omega: Extract lag basis matrix In asw221/dlm: Distributed Lag Models for Built Environment Applications

Description

Extract lag basis matrix, Ω = [C_0, K_1]. See the definition below (which is borrowed from `basis`)

Usage

 ```1 2 3 4 5 6 7``` ```omega(object, ...) ## S4 method for signature 'LagBasis' omega(object, ...) ## S4 method for signature 'SmoothLag' omega(object, ...) ```

Arguments

 `object` An object storing details of the basis decomposition `...` additional arguments

Value

A square numeric matrix

Methods (by class)

• `LagBasis`: Method for `"LagBasis"` objects

• `SmoothLag`: Method for `"LagBasis"` objects

Decomposition

Once a basis function (δ()) and radii (r) are chosen, define the matrix, C_1[i, j] = δ(r_i, r_j), and let,

C_0 = [1, r]

C_1 = Q * R

M_1 = Q[-(1:2)]

K_1 = C_1 * M_1 * (M_1' * C_1 * M_1)^-0.5

where A[-j] denotes a matrix A with column(s) j removed. Then the (scaled) distributed lag effects are β = C_0 * α + K_1 * b, where b_l ~ N(0, σ^2_b), for l = 1, ..., L - 2.

asw221/dlm documentation built on May 8, 2019, 5:59 p.m.