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MULTICOLLINEARITY

KULIAH 12. MULTICOLLINEARITY. What’s Multicolinearity ?. Nature of the problem: X’X matrix must not be singular  why? Ada hubungan linier antar beberapa ( atau semua ) variabel bebas . Perfect: Not perfect:. ilustrasi. Penyebab.

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MULTICOLLINEARITY

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  1. KULIAH 12 MULTICOLLINEARITY

  2. What’s Multicolinearity? • Nature of the problem: X’X matrix must not be singular  why? • Ada hubungan linier antarbeberapa (atausemua) variabelbebas. • Perfect: • Not perfect:

  3. ilustrasi

  4. Penyebab • Metodepengumpulan data,sampeldiambildaripopulasidgnlingkupterbatas • Keterbatasan model/populasi, ex: Y= konsumsilistrik, X1 = pendapatanruta, X2 = luasrumah • Spesifikasi model, ex: menambahkanvariabelpolinomialpada data X ygterbatas • Overdetermined model: #paramater > # obs • Common trend, ex: income, poupulation, wealth growing over time at more or less the same rate

  5. Efekthdestimasi • Perfect collinearity: no coefficient estimates , s.e. = ∞ ! Apaarti ? • High collinearity: maybe there are coefficient estimates , s.e. = very large Bgmdgn CI? • BgmkabarBLUE?

  6. Konsekuensi model ber-multicollinearity

  7. R2tinggivs t-value ApakomentarAnda ?

  8. Ceklbhljt ApakomentarAnda?

  9. Sensitivitasthdperubahan data  Estimasi parameter tidakstabil

  10. Diagnosa (ingat-2 tugasyl !) • 1. High R2 but few significant t ratios. • 2. High pair-wise correlations among regressors. (tapikdgterjadijugameskirijrendah) • 3. Examination of partial correlations. Misal:  = 1  if rij= 0.5  R2tinggitapi partial-R2rendah

  11. Diagnosa (ingat-2 tugasyl !) • 4. Auxiliary regressions. • to regress each Xi on the remaining X variables and compute the corresponding R2 (R2i ) • Fi sig  Xicollinearity with other X • Rule of thumb: R2i >R2  multicollinearity problem

  12. 5. Eigenvalues and condition index. (SAS) • -------10 ---CI----30--------- • 6. Tolerance (TOL) and variance inflation factor (VIF). severe low moderate strong

  13. VIF • r23 = koef. korelasiantara X2 dan X3 •  r23  , ,  •  r23 = 1 ?

  14. VIF • Kecepatankenaikanvar-covar variance inflation factor (VIF)

  15. VIF – RLB dgn k-variabel •  VIF   prob. multikolinierity • Rule of thumb: VIF > 10  high multicollinearity • 0 ≤ TOLj ≤ 1

  16. Remedial • Do nothing ??! • 1. Apriori information: berdasarteori or pengalamansebelumnya • didapat didapatdarihubungan

  17. Remedial • 2. Combining cross-sectional and time series data. • Time series view: Price & income sgtberkorelasi multikolinieriti •  estimate regresi (time series) • Dimana (regresicross section)

  18. Remedial • 3. Dropping a variable(s) and specification bias. • Ex: consumption = f (income, wealth) (cthsebelumnya) •  income & wealth berkorelasi  hapus wealth dari model • Tapijikateorimenyatakanbhwfungsidiatasberlaku, makamenghapus wealth dari model akanmengakibatkan bias spesifikasi. • True model: • Estimated by:  • b32 = koefregresi b3atas b2 • Jika > 0  b12 over estimate dariβ2 (bias +) • Jika< 0  b12 under estimate dariβ2 (bias -)

  19. Remedial • 4. Transformasivariabel • First differencing • Ratio transformation • Y = konsumsi, X2 = PDB, X3 = JmlPddk •  PDB & JmlPddk “grow over time”  berkorelasi • Regresi per kapitapenduduk: Be careful of new problem: serially correlated error, heteroscedasticity,

  20. Remedial • 5. Menambahjumlah data (observasi) • n = 10  • n = 40  • 6. Reducing collinearity in polynomial regressions. Transform variables in deviation form. • 7. Other methods of remedying multicollinearity, ex: factor analysis, ridge regression, principal component regression

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