A Comparison of Approaches to Stepwise Regression for Global

Proceedings of BS2013: 13th Conference of International Building Performance Simulation Association, Chambéry, France, August 26-28

A COMPARISON OF APPROACHES TO STEPWISE REGRESSION FOR GLOBAL SENSITIVITY ANALYSIS USED WITH EVOLUTIONARY OPTIMIZATION

- 2551 - Proceedings of BS2013: 13th Conference of International Building Performance Simulation Association, Chambéry, France, August 26-28

Selection Approach Forward selection: Sampling Method and Sample Size Backward elimination: Bidirectional elimination:    Selection Criterion  F-test: Data Type of Input Variables AIC (Akaike information criterion): BIC (Bayesian information criterion):  Accuracy Metric R  R2 (coefficient of determination): 

- 2552 - Proceedings of BS2013: 13th Conference of International Building Performance Simulation Association, Chambéry, France, August 26-28

PRESS (predicted error sum of squares): Input Variables, Objective Functions and Design Constraints Genetic Algorithm (GA) Example Building and Performance Model OPTIMIZATION VARIABLE UNITS LO WER UPPER INCREMENT BOUND BOUND

- 2553 - Proceedings of BS2013: 13th Conference of International Building Performance Simulation Association, Chambéry, France, August 26-28

The impact of data type of input variables The impact of selection criterion The impact of sampling method and sample size

- 2554 - Proceedings of BS2013: 13th Conference of International Building Performance Simulation Association, Chambéry, France, August 26-28

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VARIABLE NAME RANK-TRANSFORMED DATA RAW DATA August August WITHOUT PHYSICAL MEANING WITH PHYSICAL MEANING RANDOM OPTIMIZATION RANDOM OPTIMIZATION RANDOM OPTIMIZATION 1000 100 FIRST 100 LAST 100 LAST 1000 1000 100 FIRST 100 LAST 100 LAST 1000 1000 100 FIRST 100 LAST 100 LAST 1000 France, France,

Chambéry, Chambéry,

Association, Association, 2 R value 0.839 0.852 0.883 0.783 0.664 0.844 0.833 0.856 0.971 0.863 0.838 0.82 0.856 0.963 0.849 - Simulation Simulation 2556 -

Performance Performance VARIABLE NAME RANK-TRANSFORMED DATA RAW DATA WITHOUT PHYSICAL MEANING WITH PHYSICAL MEANING RANDOM OPTIMIZATION RANDOM OPTIMIZATION RANDOM OPTIMIZATION 1000 100 FIRST 100 LAST 100 LAST 1000 1000 100 FIRST 100 LAST 100 LAST 1000 1000 100 FIRST 100 LAST 100 LAST 1000 Building Building

International International

BS2013: BS2013:

of Conference Conference R2 value 0.85 0.839 0.687 0.911 0.785 0.645 0.628 0.454 0.934 0.898 0.645 0.628 0.406 0.933 0.897 Proceedings Proceedings 13th 26-28

VARIABLE NAME RANK-TRANSFORMED DATA RAW DATA

August August WITHOUT PHYSICAL MEANING WITH PHYSICAL MEANING RANDOM OPTIMIZATION RANDOM OPTIMIZATION RANDOM OPTIMIZATION 1000 100 FIRST 100 LAST 100 LAST 1000 1000 100 FIRST 100 LAST 100 LAST 1000 1000 100 FIRST 100 LAST 100 LAST 1000

France, France, Chambéry, Chambéry,

Association, Association, R2 value 0.837 0.844 0.867 0.751 0.663 0.842 0.81 0.853 0.97 0.861 0.837 0.8 0.853 0.959 0.849 - Simulation Simulation 2557

VARIABLE NAME RANK-TRANSFORMED DATA RAW DATA

Performance Performance WITHOUT PHYSICAL MEANING WITH PHYSICAL MEANING RANDOM OPTIMIZATION RANDOM OPTIMIZATION RANDOM OPTIMIZATION 1000 100 FIRST 100 LAST 100 LAST 1000 1000 100 FIRST 100 LAST 100 LAST 1000 1000 100 FIRST 100 LAST 100 LAST 1000

Building Building

International International of

BS2013: BS2013: of Conference Conference R2 value 0.848 0.832 0.664 0.9 0.782 0.643 0.563 0.454 0.927 0.896 0.643 0.563 0.364 0.927 0.896 Proceedings Proceedings 13th Proceedings of BS2013: 13th Conference of International Building Performance Simulation Association, Chambéry, France, August 26-28

18 16 14 12 10 8 F-test: α-value =0.05 6 F-test: α-value =0.02 4 F-test: α-value =0.01 2

The numberof selected variables AIC 0 BIC 100 100 100

1000 1000 1000 PRESS Last100 Last100 Last100 First100 First100 First100 Last 1000 1000Last Last 1000 Random Optimization Random Optimization Random Optimization Without physical With physical meaning meaning Rank-transformed data Raw data

14 12 10

6 F-test: α-value =0.05

4 F-test: α-value =0.02 F-test: α-value =0.01 2

The numberof selected variables AIC 0 BIC 100 100 100

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