best_approx_poly: This function returns the coefficients (functions of V =...

In cgaillac/MarginalFElogit: Estimation of Average Marginal Effects in Fixed Effect Logit Models

This function returns the coefficients (functions of V = exp(X'beta)) of the best (in the uniform sense) approximation of Omega(·, x, beta) * h(·, x, beta) by a polynomial of degree at most T. It also returns the coefficients of the original polynomial, its top coefficients, and the derivative of the coefficients of the approximating polynomials with respect to beta. See Assumption 3 in DDL and the discussion under that assumption for the exact formulae of the functions. Here, we ignore the beta factor at the start, and use the h corresponding to the AME, unless forATE is TRUE.

Description

This function returns the coefficients (functions of V = exp(X'beta)) of the best (in the uniform sense) approximation of Omega(·, x, beta) * h(·, x, beta) by a polynomial of degree at most T. It also returns the coefficients of the original polynomial, its top coefficients, and the derivative of the coefficients of the approximating polynomials with respect to beta. See Assumption 3 in DDL and the discussion under that assumption for the exact formulae of the functions. Here, we ignore the beta factor at the start, and use the h corresponding to the AME, unless forATE is TRUE.

Usage

best_approx_poly(Vtilde, Xtilde, forATE = FALSE, signFactorCoeffshATE = NULL)

Arguments

Vtilde	a matrix of size n x Tmax containing the exp((x-x_t)'beta) for each observation, t being the period at which the AME is being computed. For the ATE, we want Vtilde = exp(x'beta - v(x, beta)).
Xtilde	an array of size n x Tmax x dimX containing, for each observation, X - X_t where t is the period at which the AME is being computed. For the ATE we want X - X_t^(1 - X_tk) (i.e. the second term is the same as X_t except the k_th coordinate changes from 0 to 1 or from 1 to 0).
forATE	(default FALSE) If TRUE, we return the formula used for the ATE instead of for the AME.
signFactorCoeffshATE	(default NULL) The sign to multiply the function h by in the ATE case. This parameter is unnecessary for the AME.

Value

a list containing: - bestPoly: a matrix of size n x (Tmax + 1) where each row represents the coefficient of the best approximation polynomial of Omega(., x, beta). Coefficients start with the constant coefficient, and there are (Tobsd[i] + 1) coefficients on each row, where Tobsd[i] is the number of periods observed for the relevant individuals. Subsequent entries on the rows are 0s - topCoeffOmega: a vector of length n containing the top coefficient of the original Omega coefficient for each individual. - derivCoeffsOmegaDbeta: derivative of the coefficients stored in bestPoly relative to beta. - coeffsOmega: a matrix of size n x (Tmax + 2) where each row represents the coefficient of the polynomial Omega(., x, beta). Coefficients start with the constant coefficient and there are (Tobsd[i] + 2) coefficients on each row where Tobsd[i] is the number of periods observed for the relevant individuals. Subsequent entries on the rows are 0s.

cgaillac/MarginalFElogit documentation built on Dec. 24, 2024, 3:23 p.m.