Converting logit regression coefficients

[Lindsey Buck]

Hi all,

I am wondering if there is a way to convert logit regression coefficients into percentages. Can you help? Thanks!

[Ken Chui]

Percent of what? Could perhaps post an example output and provide an example for conversion?

[Lindsey Buck]

So, for instance, let's say I do this:

logit yvar xvar othervars

Is there a way that I can get the coefficient off of the xvar to show me that if I increase the xvar by 1 unit, how much does the Y var increase or decrease in a percent?

[Clyde Schechter]

As phrased, the answer to your question is no. The percentage point change in Y associated with a unit increase in xvar will depend on the starting value of xvar, and also on the values of othervars. Your question has infinitely many answers, so, in effect, it has no answer.

That said, if you specify the starting values of xvar and othervars, then you can get the percentage point increase in Y associated with a unit increase in xvar from that starting configuration by using the -margins- command:

margins, dydx(xvar) at(........)

where you replace ....... by an appropriate specification of the values of all variables. See -help margins- for details of the syntax for this.

People are sometimes interested in the average percentage point change in Y with a unit change in xvar, the average being taken over all combinations of xvar and othervars in the estimation sample. That can be done as:

margins, dydx(xvar)

And people are sometimes interested in the percentage point change in Y with a unit change in xvar with all variables set at their mean values (note that this is very different from the preceding):

margins, dydx(xvar) atmeans

[Dirk Enzmann]

If, instead, you are interested to translate the odds ratios in risk ratios (relative risks) per unit change of the independent variables, you can use -binreg ..., rr-. However, this does not always converge. Alternatively you can use -poisson ..., vce(robust) irr-. For more information and alternative methods see: Cummings, P. (2009). Methods for estimating adjusted risk ratios. The Stata Journal, 9(2), 175-196.

Example:

. sysuse auto
(1978 Automobile Data)

. binreg foreign mpg headroom, rr

Iteration 1:   deviance =  271.0127
Iteration 2:   deviance =  81.67472
Iteration 3:   deviance =  78.09047
Iteration 4:   deviance =  77.74763
Iteration 5:   deviance =  77.74443
Iteration 6:   deviance =  77.74442
Iteration 7:   deviance =  77.74442

Generalized linear models                         Number of obs   =         74
Optimization     : MQL Fisher scoring             Residual df     =         71
                   (IRLS EIM)                     Scale parameter =          1
Deviance         =   77.7444237                   (1/df) Deviance =   1.094992
Pearson          =  68.79482381                   (1/df) Pearson  =   .9689412

Variance function: V(u) = u*(1-u)                 [Bernoulli]
Link function    : g(u) = ln(u)                   [Log]

                                                  BIC             =  -227.8442

------------------------------------------------------------------------------
             |                 EIM
     foreign | Risk Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         mpg |   1.078314   .0117803     6.90   0.000     1.055471    1.101652
    headroom |    .793299   .1541072    -1.19   0.233     .5421025    1.160893
       _cons |   .1005949   .0583758    -3.96   0.000     .0322566    .3137133
------------------------------------------------------------------------------
Note: _cons estimates baseline risk.

. poisson foreign mpg headroom, vce(robust) irr

Iteration 0:   log pseudolikelihood =  -44.35289  
Iteration 1:   log pseudolikelihood = -44.352045  
Iteration 2:   log pseudolikelihood = -44.352045  

Poisson regression                              Number of obs     =         74
                                                Wald chi2(2)      =      21.54
                                                Prob > chi2       =     0.0000
Log pseudolikelihood = -44.352045               Pseudo R2         =     0.0890

------------------------------------------------------------------------------
             |               Robust
     foreign |        IRR   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         mpg |   1.073029   .0230139     3.29   0.001     1.028858    1.119097
    headroom |   .6735429   .1282538    -2.08   0.038     .4637482    .9782464
       _cons |   .1774262   .1608975    -1.91   0.057     .0299994    1.049356
------------------------------------------------------------------------------
Note: _cons estimates baseline incidence rate.

[Lindsey Buck]

Thank you so much!!!!!!!!!!!!!