On the methodological framework of composite index under complex surveys and its application in development of food consumption index for India

Indices are created by consolidating multidimensional data into a single representative measure known as an index, using a fundamental mathematical model. Most present indices are essentially the averages or weighted averages of the variables under study, ignoring multicollinearity among the variables, with the exception of the existing Ordinary Least Squares (OLS) estimator based OLS-PCA index methodology. Many existing surveys adopt survey designs that incorporate survey weights, aiming to obtain a representative sample of the population while minimizing costs. Survey weights play a crucial role in addressing the unequal probabilities of selection inherent in complex survey designs, ensuring accurate and representative estimates of population parameters. However, the existing OLS-PCA based index methodology is designed for simple random sampling and is incapable of incorporating survey weights, leading to biased estimates and erroneous rankings that can result in flawed inferences and conclusions for survey data. To address this limitation, we propose a novel Survey Weighted PCA (SW-PCA) based Index methodology, tailored for survey-weighted data. SW-PCA incorporates survey weights, facilitating the development of unbiased and efficient composite indices, improving the quality and validity of survey-based research. Simulation studies demonstrate that the SW-PCA based index outperforms the OLS-PCA based index that neglects survey weights, indicating its higher efficiency. To validate the methodology, we applied it to a Household Consumer Expenditure Survey (HCES), NSS 68th Round survey data to construct a Food Consumption Index for different states of India. The result was significant improvements in state rankings when survey weights were considered. In conclusion, this study highlights the crucial importance of incorporating survey weights in index construction from complex survey data. The SW-PCA based Index provides a valuable solution, enhancing the accuracy and reliability of survey-based research, ultimately contributing to more informed decision-making.