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Dealing with data

Dealing with data. All variables ok? / getting acquainted Base model Final model(s) Assumption checking on final model(s) Conclusion (s) / Inference. Better models Better variables ( interaction , transformations ) Assumption checking Outliers and influential cases

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Dealing with data

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  1. Dealingwith data • All variables ok? / gettingacquainted • Base model • Final model(s) • Assumptionchecking on final model(s) • Conclusion(s) / Inference Bettermodels Better variables (interaction, transformations) Assumptionchecking Outliersandinfluential cases Creatingsubsets of the data

  2. Finding help

  3. Stata manuals You have all these as pdf! Check the folder /Stata12/docs

  4. ASSUMPTION CHECKING AND OTHER NUISANCES • In regression analysis with Stata • In logistic regression analysis with Stata NOTE: THIS WILL BE EASIER IN Stata THAN IT WAS IN SPSS

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

  6. 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

  7. 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  part 2 of this course

  8. The rest, 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)

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

  10. 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

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

  12. Misspecification tests(replaces: all relevant predictor variables included [Ramsey]) Also run “ovtest, rhs” here. Both tests should be non-significant. Note that there are two ways to interpret “all relevant predictor variables included”

  13. Homoscedasticity: all residuals are from a distribution with the samevariance This can be done in Stata too (check for yourself) 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.

  14. 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

  15. Errorsdistributednormally Errorsshouldbedistributednormally (justthe errors, not the variables themselves!) Detect: look at the residual plots, test fornormality, or save residualsand test directly Consequences: rule of thumb: ifn>600, noproblem. Otherwiseconfidenceintervals are wrong. Cure: try to fit a bettermodel (or use more difficultways of modelinginstead- askan expert).

  16. Errorsdistributednormally First calculate the residuals (after regress): predict e, resid Then test for normality swilke

  17. Assumption checking in logistic regression with Stata Note: based on http://www.ats.ucla.edu/stat/stata/webbooks/logistic/chapter3/statalog3.htm

  18. Assumptions in logistic regression • Y is 0/1 • Independence of errors (as in multiple regression) • No cases where you have complete separation (Stata will try to remove these cases automatically) • Linearity in the logit (comparable to “the true model should be linear” in multiple regression) – “specification error” • No multi-collinearity (as in m.r.) Think!

  19. Think! • What will happen if you try logit y x1 x2 in this case?

  20. This! Because all cases with x==1 lead to y==1, the weight of x should be +infinity. Stata therefore rightly disregards these cases. Do realize that, even though you do not see them in the regression, these are extremely important cases!

  21. (checking for)multi-collinearity • In regression, we had “vif” • Here we need to download a command that a user-created: “collin” (try “finditcollin” in Stata)

  22. (checking for)specification error • The equivalent for “ovtest” is the command “linktest”

  23. (checking for)specification error – part 2

  24. Further things to do: • Check for useful transformations of variables, and interaction effects • Check for outliers / influential cases: 1) using a plot of stdres (against n) and dbeta(against n) 2) using a plot of ldfbeta’s(against n) 3) using regress and diag (but don’t tell anyone that I suggested this)

  25. Checking for outliers / influential cases … check the file auto_outliers.do for this …

  26. Dealingwith data • All variables ok? / gettingacquainted • Base model • Final model(s) • Assumptionchecking on final model(s) • Conclusion(s) / Inference Bettermodels Better variables (interaction, transformations) Assumptionchecking Outliersandinfluential cases Creatingsubsets of the data

  27. Example analyses on ideas.dta

  28. For next week:improve the logisticregressionyou had Annotated output: as ifyouwriteanexamassignment ... • Create do-file withcommentsin it • Run itandaddfurthercomments on the outcomes in the log file • Submit do-file andlog-file Useyourownassignment, and the skills youmasteredtoday. Deadline: comingWednesday

  29. Online also:the taxi tipping data

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