One key characteristic of PCA is the ability to calculate coefficients (weights) based solely on the statistical relationship between variables. While other weighting schemes may be used, PCA is particularly useful when there is a preference to objectively assign weights.

Some significant advances have been made with respect to using PCA to determine weights. These changes have been made to deal with policy preferences regarding the relative importance of criteria. Over the course of the Sri Lanka and Chile pilots, for example, calculation methods were developed to add restrictions to PCA that can attain the following: require a particular coefficient sign (+/-) associated with specified variables; require that criteria are weighted to reflect a pre-set order of importance (a weighting order); and require a minimum weight for a variable.

> 9 This can be done with either scaling methods or via approaches like ALSOS. The transformation of categorical and ordinal qualitative and quantitative data into usable numerical data may be done using the Alternating Least Squares Optimal Scaling (ALSOS) algorithm, a widely-accepted transformation approach. Within a quantified ordinal variable, the numbers assigned by the ALSOS algorithm to each category reflect the distance between categories, revealing the implicit metric of the variable (Perreault & Young, 1976).

> 10 Numerical values are standardized via a standardization formula that can be coded into Excel. The standard score z of a raw score x is z_ij= (x_ij-μ_j)/ _j, where μ is the sample mean and  is the standard deviation of the variable j.

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