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Regression Analysis of Collinear Data using r-k Class Estimator: Socio-Economic and Demographic Factors Affecting the Total Fertility Rate (TFR) in India
Authors: Piyush Kant Rai, Sarla Pareek and Hemlata Joshi
Source: Journal of Data Science , 11(2013), 321-340
Topic(s): Data models
Country: Asia
Published: JAN 2013
Abstract: A basic assumption concerned with general linear regression model is that there is no correlation (or no multicollinearity) between the explanatory variables. When this assumption is not satisfied, the least squares estimators have large variances and become unstable and may have a wrong sign. Therefore, we resort to biased regression methods, which stabilize the parameter estimates. Ridge regression (RR) and principal component regression (PCR) are two of the most popular biased regression methods which can be used in case of multicollinearity. But the r-k class estimator, which is composed by combining the RR estimator and the PCR estimator into a single estimator gives the better estimates of the regression coefficients than the RR estimator and PCR estimator. This paper explores the multiple regression technique using r-k class estimator between TFR and other socio-economic and demographic variables and the data has been taken from the National Family Health Survey-III (NFHS-III): 29 states of India. The analysis shows that use of contraceptive devices shares the greatest impact on fertility rate followed by maternal care, use of improved water, female age at marriage and spacing between births. Key words: Multicollinearity, principal component regression (PCR) estimator, r-k class estimator, ridge regression (RR) estimator, total fertility rate (TFR).