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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
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



Stata manuals
Stata manuals

You have all these as pdf!

Check the folder /Stata12/docs


Assumption checking and other nuisances
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


Assumption checking

in “normal” multiple regression

with Stata


Assumptions in regression analysis
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


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


The rest in stata
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)


Finding the commands
Finding the commands

  • “help regress”

  •  “regress postestimation”

    and you will find most of them (and more) there


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


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


Misspecification tests replaces all relevant predictor variables included ramsey
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”


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.


Testing for heteroscedasticity in stata
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


Errors distributed normally
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).


Errors distributed normally1
Errorsdistributednormally

First calculate the residuals (after regress):

predict e, resid

Then test for normality

swilke


Assumption checking in

logistic regression

with Stata

Note: based on

http://www.ats.ucla.edu/stat/stata/webbooks/logistic/chapter3/statalog3.htm


Assumptions in logistic regression
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!


Think!

  • What will happen if you try

    logit y x1 x2 in this case?


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!


Checking for multi collinearity
(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)


Checking for specification error
(checking for)specification error

  • The equivalent for “ovtest” is the command “linktest”


(checking for)specification error – part 2


Further things to do
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)


Checking for outliers influential cases
Checking for outliers / influential cases

… check the file auto_outliers.do for this …


Dealing with data1
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


Example analyses on ideas dta
Example analyses on ideas.dta


For next week i mprove the logistic regression you had
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


Online also the taxi tipping data
Online also:the taxi tipping data


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