Dear all,
Are there other ways to combine a set of pre-decided/selected variables into a single variable? Like Human Development Index combines 3 different components, would other ways could also be constructed for the same?
If so, please suggest some concepts/methods for the same.
Thanks.
There is no general algorithm, it is a piece of art in economic modelling. There were plenty of indices constructed, but few of them (like HDI) survived. You should describe your set up (initial variables) and the objective. Then somebody may give you some advice.
It depends upon your study, their are techniques that may help to construct the index, via calculating the weightages of the respective variables. I am attaching on paper I think this may help you a lot
It can be simple, can be more complex - there is number of ways. The most difficult part actually is to select indicators used for index that really are well designed in describing phenomenon you want to picture with it. In case of comparing countries it is better to have as indicators ones which are well established in statistical practice and there are good data available to estimate it. Otherwise indicators - and the index - will be strongly contested. HDI survived because uses widely used, accepted and uncontested indicators. Many attempts to broaden, deepen it or supplement it by adding more sophisticated indicators failed because these indicators were very demanding with respect to data needed and required a lot of (guess)timates. More complex indicators are used and more sophisticated weighting system is applied, less chances that index will be understood and accepted.
You could consider using principal component analysis
Article Principal Component Analysis
Dear SJ, I have faced the same problem in October 2015, even if in a field of investigation different from that typical of HDI. My problem was to elaborate an index of social and economic vulnerability of subnational areas of Italy. I have worked with 21 variables, that I have synthetized with a method that is a combination of the HDI and the Mazziotta and Pareto Index. If you are interested to my solution you can refer to my article "The vulnerability of sub-national areas to unexpected socio-economic disturbances: the case of Italy" (Fabbri Foundation Political Laboratory, 29 october 2015), which I enclose.
Article The vulnerability of sub-national areas to economic and fina...
You can take a look at the Worldwide Governance Indicator by the Word Bank. Maybe the calculation method used there can be helpfull for you
It really depends on what you want to achieve. The HDI is deliberately constructed to combine three variables with equal weights. In that, it is more normative in its construction: the people behind it chose the weights that they assign to the components.
Principal component analysis can be used when you have several original variables that you want to reduce to a single index, but you have no priors as to what weights you should use. PCA will determine these weights for you optimally, looking for common sources of variation in the original variables.
I suggest to look at the article Chapter: Well-being in the world: a stochastic measure at the turn of the millennium Stefano Pisani · Francesco Carlucci, published on my research gate profile.
Principal component analysis. read its theory from any of the Multivariate analysis book .
It seems you want to construct an indicator using several variables. There is a handbook edited by OECD especifically oriented towards the construction of composite indicators. Here's the link
www.oecd.org/std/42495745.pdf
Hope it helps
If you are interested in creating an indicator or an index like HDI, you should firstly define your goal and then based on the defined goal, try to find proper variables.