Assumption checking in “normal” multiple regression with Stata

1. Assumption checking in “normal” multiple regression with Stata

2. Assumptions in regression analysis • No multi-collinearity • All relevant predictor variables • included • Homoscedasticity: all residuals are • from a distribution with the same variance • Linearity: the “true” model should be • linear. • Independent errors: having information • about the value of a residual should not • give you information about the value of • other residuals • Errors are distributed normally

3. FIRST THE ONE THAT LEADS TO NOTHING NEW IN STATA (NOTE: SLIDE TAKEN LITERALLY FROM MMBR) Independent errors: havinginformationabout the value of a residualshouldnotgiveyouinformationabout the value of otherresiduals Detect: askyourselfwhetherit is likelythatknowledgeaboutoneresidualwouldtellyousomethingabout the value of anotherresidual. Typical cases: -repeatedmeasures -clusteredobservations (peoplewithinfirms / pupilswithin schools) Consequences: as forheteroscedasticity Usually, yourconfidenceintervals are estimatedtoosmall (thinkaboutwhythat is!). Cure: usemulti-level analyses

4. In Stata: Example: the Stata “auto.dta” data set sysuse auto corr (correlation) vif (variance inflation factors) ovtest (omitted variable test) hettest (heterogeneity test) predict e, resid swilk (test for normality)

5. Finding the commands • “help regress” •  “regress postestimation” and you will find most of them (and more) there

6. Multi-collinearity A strongcorrelationbetweentwoor more of your predictor variables Youdon’t want it, because: • It is more difficult to gethigher R’s • The importance of predictorscanbedifficult to establish (b-hatstend to go to zero) • The estimatesforb-hats are unstableunderslightly different regressionattempts (“bouncingbeta’s”) Detect: • Look at correlation matrix of predictor variables • calculateVIF-factorswhile running regression Cure: Delete variables sothatmulti-collinearitydisappears, forinstancebycombiningtheminto a single variable

7. Stata: calculating the correlation matrix (“corr”) and VIF statistics (“vif”)

8. Misspecification tests(replaces: all relevant predictor variables included)

9. Homoscedasticity: all residuals are from a distribution with the samevariance Consequences: Heteroscedasticiy does notnecessarilylead to biases in yourestimatedcoefficients (b-hat), butit does lead to biases in the estimate of the width of the confidence interval, and the estimation procedure itself is notefficient.

10. Testing for heteroscedasticity in Stata • Your residuals should have the same variance for all values of Y hettest • Your residuals should have the same variance for all values of X hettest, rhs

11. Errorsdistributednormally Errors are distributednormally (justthe errors, not the variables themselves!) Detect: look at the residual plots, test fornormality Consequences: rule of thumb: ifn>600, noproblem. Otherwiseconfidenceintervals are wrong. Cure: try to fit a better model, oruse more difficultways of modelinginstead (askan expert).

12. Errorsdistributednormally First calculate the errors: predict e, resid Then test for normality swilke