Z_byname: Z matrix from 'X_0' and 'X_T' matrices
In MatthewHeun/LMDIR: Log Mean Divisia Index Decomposition in R

View source: R/util.R

Z_byname

R Documentation

Z matrix from `X_0` and `X_T` matrices

Description

The formula for Z is

Z_ij = logmean(v_Ti1, v_0i1) * log(X_Tij / X_0ij)

where v is a column vector formed by row products of X. The 0 and T subscripts on X and v indicate an initial time (0) and a final time (T). The i and j subscripts on Z, v, and X are matrix indices.

Usage

Z_byname(X_0, X_T, fillrow = NULL)

Arguments

`X_0`	an `X` matrix for initial time `0`
`X_T`	an `X` matrix for final time `T`
`fillrow`	a row vector of type `matrix` with column names identical to `X_0` and `X_T`. (See details.)

Details

Z and X are category-by-factor matrices, and v is a category-by-1 column vector.

When a category comes and goes through time, the category row can be absent from the X matrix at one time but present in the X matrix at an adjacent time. If the missing category row is replaced by 0s, the LMDI algorithm fails due to log(0) errors. The usual advice is to insert a row consisting not of 0s but rather filled with small numbers (e.g., 1e-10).

But the usual advice doesn't represent reality for some LMDI decomposition analyses. For example, the missing row may be caused by only one of the many factors being zero, the other factors being non-zero. To provide greater flexibility, this function provides the fillrow argument. Callers can supply their own fillrow, a single-row matrix with column names identical to X_0 and X_T. If fillrow is not specified, the usual advice will be followed, and a row vector consisting of very small values (1e-10) for each factor will be inserted into X_0 or X_T, as appropriate.

Note that the lmdi() function passes its fillrow argument, if present, to Z_byname.

The nomenclature for this function comes from Ang, Zhang, and Choi (1998). This function fully accounts for the degenerate cases found in Table 2, p. 492 of Ang, Zhang, and Choi (1998). When 0s are encountered in emptyrow, this function employs the method for dealing with the log(0) problem suggested by Wood and Lenzen (2006).