ppi_cW {scorematchingad}

Quickly Generate a Vector of Windham Exponents for the PPI Model

Description

These functions help to quickly generate a set of Windham exponents for use in ppi_robust() or Windham(). Rows and columns of A_L and b_L corresponding to components with strong concentrations of probability mass near zero have non-zero constant tuning exponent, and all other elements have a tuning constant of zero. All elements of \beta have a tuning exponent of zero.

The function ppi_cW_auto() automatically detects concentrations near zero by fitting a PPI distribution with A_L=0 and b_L=0 (i.e. a Dirichlet distribution) with the centred log-ratio transformation of the manifold.

Usage

ppi_cW(cW, ...)

ppi_cW_auto(cW, Y)

Arguments

cW

The value of the non-zero Windham tuning exponents.

...

Values of TRUE or FALSE in the same order of the components specifying that a component has probability mass concentrated near zero.

Y

A matrix of observations

Details

The Windham robustifying method involves weighting observations by a function of the proposed model density (Windham 1995). Scealy et al. (2024) found that only some of the tuning constants should be non-zero: the tuning exponents corresponding to \beta should be zero to avoid infinite weights;and to improve efficiency any rows or columns of A_L corresponding to components without concentrations of probability mass (i.e. outliers can't exist) should have exponents of zero. Scealy et al. (2024) set the remaining tuning exponents to a constant.

Value

A vector of the same length as the parameter vector of the PPI model. Elements of A_L will have a value of cW if both their row and column component has probability mass concentrated near zero. Similarly, elements of b_L will have a value of cW if their row corresponds to a component that has a probability mass concentrated near zero. All other elements are zero.

References

Scealy JL, Hingee KL, Kent JT, Wood ATA (2024). “Robust score matching for compositional data.” Statistics and Computing, 34, 93. doi:10.1007/s11222-024-10412-w.

Windham MP (1995). “Robustifying Model Fitting.” Journal of the Royal Statistical Society. Series B (Methodological), 57(3), 599–609. 2346159, http://www.jstor.org/stable/2346159.

Examples

Y <- rppi_egmodel(100)$sample
ppi_cW_auto(0.01, Y)
ppi_cW(0.01, TRUE, TRUE, FALSE)