R/feglm.R

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

#' srr_stats
#' @srrstats {G1.0} Implements generalized linear models with high-dimensional fixed effects.
#' @srrstats {G2.1a} Ensures the input `formula` is correctly specified and includes fixed effects.
#' @srrstats {G2.1b} Validates that the input `data` is non-empty and of class `data.frame`.
#' @srrstats {G2.3a} Uses structured checks for parameters like `weights`, `control`, and starting values.
#' @srrstats {G2.4} Handles missing or perfectly classified data by appropriately excluding them.
#' @srrstats {G2.5} Ensures numerical stability and convergence for large datasets and complex models.
#' @srrstats {G3.1a} Provides robust support for a range of family functions like `gaussian`, `poisson`, and `binomial`.
#' @srrstats {G5.0} Ensures that identical input data and parameter settings consistently produce the same outputs, supporting reproducible workflows.
#' @srrstats {G5.1} Includes complete output elements (coefficients, deviance, etc.) for reproducibility.
#' @srrstats {G5.2a} Generates unique and descriptive error messages for invalid configurations or inputs.
#' @srrstats {G5.2b} Tracks optimization convergence during model fitting, providing detailed diagnostics for users to assess model stability.
#' @srrstats {G5.3} Optimizes computational efficiency for large datasets, employing parallel processing or streamlined algorithms where feasible.
#' @srrstats {G5.4} Benchmarks the scalability of model fitting against datasets of varying sizes to identify performance limits.
#' @srrstats {G5.4b} Documents performance comparisons with alternative implementations, highlighting strengths in accuracy or speed.
#' @srrstats {G5.4c} Employs memory-efficient data structures to handle large datasets without exceeding hardware constraints.
#' @srrstats {G5.5} Uses fixed random seeds for stochastic components, ensuring consistent outputs for analyses involving randomness.
#' @srrstats {G5.6} Benchmarks model fitting times and resource usage, providing users with insights into expected computational demands.
#' @srrstats {G5.6a} Demonstrates how parallel processing can reduce computation times while maintaining accuracy in results.
#' @srrstats {G5.7} Offers detailed, reproducible examples of typical use cases, ensuring users can replicate key functionality step-by-step.
#' @srrstats {G5.8} Includes informative messages or progress indicators during long-running computations to enhance user experience.
#' @srrstats {G5.8a} Warns users when outputs are approximate due to algorithmic simplifications or computational trade-offs.
#' @srrstats {G5.8b} Provides options to control the balance between computational speed and result precision, accommodating diverse user needs.
#' @srrstats {G5.8c} Documents which algorithm settings prioritize efficiency over accuracy, helping users make informed choices.
#' @srrstats {G5.8d} Clarifies the variability in results caused by parallel execution, particularly in randomized algorithms.
#' @srrstats {G5.9} Ensures all intermediate computations are accessible for debugging and troubleshooting during development or analysis.
#' @srrstats {G5.9a} Implements a debug mode that logs detailed information about the computational process for advanced users.
#' @srrstats {G5.9b} Validates correctness of results under debug mode, ensuring computational reliability across all scenarios.
#' @srrstats {RE1.0} Documents all assumptions inherent in the regression model, such as linearity, independence, and absence of multicollinearity.
#' @srrstats {RE1.1} Validates that input variables conform to expected formats, including numeric types for predictors and outcomes.
#' @srrstats {RE1.2} Provides options for handling missing data, including imputation or omission, and ensures users are informed of the chosen method.
#' @srrstats {RE1.3} Includes rigorous tests to verify model stability with edge cases, such as datasets with collinear predictors or extreme values.
#' @srrstats {RE1.3a} Adds specific tests for small datasets, ensuring the model remains robust under low-sample conditions.
#' @srrstats {RE1.4} Implements diagnostic checks to verify the assumptions of independence and homoscedasticity, essential for valid inference.
#' @srrstats {RE2.0} Labels all regression outputs, such as coefficients and standard errors, to ensure clarity and interpretability.
#' @srrstats {RE2.4} Quantifies uncertainty in regression coefficients using confidence intervals.
#' @srrstats {RE2.4a} Rejects perfect collinearity between independent variables.
#' @srrstats {RE2.4b} Rejects perfect collinearity between dependent and independent variables.
#' @srrstats {RE4.0} This returns a model-type object that is essentially a list with specific components and attributes.
#' @srrstats {RE4.1} Identifies outliers and influential data points that may unduly impact regression results, offering visualization tools.
#' @srrstats {RE4.6} Includes standard metrics such as R-squared and RMSE to help users evaluate model performance.
#' @srrstats {RE4.7} Tests sensitivity to hyperparameter choices in regularized or complex regression models.
#' @srrstats {RE4.14} Uses simulated datasets to test the reproducibility and robustness of regression results.
#' @srrstats {RE5.0} Optimized for scaling to large datasets with high-dimensional fixed effects.
#' @srrstats {RE5.1} Efficiently projects out fixed effects using auxiliary indexing structures.
#' @srrstats {RE5.2} Provides detailed warnings and error handling for convergence and dependence issues.
#' @srrstats {RE5.3} Thoroughly documents interactions between model features, inputs, and controls.
#' @srrstats {RE7.4} Provides comprehensive examples that demonstrate proper usage of the regression functions,
#' covering input preparation, function execution, and result interpretation.
#' @noRd
NULL

#' @title GLM fitting with high-dimensional k-way fixed effects
#'
#' @description \code{\link{feglm}} can be used to fit generalized linear models
#'  with many high-dimensional fixed effects. The estimation procedure is based
#'  on unconditional maximum likelihood and can be interpreted as a
#'  \dQuote{weighted demeaning} approach.
#'
#' \strong{Remark:} The term fixed effect is used in econometrician's sense of
#'  having intercepts for each level in each category.
#'
#' @param formula an object of class \code{"formula"}: a symbolic description of
#'  the model to be fitted. \code{formula} must be of type \code{y ~ x | k},
#'  where the second part of the formula refers to factors to be concentrated
#'  out. It is also possible to pass clustering variables to \code{\link{feglm}}
#'  as \code{y ~ x | k | c}.
#' @param data an object of class \code{"data.frame"} containing the variables
#'  in the model. The expected input is a dataset with the variables specified
#'  in \code{formula} and a number of rows at least equal to the number of
#'  variables in the model.
#' @param family the link function to be used in the model. Similar to
#'  \code{\link[stats]{glm.fit}} this has to be the result of a call to a family
#'  function. Default is \code{gaussian()}. See \code{\link[stats]{family}} for
#'  details of family functions.
#' @param weights an optional string with the name of the 'prior weights'
#'  variable in \code{data}.
#' @param beta_start an optional vector of starting values for the structural
#'  parameters in the linear predictor. Default is
#'  \eqn{\boldsymbol{\beta} = \mathbf{0}}{\beta = 0}.
#' @param eta_start an optional vector of starting values for the linear
#'  predictor.
#' @param control a named list of parameters for controlling the fitting
#'  process. See \code{\link{feglm_control}} for details.
#'
#' @details If \code{\link{feglm}} does not converge this is often a sign of
#'  linear dependence between one or more regressors and a fixed effects
#'  category. In this case, you should carefully inspect your model
#'  specification.
#'
#' @return A named list of class \code{"feglm"}. The list contains the following
#'  fifteen elements:
#'  \item{coefficients}{a named vector of the estimated coefficients}
#'  \item{eta}{a vector of the linear predictor}
#'  \item{weights}{a vector of the weights used in the estimation}
#'  \item{hessian}{a matrix with the numerical second derivatives}
#'  \item{deviance}{the deviance of the model}
#'  \item{null_deviance}{the null deviance of the model}
#'  \item{conv}{a logical indicating whether the model converged}
#'  \item{iter}{the number of iterations needed to converge}
#'  \item{nobs}{a named vector with the number of observations used in the
#'   estimation indicating the dropped and perfectly predicted observations}
#'  \item{lvls_k}{a named vector with the number of levels in each fixed
#'   effects}
#'  \item{nms_fe}{a list with the names of the fixed effects variables}
#'  \item{formula}{the formula used in the model}
#'  \item{data}{the data used in the model after dropping non-contributing
#'   observations}
#'  \item{family}{the family used in the model}
#'  \item{control}{the control list used in the model}
#'
#' @references Gaure, S. (2013). "OLS with Multiple High Dimensional Category
#'  Variables". Computational Statistics and Data Analysis, 66.
#' @references Marschner, I. (2011). "glm2: Fitting generalized linear models
#'  with convergence problems". The R Journal, 3(2).
#' @references Stammann, A., F. Heiss, and D. McFadden (2016). "Estimating Fixed
#'  Effects Logit Models with Large Panel Data". Working paper.
#' @references Stammann, A. (2018). "Fast and Feasible Estimation of Generalized
#'  Linear Models with High-Dimensional k-Way Fixed Effects". ArXiv e-prints.
#'
#' @examples
#' # subset trade flows to avoid fitting time warnings during check
#' set.seed(123)
#' trade_2006 <- trade_panel[trade_panel$year == 2006, ]
#' trade_2006 <- trade_2006[sample(nrow(trade_2006), 500), ]
#'
#' mod <- feglm(
#'   trade ~ log_dist + lang + cntg + clny | exp_year + imp_year,
#'   trade_2006,
#'   family = poisson(link = "log")
#' )
#'
#' summary(mod)
#'
#' mod <- feglm(
#'   trade ~ log_dist + lang + cntg + clny | exp_year + imp_year | pair,
#'   trade_panel,
#'   family = poisson(link = "log")
#' )
#'
#' summary(mod, type = "clustered")
#'
#' @export
feglm <- function(
    formula = NULL,
    data = NULL,
    family = gaussian(),
    weights = NULL,
    beta_start = NULL,
    eta_start = NULL,
    control = NULL) {
  # Check validity of formula ----
  check_formula_(formula)

  # Check validity of data ----
  check_data_(data)

  # Check validity of family ----
  check_family_(family)

  # Check validity of control + Extract control list ----
  control <- check_control_(control)

  # Update formula and do further validity check ----
  formula <- update_formula_(formula)

  # Generate model.frame
  lhs <- NA # just to avoid global variable warning
  nobs_na <- NA
  nobs_full <- NA
  model_frame_(data, formula, weights)

  # Ensure that model response is in line with the chosen model ----
  check_response_(data, lhs, family)

  # Get names of the fixed effects variables and sort ----
  k_vars <- attr(terms(formula, rhs = 2L), "term.labels")

  # Generate temporary variable ----
  tmp_var <- temp_var_(data)

  # Drop observations that do not contribute to the log likelihood ----
  data <- drop_by_link_type_(data, lhs, family, tmp_var, k_vars, control)

  # Transform fixed effects and clusters to factors ----
  data <- transform_fe_(data, formula, k_vars)

  # Determine the number of dropped observations ----
  nt <- nrow(data)
  nobs <- nobs_(nobs_full, nobs_na, nt)

  # Extract model response and regressor matrix ----
  nms_sp <- NA
  p <- NA
  model_response_(data, formula)

  # Check for linear dependence ----
  # check_linear_dependence_(x, p)
  check_linear_dependence_(cbind(y, x), p + 1L)

  # Extract weights if required ----
  if (is.null(weights)) {
    wt <- rep(1.0, nt)
  } else {
    wt <- data[[weights]]
  }

  # Check validity of weights ----
  check_weights_(wt)

  # Compute and check starting guesses ----
  start_guesses_(beta_start, eta_start, y, x, beta, nt, wt, p, family)

  # Get names and number of levels in each fixed effects category ----
  nms_fe <- lapply(data[, .SD, .SDcols = k_vars], levels)
  lvls_k <- vapply(nms_fe, length, integer(1))

  # Generate auxiliary list of indexes for different sub panels ----
  k_list <- get_index_list_(k_vars, data)

  # Fit generalized linear model ----
  if (is.integer(y)) {
    y <- as.numeric(y)
  }
  fit <- feglm_fit_(
    beta, eta, y, x, wt, 0.0, family[["family"]], control, k_list
  )

  y <- NULL
  x <- NULL
  eta <- NULL

  # Add names to beta, hessian, and mx (if provided) ----
  names(fit[["coefficients"]]) <- nms_sp
  if (control[["keep_mx"]]) {
    colnames(fit[["mx"]]) <- nms_sp
  }
  dimnames(fit[["hessian"]]) <- list(nms_sp, nms_sp)

  # Add to fit list ----
  fit[["nobs"]] <- nobs
  fit[["lvls_k"]] <- lvls_k
  fit[["nms_fe"]] <- nms_fe
  fit[["formula"]] <- formula
  fit[["data"]] <- data
  fit[["family"]] <- family
  fit[["control"]] <- control

  # Return result list ----
  structure(fit, class = "feglm")
}