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Biostatistics-Lecture 7 Variable selection methods

Biostatistics-Lecture 7 Variable selection methods. Ruibin Xi Peking University School of Mathematical Sciences. Stepwise selection. Backward Elimination. Stepwise selection. For ward Selection. Drawbacks of stepwise selection. One-at-a-time: may miss optimal

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Biostatistics-Lecture 7 Variable selection methods

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  1. Biostatistics-Lecture 7Variable selection methods Ruibin Xi Peking University School of Mathematical Sciences

  2. Stepwise selection • Backward Elimination

  3. Stepwise selection • Forward Selection

  4. Drawbacks of stepwise selection • One-at-a-time: may miss optimal • P-values of the remaining predictors tends to be overstated • Multiple testing • Model tends to be smaller than desirable for prediction purpose • Variable not in the model may still be correlated with the response

  5. Stepwise selection—An example • Interested in factors related to the life expectancy (50 US states,1969-71 ) • Per capita income (1974) • Illiteracy (1970,percent of population) • Murder rate per 100,000 population • Percent high-school graduates • Mean number of days with min temperature < 30 degree • Land area in square mile

  6. Criterion-based procedures • The Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC) • Adjusted R2—Ra2

  7. Criterion-based procedures • Mallow’s Cp statistic: • The mean squared prediction error (MSPE) • Can be estimated by • Under true model

  8. Penalized methods • Ridge regression • Lasso • ElasticNet

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