Handout09 - Lecture 9 1. Math scores: comparison of subset...

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Lecture 9 1. Math scores: comparison of subset selection results 2. Math scores: conclusion 3. Continuous and categorical predictors 4. Indicator variables 5. Proc GLM and Proc Reg 1 Model selection “by hand” Full model: Parameter Standard Variable DF Estimate Error t Value Pr > |t| Intercept 1 71.49920 2.07620 34.44 <.0001 log_lep 1 -0.65463 0.13643 -4.80 <.0001 log_lunch 1 -1.89919 0.27951 -6.79 <.0001 Special_Ed_pct 1 -0.07866 0.03944 -1.99 0.0468 log_mobility 1 -1.53474 0.29114 -5.27 <.0001 drop_out_pct 1 -0.56735 0.15351 -3.70 0.0002 log_8th_grade 1 0.21923 0.30184 0.73 0.4681 log_total_students 1 -0.72168 0.39947 -1.81 0.0716 operating_budget 1 -0.46716 0.30285 -1.54 0.1237 total_budget 1 -0.05989 0.23671 -0.25 0.8004 Within the correlated pairs of predictors related to number of students and budget, drop the predictor with larger p -value. 2
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Reduced model 1. Parameter Standard Variable DF Estimate Error t Value Pr > |t| Intercept 1 71.10315 1.99172 35.70 <.0001 log_lep 1 -0.62906 0.13448 -4.68 <.0001 log_lunch 1 -1.96629 0.26792 -7.34 <.0001 Special_Ed_pct 1 -0.06668 0.03809 -1.75 0.0808 log_mobility 1 -1.53766 0.28483 -5.40 <.0001 drop_out_pct 1 -0.58086 0.14566 -3.99 <.0001 log_total_students 1 -0.47905 0.22238 -2.15 0.0318 operating_budget 1 -0.53618 0.15552 -3.45 0.0006 Should we drop anything else? No: for large observational dataset, keep predictors with p < .1 or p < .2 3 Automatic subset selection Proc Reg is one of several regression procedures that offers automatic selection of a smaller model from a full model. Backwards Starting from full model, sequentially drop predictors with p > speciFed cutoff. Done by hand, the most common simple procedure among analysts. Forwards Start with single predictor with lowest p -value in univariate regression, sequentially add predictors with lowest p -value. Stepwise Start with Forwards but consider Backwards at each step. • Maximize a criterion ( R 2 , adjusted R 2 , Mallows’s C p ): Fnd models of 1, 2, 3, . .., predictors with largest values of the criterion 4
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Reduced Model 2. Backward selection: default value to stay is p < .1 Proc Reg data=B; model mathscore = log_lep log_lunch Special_Ed_pct log_mobility drop_out_pct log_8th_grade log_total_students operating_budget total_budget / selection = backward; 5 Backward Elimination: Step 2 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 71.10464 2.00647 7777.15867 1255.83 <.0001 log_lep -0.64116 0.13503 139.61877 22.55 <.0001 log_lunch -1.92395 0.27252 308.66742 49.84 <.0001 Special_Ed_pct -0.07194 0.03834 21.79910 3.52 0.0613 log_mobility -1.51180 0.28692 171.93641 27.76 <.0001 drop_out_pct -0.60028 0.14659 103.84724 16.77 <.0001 log_total_students -0.48301 0.22450 28.66555 4.63 0.0320 operating_budget -0.54765 0.15652 75.81050 12.24 0.0005 Bounds on condition number: 1.961, 78.446 -------------------------------------------------------------------------- All variables left in the model are significant at the 0.1000 level. So Reduced Model 2 = Reduced Model 1 (7 predictors) p -values differ because stepwise uses Type II sums of squares, not Type III 6
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Reduced Model 3. Forward selection: default value to include is p < .5 No other variable met the 0.5000 significance level for entry into the model.
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Handout09 - Lecture 9 1. Math scores: comparison of subset...

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