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Density specifications for continuous exposures

Source: R/density.R
dens_normal.Rd

Weights for a continuous exposure are a ratio of densities. Both densities are evaluated on the standardized residual \(z_i = (A_i - \mu_i) / \sigma\), where \(A_i\) is the exposure, \(\mu_i\) the fitted conditional mean, and \(\sigma\) the residual spread, so a specification describes a density on a standardized scale rather than on the scale of the exposure itself.

These constructors name the family and record the parameters that identify it. Pass one to the .density argument of wt_ate() or wt_cens(), which also accept the strings "normal", "laplace", and "kernel" for the families that need no parameters, and a bare function of one argument, which is wrapped with dens_fn().

  • dens_normal() is the standard normal density, the default.

  • dens_laplace() is the standard Laplace density, \(\exp(-|z|) / 2\), which puts more mass in the tails than the normal.

  • dens_t() is Student's t density with df degrees of freedom, heavier tailed still, and heavier the smaller df is.

  • dens_kernel() is a kernel density estimate of the standardized residuals, fit with stats::density() and interpolated to each observation. It assumes no family at all, at the cost of a density that is not a smooth function of the model's parameters: weights built from it have no closed-form standard error, and ipw() reports none for them at all. Bootstrap the whole fit by hand to put an interval around such an estimate.

  • dens_fn() is a density you write yourself.

Usage

dens_normal()

dens_laplace()

dens_t(df)

dens_kernel(bw = "nrd0", adjust = 1, kernel = "gaussian", n = 512)

dens_fn(f)

Arguments

df

Degrees of freedom for Student's t, a single positive, finite number.

bw

The bandwidth passed to stats::density(): a single positive number, or the name of one of its selection rules ("nrd0", "nrd", "ucv", "bcv", "SJ", "SJ-ste", or "SJ-dpi").

adjust

A single positive number the bandwidth is multiplied by, as in stats::density(). Values above 1 smooth the estimate further.

kernel

The smoothing kernel, one of the kernels stats::density() accepts.

n

The number of grid points stats::density() evaluates, at least 2. The estimate is interpolated between them, so a larger n follows the shape of the residuals more closely.

f

A function of one argument, the standardized residual, returning one non-negative, finite density value for each element it is given.

Value

An object of class propensity_density: a list with the elements family, params, and fn. fn is the function that evaluates the density, and is NULL for dens_kernel().

Examples

dens_normal()
#> <density: normal>

dens_t(df = 4)
#> <density: t(df = 4)>

dens_kernel(adjust = 1.5)
#> <density: kernel(bw = "nrd0", adjust = 1.5, kernel = "gaussian", n = 512)>

dens_fn(function(z) stats::dt(z, df = 4))
#> <density: function>