Model interpretation is essential in the social sciences. If one wants to know the effect of
x on the dependent variable
y, marginal effects are an easy way to get the answer.
STATA includes a
margins command that has been ported to R
by Thomas J. Leeper
of the London School of Economics and Political Science.
You can find the source code of the package
on github. In this short blog post, I demo some of the
First, let’s load some packages:
library(ggplot2) library(tibble) library(broom) library(margins) library(Ecdat)
As an example, we are going to use the
Participation data from the
Labor Force Participation Description a cross-section number of observations : 872 observation : individuals country : Switzerland Usage data(Participation) Format A dataframe containing : lfp labour force participation ? lnnlinc the log of nonlabour income age age in years divided by 10 educ years of formal education nyc the number of young children (younger than 7) noc number of older children foreign foreigner ? Source Gerfin, Michael (1996) “Parametric and semiparametric estimation of the binary response”, Journal of Applied Econometrics, 11(3), 321-340. References Davidson, R. and James G. MacKinnon (2004) Econometric Theory and Methods, New York, Oxford University Press, http://www.econ.queensu.ca/ETM/, chapter 11. Journal of Applied Econometrics data archive : http://qed.econ.queensu.ca/jae/.
The variable of interest is
lfp: whether the individual participates in the labour force or not.
To know which variables are relevant in the decision to participate in the labour force,
one could estimate a logit model, using
logit_participation = glm(lfp ~ ., data = Participation, family = "binomial")
Now that we ran the regression, we can take a look at the results. I like to use
to look at the results of regressions, as
tidy() returns a nice
data.frame, but you could use
summary() if you’re only interested in reading the output:
## term estimate std.error statistic p.value ## 1 (Intercept) 10.37434616 2.16685216 4.7877499 1.686617e-06 ## 2 lnnlinc -0.81504064 0.20550116 -3.9661122 7.305449e-05 ## 3 age -0.51032975 0.09051783 -5.6378920 1.721444e-08 ## 4 educ 0.03172803 0.02903580 1.0927211 2.745163e-01 ## 5 nyc -1.33072362 0.18017027 -7.3859224 1.514000e-13 ## 6 noc -0.02198573 0.07376636 -0.2980454 7.656685e-01 ## 7 foreignyes 1.31040497 0.19975784 6.5599678 5.381941e-11
From the results above, one can only interpret the sign of the coefficients. To know how much a
variable influences the labour force participation, one has to use
effects_logit_participation = margins(logit_participation) print(effects_logit_participation)
## Average marginal effects
## glm(formula = lfp ~ ., family = "binomial", data = Participation)
## lnnlinc age educ nyc noc foreignyes ## -0.1699 -0.1064 0.006616 -0.2775 -0.004584 0.2834
summary() on the object returned by
margins() provides more details:
## factor AME SE z p lower upper ## age -0.1064 0.0176 -6.0494 0.0000 -0.1409 -0.0719 ## educ 0.0066 0.0060 1.0955 0.2733 -0.0052 0.0185 ## foreignyes 0.2834 0.0399 7.1102 0.0000 0.2053 0.3615 ## lnnlinc -0.1699 0.0415 -4.0994 0.0000 -0.2512 -0.0887 ## noc -0.0046 0.0154 -0.2981 0.7656 -0.0347 0.0256 ## nyc -0.2775 0.0333 -8.3433 0.0000 -0.3426 -0.2123
And it is also possible to plot the effects with base graphics:
This uses the basic R plotting capabilities, which is useful because it is a simple call to the
plot() but if you’ve been using
ggplot2 and want this graph to have the same look as
the others made with
ggplot2 you first need to save the summary in a variable.
Let’s overwrite this
effects_logit_participation variable with its summary:
effects_logit_participation = summary(effects_logit_participation)
And now it is possible to use
ggplot2 to create the same plot:
ggplot(data = effects_logit_participation) + geom_point(aes(factor, AME)) + geom_errorbar(aes(x = factor, ymin = lower, ymax = upper)) + geom_hline(yintercept = 0) + theme_minimal() + theme(axis.text.x = element_text(angle = 45))
So an infinitesimal increase, in say, non-labour income (
lnnlinc) of 0.001 is associated with a
decrease of the probability of labour force participation by 0.001*17 percentage points.
You can also extract the marginal effects of a single variable, with
head(dydx(Participation, logit_participation, "lnnlinc"))
## dydx_lnnlinc ## 1 -0.15667764 ## 2 -0.20014487 ## 3 -0.18495109 ## 4 -0.05377262 ## 5 -0.18710476 ## 6 -0.19586986
Which makes it possible to extract the effects for a list of individuals that you can create yourself:
my_subjects = tribble( ~lfp, ~lnnlinc, ~age, ~educ, ~nyc, ~noc, ~foreign, "yes", 10.780, 7.0, 4, 1, 1, "yes", "no", 1.30, 9.0, 1, 4, 1, "yes" ) dydx(my_subjects, logit_participation, "lnnlinc")
## dydx_lnnlinc ## 1 -0.09228119 ## 2 -0.17953451
I used the
tribble() function from the
tibble package to create this test data set, row by
row. Then, using
dydx(), I get the marginal effect of variable
lnnlinc for these two individuals.
No doubt that this package will be a huge help convincing more social scientists to try out R and
make a potential transition from STATA easier.