Yes, it is the marginal effect. The marginal effect (dy/dx) is the slope of the gradient at x. It is thus NOT for a 1 unit increase in x, but for a marginal change in x. Remember that, for nonlinear functions, the marginal effect is more accurate in predicting a change in y the smaller (!) the change of x is. Since you are interested in a 1% change, 1% is probably justifiable as being a small change. Thus, if you increase x by 1%, the change in y should be approximately 0.01*abs(x)*margeff. This assumes that the linear extrapolation done with a marginal effect is reasonably accurate for a prediction of y at x+delta(x).
You could also compute the effect at a 1% increase in x directly (see code below). Predict the regression, but substitue x by z=x+0.01*abs(x). This gives you the predicted odds (predict.1percent) at z (which is one percent greater than x). From the odds, you can easily compute the probabilities (probs). Then subtract the fitted probabilities at x from the predicted probabilities at z, which gives you the difference in probability. In the example I sent you, this gives a change in probability of 0.001255946. This is already much smaller than the marginal effect that would be estimated at around 0.002 for a 1 percent change in x (0.2*0.01=0.002), which already indicates the declining accuracy of the marginal effect as the distance from x increases. z=x+0.01*abs(x) predict.1percent=predict(reg,list(x=z)) probs=exp(predict.1percent)/(1+exp(predict.1percent)) mean(probs-fitted(reg)) HTH, Daniel ------------------------- cuncta stricte discussurus ------------------------- -----Ursprüngliche Nachricht----- Von: Roberto Patuelli [mailto:roberto.patue...@usi.ch] Gesendet: Monday, November 09, 2009 1:54 PM An: Daniel Malter; r-help@r-project.org Betreff: Re: [R] Percentage effects in logistic regression Dear Daniel, Thanks for your prompt reply. Indeed I was aware of the possibility of computing at mean(x) or doing the mean afterwards. But what you suggest is marginal effects, right? Isn't that the effect on y of a 1-unit increase in x (what I was not interested in)? I'm interested in the effect on y of a 1% increase in x (called percentage effects, right?). Could you please clarify? Thanks Roberto ----- Original Message ----- From: "Daniel Malter" <dan...@umd.edu> To: "Patuelli Roberto" <roberto.patue...@usi.ch>; <r-help@r-project.org> Sent: Monday, November 09, 2009 7:44 PM Subject: AW: [R] Percentage effects in logistic regression Somebody might have done this, but in fact it's not difficult to compute the marginal effects yourself (which is the beauty of R). For a univariate logistic regression, I illustrate two ways to compute the marginal effects (one corresponds to the mfx, the other one to the margeff command in Stata). With the first you compute the marginal effect based on the mean fitted values; with the second you compute the marginal effect based on the fitted values for each observation and then mean over the individual marginal effects. Often the second way is considered better. You can easily extend the R-code below to a multivariate regression. ##### #####Simulate data and run regression ##### set.seed(343) x=rnorm(100,0,1) #linear predictor lp=exp(x)/(1+exp(x)) #probability y=rbinom(100,1,lp) #Bernoulli draws with probability lp #Run logistic regression reg=glm(y~x,binomial) summary(reg) ##### #####Regression output ##### Coefficients: Estimate Std. Error z value Pr(>|z|) (Intercept) 0.1921 0.2175 0.883 0.377133 x 0.9442 0.2824 3.343 0.000829 *** --- Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1 (Dispersion parameter for binomial family taken to be 1) Null deviance: 138.47 on 99 degrees of freedom Residual deviance: 125.01 on 98 degrees of freedom AIC: 129.01 ##### #####Compute marginal effects ##### #Way 1 mean(fitted(reg))*mean(1-fitted(reg))*coefficients(reg)[2] 0.2356697 #Way 2 mean(fitted(reg)*(1-fitted(reg))*coefficients(reg)[2]) 0.2057041 ##### #####Check with Stata ##### Logistic regression Number of obs = 100 LR chi2(1) = 13.46 Prob > chi2 = 0.0002 Log likelihood = -62.506426 Pseudo R2 = 0.0972 ---------------------------------------------------------------------------- -- y | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+-------------------------------------------------------------- -- x | .9441896 .2824403 3.34 0.001 .3906167 1.497762 _cons | .1920529 .2174531 0.88 0.377 -.2341474 .6182532 ---------------------------------------------------------------------------- -- ##### #####Compute marginal effects in Stata ##### #Way 1 Marginal effects after logit y = Pr(y) (predict) = .52354297 ---------------------------------------------------------------------------- -- variable | dy/dx Std. Err. z P>|z| [ 95% C.I. ] X ---------+------------------------------------------------------------------ -- x | .2355241 .07041 3.35 0.001 .097532 .373516 -.103593 ---------------------------------------------------------------------------- -- #Way 2 Average marginal effects on Prob(y==1) after logit ---------------------------------------------------------------------------- -- y | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+-------------------------------------------------------------- -- x | .2057041 .0473328 4.35 0.000 .1129334 .2984747 ---------------------------------------------------------------------------- -- HTH, Daniel ------------------------- cuncta stricte discussurus ------------------------- -----Ursprüngliche Nachricht----- Von: r-help-boun...@r-project.org [mailto:r-help-boun...@r-project.org] Im Auftrag von Roberto Patuelli Gesendet: Monday, November 09, 2009 12:04 PM An: r-help@r-project.org Betreff: [R] Percentage effects in logistic regression Dear ALL, I'm trying to figure out what the percentage effects are in a logistic regression. To be more clear, I'm not interested in the effect on y of a 1-unit increase in x, but on the percentage effect on y of a 1% increase in x (in economics this is also often called an "elasticity"). For example, if my independent variables are in logs, the betas can be directly interpreted as percentage effects both in OLS and Poisson regression. What about the logistic regression? Is there a package (maybe effects?) that can compute these automatically? Thanks and best regards, Roberto Patuelli ******************** Roberto Patuelli, Ph.D. Istituto Ricerche Economiche (IRE) (Institute for Economic Research) Università della Svizzera Italiana (University of Lugano) via Maderno 24, CP 4361 CH-6904 Lugano Switzerland Phone: +41-(0)58-666-4166 Fax: +39-02-700419665 ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
