Differentiate an Estimated Model Function with Respect to One Variable, or calculate a discrete difference (“first difference”) as appropriate.
dydx(data, model, variable, ...) # S3 method for default dydx(data, model, variable, type = c("response", "link"), change = c("dydx", "minmax", "iqr", "sd"), eps = 1e-07, as.data.frame = TRUE, ...) # S3 method for factor dydx(data, model, variable, type = c("response", "link"), fwrap = FALSE, as.data.frame = TRUE, ...) # S3 method for ordered dydx(data, model, variable, type = c("response", "link"), fwrap = FALSE, as.data.frame = TRUE, ...) # S3 method for logical dydx(data, model, variable, type = c("response", "link"), as.data.frame = TRUE, ...)
| data | The dataset on which to to calculate \(\hat{y}\). |
|---|---|
| model | The model object to pass to |
| variable | A character string specifying the variable to calculate the derivative or discrete change for. |
| … | Ignored. |
| type | The type of prediction. Default is “response”. |
| change | For numeric variables, a character string specifying the type of change to express. The default is the numerical approximation of the derivative. Alternative values are occasionally desired quantities: “minmax” (the discrete change moving from |
| eps | If |
| as.data.frame | A logical indicating whether to return a data frame (the default) or a matrix. |
| fwrap | A logical specifying how to name factor columns in the response. |
A data frame, typically with one column unless the variable is a factor with more than two levels. The names of the marginal effect columns begin with “dydx_” to distinguish them from the substantive variables of the same names.
These functions provide a simple interface to the calculation of marginal effects for specific variables used in a model, and are the workhorse functions called internally by marginal_effects.
dydx is an S3 generic with classes implemented for specific variable types. S3 method dispatch, somewhat atypically, is based upon the class of data[[variable]].
For numeric (and integer) variables, the method calculates an instantaneous marginal effect using a simple “central difference” numerical differentiation:
$$\frac{f(x + \frac{1}{2}h) - f(x - \frac{1}{2}h)}{dh}$$, where (\(h = \max(|x|, 1) \sqrt{\epsilon}\) and the value of \(\epsilon\) is given by argument eps. This procedure is subject to change in the future.
For factor variables (or character variables, which are implicitly coerced to factors by modelling functions), discrete first-differences in predicted outcomes are reported instead (i.e., change in predicted outcome when factor is set to a given level minus the predicted outcome when the factor is set to its baseline level). These are sometimes called “partial effects”. If you want to use numerical differentiation for factor variables (which you probably do not want to do), enter them into the original modelling function as numeric values rather than factors.
For ordered factor variables, the same approach as factors is used. This may contradict the output of modelling function summaries, which rely on options("contrasts") to determine the contrasts to use (the default being contr.poly rather than contr.treatment, the latter being used normally for unordered factors).
For logical variables, the same approach as factors is used, but always moving from FALSE to TRUE.
Miranda, Mario J. and Paul L. Fackler. 2002. Applied Computational Economics and Finance. p. 103.
Greene, William H. 2012. Econometric Analysis. 7th edition. pp. 733--741.
Cameron, A. Colin and Pravin K. Trivedi. 2010. Microeconometric Using Stata. Revised edition. pp. 106--108, 343--356, 476--478.
require("datasets") x <- lm(mpg ~ cyl * hp + wt, data = head(mtcars)) # marginal effect (numerical derivative) dydx(head(mtcars), x, "hp")#> dydx_hp #> 1 0.6845469 #> 2 0.6845469 #> 3 1.0942088 #> 4 0.6845469 #> 5 0.2748850 #> 6 0.6845469# other discrete differences ## change from min(mtcars$hp) to max(mtcars$hp) dydx(head(mtcars), x, "hp", change = "minmax")#> dydx_hp #> 1 56.13285 #> 2 56.13285 #> 3 89.72512 #> 4 56.13285 #> 5 22.54057 #> 6 56.13285## change from 1st quartile to 3rd quartile dydx(head(mtcars), x, "hp", change = "iqr")#> dydx_hp #> 1 3.422734 #> 2 3.422734 #> 3 5.471044 #> 4 3.422734 #> 5 1.374425 #> 6 3.422734## change from mean(mtcars$hp) +/- sd(mtcars$hp) dydx(head(mtcars), x, "hp", change = "sd")#> dydx_hp #> 1 39.82549 #> 2 39.82549 #> 3 63.65876 #> 4 39.82549 #> 5 15.99223 #> 6 39.82549## change between arbitrary values of mtcars$hp dydx(head(mtcars), x, "hp", change = c(75,150))#> dydx_hp #> 1 51.34102 #> 2 51.34102 #> 3 82.06566 #> 4 51.34102 #> 5 20.61638 #> 6 51.34102# factor variables mtcars[["cyl"]] <- factor(mtcars$cyl) x <- lm(mpg ~ cyl, data = head(mtcars)) dydx(head(mtcars), x, "cyl")#> dydx_cyl6 dydx_cyl8 #> 1 -2.425 -4.1 #> 2 -2.425 -4.1 #> 3 -2.425 -4.1 #> 4 -2.425 -4.1 #> 5 -2.425 -4.1 #> 6 -2.425 -4.1