Pembentukan model rlb

1. Pembentukan model rlb Kuliahke 8 anareg Dosen: usmanbustaman

2. Model building algoritm • Data collection & preparation: experimental or not •  control experiment •  control experiment with covariates •  confirmatory observational studies •  explanatory observational studies • (explanatory) Variable selection • Model refinement/selection • Model validation • Focus padakuliah 8: •  (explanatory) Variable selection

3. Model building A B

4. A B Model building

5. (explanatory) Variable selection • Memilihvariabelbebas yang cukupmenjelaskan/memprediksivariabeltakbebas, sehingga • Kontribusivariabelbebas lain (yang tidakmasukdalam model) dapatdiabaikan. • Pertimbangan: • Menjelaskan (explanatory) vsMemprediksi (prediction) • Pertimbanganteoritisvspertimbanganstatistik • Omitting variable bias vs parsimony •  best subset (explanatory) variables

6. Sebelumitu… • Cek dependent/ndependentvariabel transformasiatautdk? • - histogram, normality plot • Cekhubunganantarvariabel • - pearson correlation • - scatter plot matrix

7. Cth: Dependent var.

8. Cth: independent var.

9. How to get the best subset… • All possible regression • Forward selection • Backward elimination • Stepwise regression

10. How to…. All possible regression •  • MSE(p) • Cp • Netter, ch. 12, p. 423

12. How to…. All possible regression

13. How to… w/ • p = jumlah parameter = 1,2,3,…,P • SSRp = Sum square regression w/ p parameter (incl. β0) • SSEp = Sum square error w/ p parameter (incl. β0) • SSTO = Sum square total • Goal: to find the point where adding more X variables is not worthwhile because it leads to a very small increase in R2.

14. Cth: regresidgnhanya X4dlm model:

15. Using plot

16. How to… w/ MSE(p) • sangatdipengaruhioleh p  p akanikut  •  use adjusted by df ( ) •  only depent on MSE  use MSE(p) •  Subset X ygmeminimumkan MSE(p) ataumendekati minimum sdmkshgpenambahanvariabel “takberguna”

17. Cth: regresidgnhanya X4dlm model:

18. Using MSE(p) plot

19. How to … w/ Cp • Estimator  • If bias = 0  Random error Bias Total MSE(p) Buktikan !

20. How to … w/ Cp • JikadiplotCpvs p: •  model dgn bias kecilakanberadasekitargarisCp = p •  model yang bias akanberada di atasgarisCp = p • So best subset is: • MemilikinilaiCpkecil  MSE kecil, atau • Bernilaisekitar p  bias kecil BgmkalauCpkeciltapi bias ?

21. Using CpPlot

22. Kendala …. • All possible regression mengandung 2(p-1) model yang harusditeliti,…. Jika p-1 = 10  ada 1024 model yang harusditeliti… •  gunakankomputer (buatalgoritma) •  pilih 5 atau 3 model terbaik •  sometimes inefficient

23. Stepwise regression • Proseduruntukmemilih best subset regression • Manual? …. Janganbuatsusahhidupygsudahsusah • GunakanKomputer ! • Steps: • 1. mulaidengan all possible RLS, hitung F*k • F*kdengannilaiterbesardan > nilaitttmasuksebagaikandidat ≈ Forward selection

24. Stepwise regression • 2. misal X4 terpilihpada step 1, makalakukan all possible RLB dgn 2 variabel, laluhitungF*k • F*kdengannilaiterbesardan > nilaitttmasuksebagaikandidat • 3. pertimbangkanadakahdarivariabel X dari model pada step sebelumnyaada yang perludi”buang” dari model, dengankriteriaF*k bernilai paling kecildan < nilaittt ≈backward elimination • 4. ulangi step 2 dan 3 hinggatakadalagivariabel yang “layak” untukmasukdalam model  best model

25. How to…. w/ stepwise regression

26. How to…. w/ stepwise regression

27. How to…. w/ stepwise regression

28. How to…. w/ stepwise regression

29. How to…. w/ stepwise regression

30. How to…. w/ stepwise regression