[R] How to plot marginal effects (MEM) in R?
David Winsemius
dwinsemius at comcast.net
Fri Jul 22 08:35:18 CEST 2016
> On Jul 21, 2016, at 2:22 PM, Faradj Koliev <faradj.g at gmail.com> wrote:
>
> Dear all,
>
> I have two logistic regression models:
>
>
> • model <- glm(Y ~ X1+X2+X3+X4, data = data, family = "binomial")
>
>
>
> • modelInteraction <- glm(Y ~ X1+X2+X3+X4+X1*X4, data = data, family = "binomial")
>
> To calculate the marginal effects (MEM approach) for these models, I used the `mfx` package:
>
>
> • a<- logitmfx(model, data=data, atmean=TRUE)
>
>
>
> •b<- logitmfx(modelInteraction, data=data, atmean=TRUE)
>
>
> What I want to do now is 1) plot all the results for "model" and 2) show the result just for two variables: X1 and X2.
> 3) I also want to plot the interaction term in ”modelInteraction”.
There is no longer a single "effect" for X1 in modelInteraction in contrast to the manner as there might be an "effect" for X2. There can only be predictions for combined situations with particular combinations of values for X1 and X4.
> model
Call: glm(formula = Y ~ X1 + X2 + X3 + X4, family = "binomial", data = data)
Coefficients:
(Intercept) X1 X2 X3 X4
-0.3601 1.3353 0.1056 0.2898 -0.3705
Degrees of Freedom: 68 Total (i.e. Null); 64 Residual
Null Deviance: 66.78
Residual Deviance: 62.27 AIC: 72.27
> modelInteraction
Call: glm(formula = Y ~ X1 + X2 + X3 + X4 + X1 * X4, family = "binomial",
data = data)
Coefficients:
(Intercept) X1 X2 X3 X4 X1:X4
90.0158 -90.0747 0.1183 0.3064 -15.3688 15.1593
Degrees of Freedom: 68 Total (i.e. Null); 63 Residual
Null Deviance: 66.78
Residual Deviance: 61.49 AIC: 73.49
Notice that a naive attempt to plot an X1 "effect" in modelInteraction might pick the -90.07 value which would then ignore both the much larger Intercept value and also ignore the fact that the interaction term has now split the X4 (and X1) "effects" into multiple pieces.
You need to interpret the effects of X1 in the context of a specification of a particular X4 value and not forget that the Intercept should not be ignored. It appears to me that the estimates of the mfx package are essentially meaningless with the problem you have thrown at it.
> a
Call:
logitmfx(formula = model, data = data, atmean = TRUE)
Marginal Effects:
dF/dx Std. Err. z P>|z|
X1 0.147532 0.087865 1.6791 0.09314 .
X2 0.015085 0.193888 0.0778 0.93798
X3 0.040309 0.063324 0.6366 0.52441
X4 -0.050393 0.092947 -0.5422 0.58770
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
dF/dx is for discrete change for the following variables:
[1] "X1" "X2" "X4"
> b
Call:
logitmfx(formula = modelInteraction, data = data, atmean = TRUE)
Marginal Effects:
dF/dx Std. Err. z P>|z|
X1 -1.0000e+00 1.2121e-07 -8.25e+06 <2e-16 ***
X2 6.5595e-03 8.1616e-01 8.00e-03 0.9936
X3 1.6312e-02 2.0326e+00 8.00e-03 0.9936
X4 -9.6831e-01 1.5806e+01 -6.13e-02 0.9511
X1:X4 8.0703e-01 1.4572e+01 5.54e-02 0.9558
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
dF/dx is for discrete change for the following variables:
[1] "X1" "X2" "X4"
I see no sensible interpretation of the phrase "X1 effect" in the comparison tables above. The "p-value" in the second table appears to be nonsense induced by throwing a model formulation that was not anticipated. There is a negligible improvement in the glm fits:
> anova(model,modelInteraction)
Analysis of Deviance Table
Model 1: Y ~ X1 + X2 + X3 + X4
Model 2: Y ~ X1 + X2 + X3 + X4 + X1 * X4
Resid. Df Resid. Dev Df Deviance
1 64 62.274
2 63 61.495 1 0.77908
So the notion that the "X1 effect" is now "highly significant" where it was before not even suggestive of significance seem to point to either an error in the underlying theory or a failure to anticipate and trap (and warn the user) that an erroneous model (or at least an unanticipated model) is being passed to a procedure.
At least the 'effects- package gives you a tiny warning about this issue, although I think it really should throw an informative error when a user attempts to estimate only a "main effect" in a model that has an interaction involving such a covariate:
> library(effects)
> effect('X1', model)
X1 effect
X1
0 0.2 0.4 0.6 0.8 1
0.06706123 0.08582757 0.10923061 0.13805139 0.17299973 0.21459275
> effect('X1', modelInteraction)
NOTE: X1 is not a high-order term in the model
X1 effect
X1
0 0.2 0.4 0.6 0.8 1
0.0002418661 0.0009864740 0.0040142251 0.0161843996 0.0629206979 0.2151098752
> effect('X1:X4', modelInteraction)
X1*X4 effect
X4
X1 6 6.2 6.4 6.6 6.8 7
0 0.1100479 0.005686142 0.0002643982 1.223058e-05 5.656287e-07 2.615838e-08
0.2 0.1285241 0.012352473 0.0010595321 8.994106e-05 7.628099e-06 6.469071e-07
0.4 0.1495811 0.026625017 0.0042357682 6.610806e-04 1.028639e-04 1.599803e-05
0.6 0.1734015 0.056446132 0.0167737545 4.841483e-03 1.385458e-03 3.954877e-04
0.8 0.2001225 0.115698003 0.0640377838 3.454327e-02 1.836677e-02 9.689636e-03
1 0.2298165 0.222481442 0.2153150766 2.083177e-01 2.014893e-01 1.948297e-01
--
David.
>
>
> I have been looking around for the solutions but haven't been able to find any. I would appreciate any suggestions.
>
> A reproducible sample:
>
>> dput(data)
> structure(list(Y = c(0L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 1L,
> 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 1L,
> 0L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 1L,
> 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 1L,
> 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L), X1 = c(1L, 0L, 1L,
> 0L, 1L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 1L, 0L, 0L, 1L,
> 1L, 0L, 0L, 0L, 1L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
> 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 1L,
> 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
> 1L, 0L), X2 = c(0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L,
> 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> 1L, 0L, 1L, 0L, 1L, 1L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L,
> 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L), X3 = c(0L, 0L, 0L, 0L, 0L,
> 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 2L, 2L, 3L, 4L, 5L, 0L, 0L,
> 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L,
> 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L
> ), X4 = c(6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L,
> 6L, 6L, 6L, 6L, 6L, 7L, 7L, 7L, 7L, 7L, 6L, 6L, 6L, 6L, 6L, 6L,
> 6L, 6L, 6L, 6L, 6L, 6L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L,
> 7L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 7L, 7L, 7L, 7L,
> 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L)), .Names = c("Y", "X1", "X2",
> "X3", "X4"), row.names = c(NA, -69L), class = "data.frame")
>
>
>
>
> [[alternative HTML version deleted]]
>
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David Winsemius
Alameda, CA, USA
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