VGAM (version 1.0-4)

# UtilitiesVGAM: Utility Functions for the VGAM Package

## Description

A set of common utility functions used by VGAM family functions.

## Usage

```param.names(string, S)
dimm(M, hbw = M)
interleave.VGAM(.M, M1, inverse = FALSE)```

## Arguments

string

Character. Name of the parameter.

M, .M

Numeric. The total number of linear/additive predictors, called \(M\). By total, it is meant summed over the number of responses. Often, \(M\) is the total number of parameters to be estimated (but this is not the same as the number of regression coefficients, unless the RHS of the formula is an intercept-only). The use of `.M` is unfortunate, but it is a compromise solution to what is presented in Yee (2015). Ideally, `.M` should be just `M`.

M1

Numeric. The number of linear/additive predictors for one response, called \(M_1\). This argument used to be called `M`, but is now renamed properly.

inverse

Logical. Useful for the inverse function of `interleave.VGAM()`.

S

Numeric. The number of responses.

hbw

Numeric. The half-bandwidth, which measures the number of bands emanating from the central diagonal band.

## Value

For `param.names()`, this function returns the parameter names for \(S\) responses, i.e., `string` is returned unchanged if \(S=1\), else `paste(string, 1:S, sep = "")`.

For `dimm()`, this function returns the number of elements to be stored for each of the working weight matrices. They are represented as columns in the matrix `wz` in e.g., `vglm.fit()`. See the matrix-band format described in Section 18.3.5 of Yee (2015).

For `interleave.VGAM()`, this function returns a reordering of the linear/additive predictors depending on the number of responses. The arguments presented in Table 18.5 may not be valid in your version of Yee (2015).

## Details

See Yee (2015) for some details about some of these functions.

## References

Yee, T. W. (2015) Vector Generalized Linear and Additive Models: With an Implementation in R. New York, USA: Springer.

`CommonVGAMffArguments`, `VGAM-package`.

## Examples

Run this code
```# NOT RUN {
param.names("shape", 1)  # "shape"
param.names("shape", 3)  # c("shape1", "shape2", "shape3")

dimm(3, hbw = 1)  # Diagonal matrix; the 3 elements need storage.
dimm(3)  # A general 3 x 3 symmetrix matrix has 6 unique elements.
dimm(3, hbw = 2)  # Tridiagonal matrix; the 3-3 element is 0 and unneeded.

M1 <- 2; ncoly <- 3; M <- ncoly * M1
mynames1 <- param.names("location", ncoly)
mynames2 <- param.names("scale",    ncoly)
(parameters.names <- c(mynames1, mynames2)[interleave.VGAM(M, M1 = M1)])
# The  following is/was in Yee (2015) and has a poor/deceptive style:
(parameters.names <- c(mynames1, mynames2)[interleave.VGAM(M, M  = M1)])
parameters.names[interleave.VGAM(M, M1 = M1, inverse = TRUE)]
# }
```

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