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Stepwise Logistic Regression with R

Stepwise Logistic Regression with RAkaike information criterion: AIC = 2k - 2 log L = 2k + Deviance, where k = number of parametersSmall numbers are betterPenalizes models with lots of parametersPenalizes models with poor fit> fullmod = glm(low ~ age+lwt+racefac+smoke+ptl+ht+ui+ftv,fami ly=binomial)> summary(fullmod)Call:glm(formula = low ~ age + lwt + racefac + smoke + ptl + ht + ui + ftv, family = binomial)Deviance Residuals: Min 1Q Median 3Q Max Coefficients: Estimate Std. Error z value Pr(>|z|) (Intercept) age lwt * racefacBlack * racefacOther * smoke * ptl ht **ui.

Stepwise Logistic Regression with R ... = 2k + Deviance, where k = number of parameters Small numbers are better Penalizes models with lots of parameters Penalizes models with poor fit > fullmod = glm(low ~ age+lwt+racefac+smoke+ptl+ht+ui+ftv,family=binomial) ... > # Here was the chosen model from earlier > redmod1 = glm(low ~ lwt+racefac ...

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Transcription of Stepwise Logistic Regression with R

1 Stepwise Logistic Regression with RAkaike information criterion: AIC = 2k - 2 log L = 2k + Deviance, where k = number of parametersSmall numbers are betterPenalizes models with lots of parametersPenalizes models with poor fit> fullmod = glm(low ~ age+lwt+racefac+smoke+ptl+ht+ui+ftv,fami ly=binomial)> summary(fullmod)Call:glm(formula = low ~ age + lwt + racefac + smoke + ptl + ht + ui + ftv, family = binomial)Deviance Residuals: Min 1Q Median 3Q Max Coefficients: Estimate Std. Error z value Pr(>|z|) (Intercept) age lwt * racefacBlack * racefacOther * smoke * ptl ht **ui.

2 Ftv ---Signif. codes: 0 ** ** * . 1 (Dispersion parameter for binomial family taken to be 1) Null deviance: on 188 degrees of freedomResidual deviance: on 179 degrees of freedomAIC: of Fisher Scoring iterations: 4> nothing <- glm(low ~ 1,family=binomial)> summary(nothing)Call:glm(formula = low ~ 1, family = binomial)Deviance Residuals: Min 1Q Median 3Q Max Coefficients: Estimate Std. Error z value Pr(>|z|) (Intercept) **---Signif. codes: 0 ** ** * . 1 (Dispersion parameter for binomial family taken to be 1)1 Null deviance: on 188 degrees of freedomResidual deviance: on 188 degrees of freedomAIC: of Fisher Scoring iterations: 4> # Here was the chosen model from earlier > redmod1 = glm(low ~ lwt+racefac+smoke+ptl+ht,family=binomial )>> backwards = step(fullmod) # Backwards selection is the defaultStart.

3 AIC= low ~ age + lwt + racefac + smoke + ptl + ht + ui + ftv Df Deviance AIC- ftv 1 age 1 <none> ptl 1 ui 1 racefac 2 lwt 1 smoke 1 ht 1 : AIC= low ~ age + lwt + racefac + smoke + ptl + ht + ui Df Deviance AIC- age 1 <none> ptl 1 ui 1 racefac 2 lwt 1 smoke 1 ht 1 : AIC= low ~ lwt + racefac + smoke + ptl + ht + ui Df Deviance AIC<none> ptl 1 ui 1 smoke 1 lwt 1 racefac 2 ht 1 > [1] 16> # backwards = step(fullmod,trace=0) would suppress step by step output.

4 > formula(backwards)low ~ lwt + racefac + smoke + ptl + ht + ui2> summary(backwards)Call:glm(formula = low ~ lwt + racefac + smoke + ptl + ht + ui, family = binomial)Deviance Residuals: Min 1Q Median 3Q Max Coefficients: Estimate Std. Error z value Pr(>|z|) (Intercept) lwt * racefacBlack * racefacOther * smoke * ptl ht **ui . ---Signif. codes: 0 ** ** * . 1 (Dispersion parameter for binomial family taken to be 1) Null deviance: on 188 degrees of freedomResidual deviance: on 181 degrees of freedomAIC: of Fisher Scoring iterations: 4> # I would be inclined to drop ptl> back2 = glm(low ~ lwt + racefac + smoke + ht + ui,family=binomial)> summary(back2)Call:glm(formula = low ~ lwt + racefac + smoke + ht + ui, family = binomial)Deviance Residuals: Min 1Q Median 3Q Max Coefficients: Estimate Std.

5 Error z value Pr(>|z|) (Intercept) lwt * racefacBlack * racefacOther * smoke **ht **ui * ---Signif. codes: 0 ** ** * . 1 (Dispersion parameter for binomial family taken to be 1) Null deviance: on 188 degrees of freedomResidual deviance: on 182 degrees of freedomAIC: of Fisher Scoring iterations: 43> redmod1$deviance; back2$deviance[1] [1] > # back2 may be slightly "better," but I like redmod1 more. > # Why? Because ptl is easier to assess than ui> > forwards = step(nothing,scope=list(lower=formula(no thing),upper=formula(fullmod)), direction="forward")Start: AIC= low ~ 1 Df Deviance AIC+ ptl 1 + lwt 1 + ui 1 + smoke 1 + ht 1 + racefac 2 + age 1 <none> + ftv 1 : AIC= low ~ ptl Df Deviance AIC+ lwt 1 + ht 1 + age 1 + racefac 2 + smoke 1 + ui 1 <none> + ftv 1.

6 AIC= low ~ ptl + lwt Df Deviance AIC+ ht 1 + racefac 2 + smoke 1 + age 1 + ui 1 <none> + ftv 1 : AIC= low ~ ptl + lwt + ht Df Deviance AIC+ racefac 2 + ui 1 + smoke 1 <none> + age 1 + ftv 1 : AIC= 4 low ~ ptl + lwt + ht + racefac Df Deviance AIC+ smoke 1 + ui 1 <none> + age 1 + ftv 1 : AIC= low ~ ptl + lwt + ht + racefac + smoke Df Deviance AIC+ ui 1 <none> + age 1 + ftv 1.

7 AIC= low ~ ptl + lwt + ht + racefac + smoke + ui Df Deviance AIC<none> + age 1 + ftv 1 > formula(redmod1)low ~ lwt + racefac + smoke + ptl + ht> formula(backwards)low ~ lwt + racefac + smoke + ptl + ht + ui> formula(forwards)low ~ ptl + lwt + ht + racefac + smoke + ui> bothways = + step(nothing, list(lower=formula(nothing),upper=formul a(fullmod)),direction="both",trace=0)> formula(forwards)low ~ ptl + lwt + ht + racefac + smoke + ui> formula(bothways)low ~ ptl + lwt + ht + racefac + smoke + ui5

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