fepoisson_asymmetric: Asymmetric Poisson Pseudo-Maximum Likelihood (APPML)...

In capybara: Fast and Memory Efficient Fitting of Linear Models with High-Dimensional Fixed Effects

Asymmetric Poisson Pseudo-Maximum Likelihood (APPML) Estimation

Description

Fits an asymmetric Poisson pseudo-maximum likelihood model with high-dimensional fixed effects using expectile regression. This approach extends standard PPML by allowing different weights for positive and negative residuals, enabling estimation of conditional expectiles rather than the conditional mean.

Usage

fepoisson_asymmetric(
  formula = NULL,
  data = NULL,
  weights = NULL,
  beta_start = NULL,
  eta_start = NULL,
  offset = NULL,
  control = NULL
)

Arguments

formula	an object of class "formula": a symbolic description of the model to be fitted. formula must be of type response ~ slopes | fixed_effects | cluster.
data	an object of class "data.frame" containing the variables in the model. The expected input is a dataset with the variables specified in formula and a number of rows at least equal to the number of variables in the model.
weights	an optional string with the name of the prior weights variable in data.
beta_start	an optional vector of starting values for the structural parameters in the linear predictor. Default is \boldsymbol{\beta} = \mathbf{0}.
eta_start	an optional vector of starting values for the linear predictor.
offset	an optional formula or numeric vector specifying an a priori known component to be included in the linear predictor. If a formula, it should be of the form ~ variable.
control	a named list of parameters for controlling the fitting process. See fit_control for details.

Details

The APPML estimator minimizes an asymmetric loss function based on expectiles. For a given expectile \tau, observations with negative residuals receive weight \tau while observations with positive residuals receive weight 1 - \tau. The algorithm iteratively:

1. Computes residuals from the current fit

2. Updates weights as w_i = |\tau - \mathbf{1}(r_i < 0)|

3. Re-fits the weighted Poisson model

4. Checks convergence using (b - b_{old})' V^{-1} (b - b_{old}) < \epsilon

The expectile parameter is specified via control = fit_control(expectile = ...). When expectile = 0.5, the estimator is equivalent to standard PPML. Values below 0.5 estimate lower conditional expectiles (more sensitive to small values), while values above 0.5 estimate upper conditional expectiles (more sensitive to large values).

Value

A named list of class "feglm" containing:

coefficients	named vector of estimated coefficients
vcov	variance-covariance matrix of coefficients
eta	linear predictor
fitted_values	fitted values from the final iteration
residuals	residuals from the final fit
weights	observation weights used in final fit
appml_weights	asymmetric weights used in APPML algorithm
deviance	the deviance of the model
null_deviance	the null deviance of the model
conv	logical indicating whether inner GLM converged
conv_outer	logical indicating whether APPML outer loop converged
iter	number of inner iterations
iter_outer	number of outer APPML iterations
expectile	the expectile value used
objective_function	final value of the convergence criterion
negative_residuals_share	proportion of negative residuals in final fit
nobs	a named vector with the number of observations
fe_levels	a named vector with the number of levels in each fixed effect
nms_fe	a list with the names of the fixed effects variables
formula	the formula used in the model
family	the family used in the model (Poisson)
control	the control list used in the model

References

Newey, W. K., & Powell, J. L. (1987). Asymmetric least squares estimation and testing. Econometrica, 55(4), 819-847.

See Also

fepoisson, feglm, fit_control

Examples

ross2004_subset <- ross2004[ross2004$year == 1999, ]
ross2004_subset <- ross2004_subset[ross2004_subset$ltrade >
  quantile(ross2004_subset$ltrade, 0.75), ]

# Lower expectile (10th) - more weight on negative residuals
fit10 <- fepoisson_asymmetric(
  ltrade ~ ldist | ctry1, ross2004_subset,
  control = fit_control(expectile = 0.1)
)

summary(fit10)

capybara documentation built on June 15, 2026, 9:10 a.m.