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ASSUMPTION CHECKING

ASSUMPTION CHECKING. In regression analysis with Stata In multi-level analysis with Stata (not much extra) In logistic regression analysis with Stata NOTE: THIS WILL BE EASIER IN STATA THAN IT WAS IN SPSS. Assumption checking in “normal” multiple regression with Stata.

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ASSUMPTION CHECKING

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  1. ASSUMPTION CHECKING • In regression analysis with Stata • In multi-level analysis with Stata (not much extra) • In logistic regression analysis with Stata NOTE: THIS WILL BE EASIER IN STATA THAN IT WAS IN SPSS

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

  3. 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

  4. 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

  5. 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)

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

  7. 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

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

  9. Misspecificationtests(replaces: all relevant predictor variables included)

  10. 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.

  11. 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

  12. 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).

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

  14. Assumption checking in multi-level multiple regression with Stata

  15. In multi-level • Test all that you would test for multiple regression – poor man’s test: do this using multiple regression! (e.g. “hettest”) Add: • xttest0 (see last week) Add (extra): Test visually whether the normality assumption holds, but do this for the random 

  16. Note: extra material(= not on the exam, bonus points if you know how to use it) tab school, gen(sch_) regy sch2 – sch28 gen coefs = . for num 2/28: replace coefs =_b[schX] if _n==X swilkcoefs

  17. Assumption checking in multi-level multiple regression with Stata

  18. Assumptions • Y is 0/1 • Ratio of cases to variables should be “reasonable” • No cases where you have complete separation (Stata will remove these cases automatically) • Linearity in the logit (comparable to “the true model should be linear” in multiple regression) • Independence of errors (as in multiple regression)

  19. Further things to do: • Check goodness of fit and prediction for different groups (as done in the do-file you have) • Check the correlation matrix for strong correlations between predictors (corr) • Check for outliers using regress and diag(but don’t tell anyone I suggested this)

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