How To Create A Composite Index In Stata

How to create an index using principal component analysis [PCA]

Suppose one has got five different measures of performance for n number of companies and one wants to create single value [index] out of these using PCA. Can one multiply the principal component loadings for each variable with the value of variable and sum these to find the index?

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ICAR-Indian Institute of Wheat and Barley Research, Karnal, Haryana (India)

PCA has multiple uses in applied economics. One of the PCA uses is indexing which we tried in the attached paper and shared for your kind perusal.

Application for Vulnerability Indexing

All Answers (20)

Istituto Superiore di Sanità

PCA is very good to find such an index if you reach a solution with one major first principal component explaining the by far major part of variance. The index corresponds to the component scores that can be exported to other statistical units by simple linear regression on the training set (Y = component score, X= measures of performances).

International Islamic University, Islamabad

You're right, but you need to avoid any dummy variables or variables with limited values.

Please can I get how to deduce the index in stata? I have many variables measuring one thing. I want to generate an index using the first principal component to run a regression.

International Islamic University, Islamabad

use pca command as follows:

pca v1 v2 v3 ... v10 [say Vs are variables]

Now you'll get an output

Choose (from above panel) a component with eigen value 1 or greater than 1.

Say you've chosen component 1, now see loadings for different variables under component 1, multiply each variable with its squared loading and add them....you'll get an index with different weights for different variables. Please remember, the sum of the squared loadings is equal to one. Take care

May i take, the value of a given variable from component matrix or and can i say square loading is equivalent to eigen valuse?

Istituto Superiore di Sanità

Read the attached paper, it is exactly about the generation of a single cumulative score by means of PCA

147.30 KB

Thank you Alessandro Giuliani,

Istituto Superiore di Sanità

Not at all, and rememeber you can use dummy variables too provided they have only binary (1/0) codes, in this case you can insert them in PCA as they were real valued variables, see: Cox, David R. "The analysis of multivariate binary data." Applied statistics (1972): 113-120.

Alessandro Giuliani - Can we rank variables using this index or is it only for ranking factors?

Istituto Superiore di Sanità

Surely yes, the loading on the first component (in the case a major leading first component does exist as in the attached paper) are a direct rank of the relevance of each variable. The rank of the statistical units is cealrly correspondent to the relative component score.

How to create an index using principal component analysis [PCA]? plz help me using step by step procedure

Punjabi University, Patiala

Dear Alessandro, I have the same problem. I was trying to develop a single index with PCA. the problem is the first principal component explain only 40 of the varation. i have six variables, the Varimax rotated correlation matrix showed that i, each variable is perfectly correlated with each component, means it becomes a singular matrix. should i take all the variables sum and divide by six instead of using the first principal component factor loading square as weight? waiting for answers any one

Institute of Agriculture and Animal Science

I could not understand the interpretation of PCA value. how can use PCA into wellbeing ranking ? Please help me

PCA is simply variable reduction technique. For instance, if you have 10 variables or activities. First, you need to standardize foe each units of variable if they have different units of measurements using Z-score. Second, run correlation matrix. The matrix by default standardizes those units. The values of correlation are correlation coefficients which indicate the direction and strength of relationships among those variables. Third, at the mean time run PCA. The number of components are equals to the number of variables. However, based on some criteria you will have less than 10 newly constructed components or variables. Two of the main criteria: Take components having Eigen values greater than 1 and the total variations at least greater than 70%. Thus, the values of PCA tells you factor loadings meaning coefficient values to what extent the merged variables are correlated or not by observing its sign (negative or positive). Nevertheless, not sure to bring the values of factor loading bringing to a single index.

Consultative Group on International Agricultural Research

Is it important to rotate the factors? My purpose is just to get an index value, and after rotating I am not getting good weights (some negative , some positive). Please guide.

Yes, some values could be negative while others could be positive. PCA can do three things as the same time. (i) standardizes different unities (ii) tells correlation coefficients or in PCA factor loading which designates the direction and strength of coefficients. The negative values indicate competition or opposition while positive values could be integration or similar connotations depending on the objective of factors. (iii) Reduces number of variables