Comparison of estimated regression coefficients using ordinary least squares method and ridge regression a demonstration using data on pediatric pulmonology - Baylon, Melba Andrea B.
This paper has presented regression data on pediatric pulmonology that attempted to estimate the regression coefficients of the socio-demographic (age, school and sex) and anthropometric (weight, standing height, sitting height and trunk height) variables to predict a spirometric measurement like peak expiratory flow rate (PEFR). Collinearity diagnostic procedures provided evidence of high correlations among the height measurements. With least squares analysis, estimates were unstable and had posed difficultes in the interpretation of the regression coefficients especially for age, weight, sitting height and trunk height. Improvement in the interpretation was provided by ridge regression, a biased regression method. Eleven values of the bias term were utilized. From these, the choice of the biasing constant, k, was determined by examination of the ridge trace and an objective method based on the sample data. Graphical plot subjectively suggested a value of k=0.2 while the objective method resulted to a value of k=0.88. The ridge estimates abruptly dropped from k=0.2 and gradually stabilized (i.e. did not change) onwards with increasing values of k.Aside from the ridge estimates, the behavior of the variance inflation factors and standard errors of these estimates were also observed. These factors also decreased when k was increased from 0. The magnitude of change of the ridge estimates from the OLS estimates were also determined.When the standardized OLS estimates were compared with the ridge estimates at k=0.88, the latter yielded smaller variance inflation factors and standard errors. This leads to the conclusion that, though biased, ridge regression is more stable than the OLS estimates.When multicollinearity is suspected, ridge regression is recommended to determine the suitability of the data for least squares analysis.
Thesis (Master of Science in Public Health, Biostatistics)--University of the Philippines Manila.
Keywords: Least squares; Ridge regression; Regression analyis; Regression coefficients