[R] logistic regression: differential importance of regressors

[Frank E Harrell Jr]

Greg Trafton wrote:
> Hi, All.  I have a logistic regression model that I have run.  The
> question came up:  which of these regressors is more important than
> another?
> 
> (I'm using Design)
> 
> Logistic Regression Model
> 
> lrm(formula = iconicgesture ~ ST + SSP + magnitude + Condition + 
>     Expertise, data = d)
> 
>           Coef    S.E.   Wald Z P     
> Intercept -3.2688 0.2854 -11.45 0.0000
> ST         2.0871 0.2730   7.64 0.0000
> SSP        0.7454 0.3031   2.46 0.0139
> magnitude -0.9905 0.6284  -1.58 0.1150
> Condition  0.9506 0.2932   3.24 0.0012
> Expertise  0.8508 0.2654   3.21 0.0013
> 
> The real question is that, since both ST and SSP load significantly
> into the model, how do I show that ST has a bigger/smaller/similar
> effect than SSP?
> 
> thanks in advance!
> greg
> 

One thing you can do is to compute what proportion of the total 
likelihood ratio chi-square statistic is due to each variable by 
removing one at a time and looking at difference in Model L.R. (assuming 
both have same observations missing).  Note that you are making heavy 
linearity assumptions.

You can also use the bootstrap to get a confidence interval on the rank 
of the chi-square statistic a variable has among all competing chi-squares.

Frank

-- 
Frank E Harrell Jr   Professor and Chair           School of Medicine
                      Department of Biostatistics   Vanderbilt University