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Published byEthelbert Tucker Modified over 9 years ago
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Assumption checking in “normal” multiple regression with Stata
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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
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3 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 heteroscedasticity Usually, your confidence intervals are estimated too small (think about why that is!). Cure: use multi-level analyses
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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)
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Finding the commands “help regress” “regress postestimation” and you will find most of them (and more) there
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6 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’s 2.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: 1.Look at correlation matrix of predictor variables 2.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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7 Stata: calculating the correlation matrix (“corr”) and VIF statistics (“vif”)
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8 Misspecification tests (replaces: all relevant predictor variables included)
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9 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.
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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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11 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).
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First calculate the errors: predict e, resid Then test for normality swilk e Errors distributed normally
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