[R] Marginal Effect larger than 1 for a binary variable (summary.Design after lrm)

[Frank E Harrell Jr]

Minyu Chen wrote:
> Dear All:
> 
> I run a logistic regression (using lrm in the Design package), and  
> after that, I use the command "summary" to get the marginal effects  
> of each variable. But one strange thing happens on my binary  
> dependent variable: The marginal effect of it jumping from 0 to 1 is  
> 1.77. I believe the marginal effect of binary variable x1 has  
> interpretation should be P(Y=1|x1=1, x2...)-P(Y=1|x1=0,x2...). As  
> both terms lies in [0,1], their difference shouldn't be larger than 1.

No, please read more of the documentation.  Effects are on the log odds 
scale; that's why you also get the anti-log of that, the odds ratio.

Frank

> 
> Besides this, I also get some boundary number for the marginal effect  
> of the same binary variable (in datasets of other years)like .98, . 
> 97, with which I am not comfortable either. I suspect I did something  
> wrong.
> 
> This is part of my model:
> 
>  > resultt1
> 
> Logistic Regression Model
> 
> lrm(formula = typemort ~ adv_binc_ratio + agem1 + regEA + regEM +
>      regGL + regN + regNI + regNW + regS + regSW + regW + regWM +
>      regY + repmethIO + repmethSR + no_dis_no_def + prevLO + prevOO +
>      prevRP + owning + adv_binc_ratio * (repmethIO + repmethSR +
>      no_dis_no_def + prevLO + prevOO + prevRP + owning) + agem1 *
>      (repmethIO + repmethSR + no_dis_no_def + prevLO + prevOO +
>          prevRP + owning), data = a)
> 
> 
> This is part of my result:
> 
>  > summary(resultt1,adv_binc_ratio=mean(a$adv_binc_ratio),agem1=mean(a 
> $agem1),repmethIO=c(0,mean(a$repmethIO),1),repmethSR=c(0,mean(a 
> $repmethSR),1),no_dis_no_def=c(0,mean(a$no_dis_no_def),1),prevLO=c 
> (0,mean(a$prevLO),1),prevOO=c(0,mean(a$prevOO),1),prevRP=c(0,mean(a 
> $prevRP),1),regEA=c(0,mean(a$regEA),1),regEM=mean(a$regEM),regGL=mean 
> (a$regGL),regN=mean(a$regN),regNI=mean(a$regNI),regNW=mean(a 
> $regNW),regS=mean(a$regS),regSW=mean(a$regSW),regW=mean(a 
> $regW),regWM=mean(a$regWM),regY=mean(a$regY),owning=c(0,mean(a 
> $owning),1))
>               Effects              Response : typemort
> 
> Factor         Low     High    Diff.   Effect S.E. Lower 0.95 Upper 0.95
> no_dis_no_def   0.0000  1.0000  1.0000  1.76  0.03  1.69       1.82
>    Odds Ratio     0.0000  1.0000  1.0000  5.79    NA  5.41       6.19
> 
> Adjusted to: adv_binc_ratio=2.611027 agem1=40.47638  
> repmethIO=0.1456293 repmethSR=0.6711471 no_dis_no_def=0.4463533  
> prevLO=0.06590113 prevOO=0.7785591 prevRP=0.06738472 owning=0.4765593
> 
> Thank you very much for your help.
> 
> Thanks,
> Minyu Chen
> 
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