Average marginal effects

The average, over the rows of newdata, of the change in a predicted quantity when one variable changes: its derivative (a numeric variable, with from and to left out) or the contrast between two of its values (from and to, for a variable of any type). Every row keeps its own values of the other variables, and the variable enters through the model's formula, so interactions and transformations of it (x:z, I(x^2), log(x)) are handled. first_difference() instead moves one model-matrix column at a single reference profile.

Usage

ame(
  object,
  variable,
  newdata,
  from = NULL,
  to = NULL,
  type = "response",
  eps = NULL,
  level = 0.95,
  offset = NULL,
  weights = NULL,
  B = 0,
  cores = 1L
)

Arguments

object: A fitted model of any class in the package.
variable: The name of a variable of the model, a column of newdata.
newdata: The rows to average over, usually the data the model was fit to.
from, to: Two values of variable for a contrast. Leave both out for the derivative of a numeric variable.
type: The quantity, as the type of the class's predict() method. The default "response" is the expected count (for a zero-truncated fit, such as cpb()'s default, the conditional mean E(Y | Y >= 1)); the two-part models also give their equation-specific quantities.
eps: The step of the central difference for the derivative; by default 1e-4 times the range of variable in newdata.
level: Confidence level.
offset: Passed to predict().
weights: Optional weights for the average over the rows: a numeric vector or the name of a column of newdata, such as the frequency weights of a fit to tabulated data (the average then equals the one over the expanded rows). By default the rows count equally.
B: Refit-bootstrap replicates for a percentile interval; 0 (default) uses the fit's own inference (see Details).
cores: Worker processes for the refits; see cpb().

Value

A data frame of class "ud_ame" with term, contrast ("dY/dx", or "to - from"), type, estimate, lower, upper, method (the interval's source) and n, the rows averaged (a row with a missing value is left out).

Details

The interval follows the rule of first_difference(). With stored bootstrap draws, the average is computed at every draw, jointly over the coefficients, the dispersion parameter and a fixed-effects fit's reference unit (the draws of a fixed-effects fit recentered on its estimate), and the percentile interval is taken. Otherwise it uses the delta method over the fit's covariance, and otherwise there is none. A row at a fixed-effects unit's own effect, or at its own zero-equation dummy, depends on a parameter the draws do not carry, so an average over such rows, the sample's average partial effect, has no interval of this kind (B below gives it one). Without the unit column in newdata every row enters at the reference unit, the mean of the identified units' effects on the log scale (a typical, geometric-mean unit), whose draws the fit carries: that is the average effect for such a unit over the rows' covariates, not the sample's average partial effect, and the two can differ substantially when the unit effects are dispersed.

A fixed-effects count family (count_reg() with fe) carries its unit dummies in its covariance, so its average partial effect has a delta-method interval. The slope of a fit on the floor support (support = "floor") is refused, since its mean jumps at integer ceilings; a contrast is available.

B > 0 gives the average a refit-bootstrap interval instead, for any class: the model is refit on B resampled copies of newdata, which must then be the data the model was fit to, resampling whole clusters of the fit's cluster, else whole units of its first fixed-effects column, else rows (a unit drawn twice becomes two units). Each replicate averages over its own rows at its own unit effects, and the percentile interval is taken. Resampling the units treats them as a sample, so this is an interval for a fixed-effects fit's average partial effect in the population of units they represent, which carries the variability of which units are drawn: with few units, or a few with large effects, it is wide and asymmetric. Each refit is the fit's own call with its data replaced and its standard errors off (on King's support, every replicate of a jackknife-corrected fit is corrected without re-running the validity gate, as in cpb_fe()'s own bootstrap, and none is when the gate refused the fit's correction); the call's other arguments are evaluated where ame() is called, as update() does, and an offset or weights given to the fit as one value per row follow the resampled rows. The run takes about B times one fit (see cores).

Examples

# \donttest{
set.seed(1); n <- 400; x <- rnorm(n); g <- factor(sample(c("a", "b"), n, TRUE))
d <- data.frame(y = rcpb(n, exp(1 + 0.4 * x + 0.3 * (g == "b")), 0.5), x = x, g = g)
fit <- cpb(y ~ x * g, data = d, truncated = FALSE, se = "bootstrap", B = 100)
ame(fit, "x", d)
#>  term contrast     type estimate lower upper             method   n
#>     x    dY/dx response    1.426 1.299 1.526 bootstrap (stored) 400
ame(fit, "g", d, from = "a", to = "b")
#>  term contrast     type estimate lower upper             method   n
#>     g    b - a response    1.108   0.9 1.307 bootstrap (stored) 400

## a fixed-effects fit's average partial effect over its own units
pd <- do.call(rbind, lapply(1:30, function(i) {
  x <- rnorm(8); data.frame(unit = i, x = x, y = rcpb(8, exp(rnorm(1, 0, 0.5) + 0.4 * x), 0.5))
}))
ffit <- cpb_fe(y ~ x, data = pd, fe = "unit")
ame(ffit, "x", pd, B = 100)
#>  term contrast     type estimate lower upper                   method   n
#>     x    dY/dx response    0.407 0.308 0.554 bootstrap (refit, B=100) 240
# }

Usage

Arguments

Value

Details

See also

Examples