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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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

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FIRST THE ONE THAT LEADS TO NOTHING NEW IN STATA (NOTE: SLIDE TAKEN LITERALLY FROM MMBR)

Independent errors: having information about the value of a residual should not give you information about the value of other residuals

Detect: ask yourself whether it is likely that knowledge about one residual would tell you something about the value of another residual.Typical cases: -repeated measures-clustered observations (people within firms / pupils within schools)

Consequences: as for heteroscedasticityUsually, your confidence intervals are estimated too small (think about why that is!).

Cure: use multi-level analyses

In Stata:Example: the Stata “auto.dta” data setsysuse auto

corr (correlation)vif (variance inflation factors)

ovtest (omitted variable test)

hettest (heterogeneity test)

predict e, residswilk (test for normality)

Finding the commands

• “help regress”• “regress postestimation”

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

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Multi-collinearity A strong correlation between two or more of your predictor variables

You don’t want it, because:1. It is more difficult to get higher R’s2. The importance of predictors can be difficult to

establish (b-hats tend to go to zero)3. The estimates for b-hats are unstable under slightly

different regression attempts (“bouncing beta’s”)

Detect: 4. Look at correlation matrix of predictor variables5. calculate VIF-factors while running regression

Cure:Delete variables so that multi-collinearity disappears, for instance by combining them into a single variable

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

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Misspecification tests(replaces: all relevant predictor

variables included)

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Homoscedasticity: all residuals are from a distribution with the same variance

Consequences: Heteroscedasticiy does not necessarily lead to biases in your estimated coefficients (b-hat), but it does lead to biases in the estimate of the width of the confidence interval, and the estimation procedure itself is not efficient.

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

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Errors distributed normally

Errors are distributed normally (just the errors, not the variables themselves!)

Detect: look at the residual plots, test for normality

Consequences: rule of thumb: if n>600, no problem. Otherwise confidence intervals are wrong.

Cure: try to fit a better model, or use more difficult ways of modeling instead (ask an expert).

First calculate the errors:predict e, resid

Then test for normalityswilk e

Errors distributed normally

Assumption checking in multi-level multiple regression

with Stata

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

Note: extra material(= not on the exam, bonus points if you know how

to use it)

tab school, gen(sch_)reg y sch2 – sch28

gen coefs = .for num 2/28: replace coefs =_b[schX] if _n==X

swilk coefs

Assumption checking in multi-level multiple regression

with Stata

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)

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)