iqr_milp: Compute inverse quantile regression estimator
In omkarakatta/ivqr: Instrumental Variables Quantile Regression

iqr_milp

R Documentation

Compute inverse quantile regression estimator

Description

Solve a mixed integer linear program to compute the inverse quantile regression estimator.

Usage

iqr_milp(
  Y,
  X,
  D,
  Z,
  Phi = linear_projection(D, X, Z),
  tau,
  O_neg = NULL,
  O_pos = NULL,
  M = NULL,
  TimeLimit = 300,
  VarHintVal_bool = FALSE,
  VarHintPri_bool = FALSE,
  BranchPriority_bool = FALSE,
  sparse = TRUE,
  attributes = list(),
  params = list(FeasibilityTol = 1e-06, LogToConsole = 0),
  start_method = NULL,
  start = NULL,
  fix = NULL,
  quietly = TRUE,
  show_progress = TRUE,
  LogFileName = "",
  LogFileExt = ".log"
)

Arguments

`Y`	Dependent variable (vector of length n)
`X`	Exogenous variable (including constant vector) (n by p_X matrix)
`D`	Endogenous variable (n by p_D matrix)
`Z`	Instrumental variable (n by p_Z matrix)
`Phi`	Transformation of X and Z to be used in the program; defaults to the linear projection of D on X and Z (matrix with n rows)
`tau`	Quantile (number between 0 and 1)
`O_neg, O_pos`	Indices for residuals whose sign is fixed to be negative and positive, respectively (vectors)
`M`	A large number that bounds the absolute value of the residuals (a positive number); defaults to 2 times the largest absolute residual from quantile regression of Y on X and D
`TimeLimit`	Maximum time (in seconds) spent on a linear program; defaults to 300, will be appended to `params`
`VarHintVal_bool`	If TRUE, instead of fixing the binary variables as determined by `O_neg,O_pos`, we will "hint" these values; defaults to FALSE; see https://www.gurobi.com/documentation/9.1/refman/varhintval.html#attr:VarHintVal; overrides `attributes`
`VarHintPri_bool`	If TRUE, we specify the strength of the "hints" according to the magnitude of the residual from a naive QR; only valid if VarHintVal_bool is TRUE; overrides `attributes`; defaults to FALSE; see https://www.gurobi.com/documentation/9.1/refman/varhintpri.html#attr:VarHintPri
`BranchPriority_bool`	If TRUE, we specify which variables will be branched on first according to the magnitude of the residual from a naive QR; defaults to FALSE; see https://www.gurobi.com/documentation/9.1/refman/branchpriority.html
`sparse`	If TRUE (default), use sparse matrices
`attributes`	named list of Gurobi attributes, see https://www.gurobi.com/documentation/9.1/refman/attributes.html and https://www.gurobi.com/documentation/9.1/refman/the_model_argument.html; defaults to empty list
`params`	Gurobi parameters, see https://www.gurobi.com/documentation/9.1/refman/parameter_descriptions.html
`start_method`	Feed into `compute_warmstart` in the default value of `start`; defaults to NULL, ignored if `start` is not NULL
`start`	Gurobi attribute, see https://www.gurobi.com/documentation/9.1/examples/mip_starts.html; If NULL (default), no starting solution will be provided; see `compute_warmstart`
`fix`	Fix decision variables; If NULL (default), no starting solution will be provided; if NA, the respective decision variable won't be fixed; decision variables are: beta_X beta_Phi_plus beta_Phi_minus ; note: abs(beta_Phi) = beta_Phi_plus + beta_Phi_minus beta_D u v a k l
`quietly`	If TRUE (default), supress messages during execution (boolean)
`show_progress`	If TRUE (default), sends progress messages during execution (boolean)
`LogFileName`	Name of Gurobi log file; If string is empty (default), Gurobi log won't be saved (string)
`LogFileExt`	Extension of Gurobi log file; If `LogFileName` is empty, then Gurobi log won't be saved and this argument will be ignored; defaults to "log" (string)