Modified Factor Analysis to Construct Composite Indices: Illustration on Urbanization Index

Abstract

This study introduces a modified factor analysis approach to develop a composite index. The methodology is illustrated using an index representing the magnitude of urbanization of a Divisional Secretariat. The new method defines a specific weight to each individual indicator variable and the index assigns a specific numerical value to the level of urbanization of an area. Densities of population, students, houses and common residences, non-resident buildings, business establishments and vehicles were the indicator variables considered in the index building process. Cronbach's alpha was used to verify the internal consistency of these indicator variables. Initially, the grouping patterns in the data have been identified through a Preliminary Factor Analysis. This resulted in a single factor explaining a substantial amount of total variability. The weight corresponding to a particular indicator variable was defined as a function of the correlation coefficient between the indicator variable and the first Principle Component. Then the scaled variables were weighted and used in the final Factor Analysis. A single factor explaining 94% of total variance was selected as the composite index. First, the Index of Urbanization was defined as a linear function of the composite index. Then it was converted into a function of original indicator variables to make it easy to update. The methodology would be applicable to any country for deriving a similar Index of Urbanization. Logical classification of local government authorities, to assist the government in various policy making and development activities is also possible with the new Index.