margins is intended as a port of (some of) the
features of Stata’s margins command. This vignette compares
output from Stata’s margins command for linear models
against the output of margins.
library("margins")
options(width = 100). quietly reg mpg cyl hp wt
. margins, dydx(*)
Average marginal effects Number of obs = 32
Model VCE : OLS
Expression : Linear prediction, predict()
dy/dx w.r.t. : cyl hp wt
------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
cyl | -.9416166 .5509165 -1.71 0.098 -2.070118 .1868846
hp | -.0180381 .0118763 -1.52 0.140 -.0423655 .0062893
wt | -3.166973 .740576 -4.28 0.000 -4.683975 -1.649972
------------------------------------------------------------------------------library("margins")
x <- lm(mpg ~ cyl + hp + wt, data = mtcars)
summary(margins(x))## factor AME SE z p lower upper
## cyl -0.9416 0.5509 -1.7092 0.0874 -2.0214 0.1382
## hp -0.0180 0.0119 -1.5188 0.1288 -0.0413 0.0052
## wt -3.1670 0.7406 -4.2764 0.0000 -4.6185 -1.7155. quietly reg mpg cyl c.hp##c.wt
. margins, dydx(*)
Average marginal effects Number of obs = 32
Model VCE : OLS
Expression : Linear prediction, predict()
dy/dx w.r.t. : cyl hp wt
------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
cyl | -.3652391 .5086204 -0.72 0.479 -1.408842 .6783638
hp | -.0252715 .0105097 -2.40 0.023 -.0468357 -.0037073
wt | -3.837584 .6730996 -5.70 0.000 -5.21867 -2.456498
------------------------------------------------------------------------------x <- lm(mpg ~ cyl + hp * wt, data = mtcars)
summary(margins(x))## factor AME SE z p lower upper
## cyl -0.3652 0.5086 -0.7181 0.4727 -1.3621 0.6316
## hp -0.0253 0.0105 -2.4046 0.0162 -0.0459 -0.0047
## wt -3.8376 0.6731 -5.7014 0.0000 -5.1568 -2.5183. quietly reg mpg i.cyl hp wt
. margins, dydx(*)
Average marginal effects Number of obs = 32
Model VCE : OLS
Expression : Linear prediction, predict()
dy/dx w.r.t. : 6.cyl 8.cyl hp wt
------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
cyl |
6 | -3.359024 1.40167 -2.40 0.024 -6.235014 -.4830353
8 | -3.185884 2.170476 -1.47 0.154 -7.639332 1.267564
|
hp | -.0231198 .0119522 -1.93 0.064 -.0476437 .0014041
wt | -3.181404 .7196011 -4.42 0.000 -4.657904 -1.704905
------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.x <- lm(mpg ~ factor(cyl) + hp + wt, data = mtcars)
summary(margins(x))## factor AME SE z p lower upper
## cyl6 -3.3590 1.4017 -2.3964 0.0166 -6.1062 -0.6118
## cyl8 -3.1859 2.1705 -1.4678 0.1422 -7.4399 1.0682
## hp -0.0231 0.0120 -1.9344 0.0531 -0.0465 0.0003
## wt -3.1814 0.7196 -4.4211 0.0000 -4.5918 -1.7710. quietly reg mpg cyl c.hp##c.hp wt
. margins, dydx(*)
Average marginal effects Number of obs = 32
Model VCE : OLS
Expression : Linear prediction, predict()
dy/dx w.r.t. : cyl hp wt
------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
cyl | -.3696041 .6163571 -0.60 0.554 -1.634264 .8950561
hp | -.0429018 .0178353 -2.41 0.023 -.0794969 -.0063066
wt | -2.873553 .7301251 -3.94 0.001 -4.371646 -1.37546
------------------------------------------------------------------------------
x <- lm(mpg ~ cyl + hp + I(hp^2) + wt, data = mtcars)
summary(margins(x))## factor AME SE z p lower upper
## cyl -0.3696 0.6164 -0.5997 0.5487 -1.5776 0.8384
## hp -0.0429 0.0178 -2.4054 0.0162 -0.0779 -0.0079
## wt -2.8736 0.7301 -3.9357 0.0001 -4.3046 -1.4425. gen hp2 = hp^2
. quietly reg mpg cyl hp2 wt
. margins, dydx(*)
Average marginal effects Number of obs = 32
Model VCE : OLS
Expression : Linear prediction, predict()
dy/dx w.r.t. : cyl hp2 wt
------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
cyl | -1.21919 .5030753 -2.42 0.022 -2.249693 -.1886869
hp2 | -.000028 .0000276 -1.01 0.320 -.0000846 .0000286
wt | -3.218637 .7570747 -4.25 0.000 -4.769435 -1.66784
------------------------------------------------------------------------------x <- lm(mpg ~ cyl + I(hp^2) + wt, data = mtcars)
summary(margins(x))## factor AME SE z p lower upper
## cyl -1.2192 0.5031 -2.4235 0.0154 -2.2052 -0.2332
## hp -0.0082 0.0081 -1.0124 0.3114 -0.0241 0.0077
## wt -3.2186 0.7571 -4.2514 0.0000 -4.7025 -1.7348. quietly logit am cyl hp wt
. margins, dydx(*)
Average marginal effects Number of obs = 32
Model VCE : OIM
Expression : Pr(am), predict()
dy/dx w.r.t. : cyl hp wt
------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
cyl | .0214527 .0469746 0.46 0.648 -.0706157 .1135212
hp | .0014339 .0006182 2.32 0.020 .0002224 .0026455
wt | -.4025475 .1154098 -3.49 0.000 -.6287466 -.1763484
------------------------------------------------------------------------------
. quietly logit am cyl hp wt
. margins, dydx(*) predict(xb)
Average marginal effects Number of obs = 32
Model VCE : OIM
Expression : Linear prediction (log odds), predict(xb)
dy/dx w.r.t. : cyl hp wt
------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
cyl | .4875978 1.071621 0.46 0.649 -1.612741 2.587936
hp | .0325917 .0188611 1.73 0.084 -.0043753 .0695587
wt | -9.14947 4.153326 -2.20 0.028 -17.28984 -1.009101
------------------------------------------------------------------------------x <- glm(am ~ cyl + hp + wt, data = mtcars, family = binomial)
# AME
summary(margins(x, type = "response"))## factor AME SE z p lower upper
## cyl 0.0215 0.0470 0.4567 0.6479 -0.0706 0.1135
## hp 0.0014 0.0006 2.3197 0.0204 0.0002 0.0026
## wt -0.4025 0.1154 -3.4880 0.0005 -0.6287 -0.1764# AME and MEM equivalent on "link" scale
summary(margins(x, type = "link"))## factor AME SE z p lower upper
## cyl 0.4876 1.0716 0.4550 0.6491 -1.6127 2.5879
## hp 0.0326 0.0189 1.7280 0.0840 -0.0044 0.0696
## wt -9.1495 4.1533 -2.2029 0.0276 -17.2898 -1.0091. quietly logit am i.cyl hp wt
. margins, dydx(*) predict(xb)
Average marginal effects Number of obs = 32
Model VCE : OIM
Expression : Linear prediction (log odds), predict(xb)
dy/dx w.r.t. : 6.cyl 8.cyl hp wt
------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
cyl |
6 | 2.765754 3.156829 0.88 0.381 -3.421517 8.953025
8 | -8.388958 13.16745 -0.64 0.524 -34.1967 17.41878
|
hp | .103209 .0960655 1.07 0.283 -.0850759 .2914939
wt | -10.67598 5.441998 -1.96 0.050 -21.3421 -.0098575
------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.
. margins, dydx(*)
Average marginal effects Number of obs = 32
Model VCE : OIM
Expression : Pr(am), predict()
dy/dx w.r.t. : 6.cyl 8.cyl hp wt
------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
cyl |
6 | .1197978 .1062873 1.13 0.260 -.0885214 .3281171
8 | -.3478575 .2067542 -1.68 0.092 -.7530883 .0573732
|
hp | .0033268 .0029852 1.11 0.265 -.0025241 .0091777
wt | -.3441297 .1188604 -2.90 0.004 -.5770919 -.1111675
------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.x <- glm(am ~ factor(cyl) + hp + wt, data = mtcars, family = binomial)
# Log-odds
summary(margins(x, type = "link"))## factor AME SE z p lower upper
## cyl6 2.7658 3.1568 0.8761 0.3810 -3.4214 8.9529
## cyl8 -8.3890 13.1671 -0.6371 0.5240 -34.1960 17.4181
## hp 0.1032 0.0961 1.0744 0.2826 -0.0851 0.2915
## wt -10.6760 5.4418 -1.9618 0.0498 -21.3418 -0.0102# Probability with continuous factors
summary(margins(x, type = "response"))## factor AME SE z p lower upper
## cyl6 0.1198 0.1063 1.1271 0.2597 -0.0885 0.3281
## cyl8 -0.3479 0.2068 -1.6825 0.0925 -0.7531 0.0574
## hp 0.0033 0.0030 1.1144 0.2651 -0.0025 0.0092
## wt -0.3441 0.1189 -2.8953 0.0038 -0.5771 -0.1112. quietly logit am cyl c.hp##c.wt
. margins, dydx(*)
Average marginal effects Number of obs = 32
Model VCE : OIM
Expression : Pr(am), predict()
dy/dx w.r.t. : cyl hp wt
------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
cyl | .0215633 .0492676 0.44 0.662 -.0749994 .1181261
hp | .0026673 .0023004 1.16 0.246 -.0018414 .007176
wt | -.5157922 .2685806 -1.92 0.055 -1.042201 .0106162
------------------------------------------------------------------------------
. margins, dydx(*) predict(xb)
Average marginal effects Number of obs = 32
Model VCE : OIM
Expression : Linear prediction (log odds), predict(xb)
dy/dx w.r.t. : cyl hp wt
------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
cyl | .5156396 1.169458 0.44 0.659 -1.776456 2.807735
hp | .0515116 .035699 1.44 0.149 -.0184571 .1214804
wt | -12.24264 7.678428 -1.59 0.111 -27.29208 2.806807
------------------------------------------------------------------------------x <- glm(am ~ cyl + hp * wt, data = mtcars, family = binomial)## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred# AME
summary(margins(x, type = "response"))## factor AME SE z p lower upper
## cyl 0.0216 0.0493 0.4377 0.6616 -0.0750 0.1181
## hp 0.0027 0.0023 1.1595 0.2462 -0.0018 0.0072
## wt -0.5158 0.2685 -1.9209 0.0547 -1.0421 0.0105# AME and MEM equivalent on "link" scale
summary(margins(x, type = "link"))## factor AME SE z p lower upper
## cyl 0.5156 1.1694 0.4409 0.6593 -1.7764 2.8077
## hp 0.0515 0.0357 1.4429 0.1490 -0.0185 0.1215
## wt -12.2426 7.6784 -1.5944 0.1108 -27.2920 2.8067. quietly probit am cyl c.hp##c.wt
. margins, dydx(*) predict(xb)
Average marginal effects Number of obs = 32
Model VCE : OIM
Expression : Linear prediction, predict(xb)
dy/dx w.r.t. : cyl hp wt
------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
cyl | .2974758 .6629205 0.45 0.654 -1.001825 1.596776
hp | .0277713 .0193121 1.44 0.150 -.0100797 .0656223
wt | -6.626949 4.096208 -1.62 0.106 -14.65537 1.401471
------------------------------------------------------------------------------
. margins, dydx(*)
Average marginal effects Number of obs = 32
Model VCE : OIM
Expression : Pr(am), predict()
dy/dx w.r.t. : cyl hp wt
------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
cyl | .022611 .0498253 0.45 0.650 -.0750447 .1202667
hp | .0025769 .0022607 1.14 0.254 -.001854 .0070077
wt | -.508829 .2625404 -1.94 0.053 -1.023399 .0057408
------------------------------------------------------------------------------x <- glm(am ~ cyl + hp * wt, data = mtcars, family = binomial(link="probit"))## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred# AME (log-odds)
summary(margins(x, type = "link"))## factor AME SE z p lower upper
## cyl 0.2975 0.6472 0.4596 0.6458 -0.9710 1.5660
## hp 0.0278 0.0184 1.5075 0.1317 -0.0083 0.0639
## wt -6.6269 3.9095 -1.6951 0.0901 -14.2894 1.0355# AME (probability)
summary(margins(x, type = "response"))## factor AME SE z p lower upper
## cyl 0.0226 0.0492 0.4598 0.6456 -0.0738 0.1190
## hp 0.0026 0.0021 1.2244 0.2208 -0.0015 0.0067
## wt -0.5088 0.2479 -2.0523 0.0401 -0.9948 -0.0229. quietly poisson carb cyl c.hp##c.wt
. margins, dydx(*) predict(xb)
Average marginal effects Number of obs = 32
Model VCE : OIM
Expression : Linear prediction, predict(xb)
dy/dx w.r.t. : cyl hp wt
------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
cyl | -.0993854 .1478936 -0.67 0.502 -.3892516 .1904808
hp | .0066519 .0024217 2.75 0.006 .0019054 .0113984
wt | .1225051 .2035185 0.60 0.547 -.2763837 .521394
------------------------------------------------------------------------------
. margins, dydx(*)
Average marginal effects Number of obs = 32
Model VCE : OIM
Expression : Predicted number of events, predict()
dy/dx w.r.t. : cyl hp wt
------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
cyl | -.2795214 .4169931 -0.67 0.503 -1.096813 .53777
hp | .0175935 .0067179 2.62 0.009 .0044267 .0307604
wt | .2075447 .4859868 0.43 0.669 -.7449719 1.160061
------------------------------------------------------------------------------x <- glm(carb ~ cyl + hp * wt, data = mtcars, family = poisson)
# AME (linear/link)
summary(margins(x, type = "link"))## factor AME SE z p lower upper
## cyl -0.0994 0.1479 -0.6720 0.5016 -0.3893 0.1905
## hp 0.0067 0.0024 2.7468 0.0060 0.0019 0.0114
## wt 0.1225 0.2035 0.6019 0.5472 -0.2764 0.5214# AME (probability)
summary(margins(x, type = "response"))## factor AME SE z p lower upper
## cyl -0.2795 0.4170 -0.6703 0.5026 -1.0968 0.5378
## hp 0.0176 0.0067 2.6189 0.0088 0.0044 0.0308
## wt 0.2075 0.4860 0.4271 0.6693 -0.7449 1.1600