ppi_robust {scorematchingad}

Robustly Estimate Parameters of the PPI Distribution

Description

ppi_robust() uses Windham() and ppi() to estimate a PPI distribution robustly. There are many arguments to the ppi() function and we highly recommend testing your arguments on ppi() first before running ppi_robust().

ppi_robust_alrgengamma() performs the Windham robustification algorithm exactly as described in Scealy et al. (2024) for score matching via log-ratio transform of the PPI model with b_L = 0. This function calls the more general Windham() and ppi().

Usage

ppi_robust(Y, cW, ...)

ppi_robust_alrgengamma(
  Y,
  cW,
  ...,
  fpcontrol = list(Method = "Simple", ConvergenceMetricThreshold = 1e-10)
)

Arguments

Y

A matrix of measurements. Each row is a measurement, each component is a dimension of the measurement.

cW

A vector of robustness tuning constants. Easy to build using ppi_cW() and ppi_cW_auto(). See Windham() for more details on cW.

...

Passed to Windham() and on to ppi().

fpcontrol

A named list of control arguments to pass to FixedPoint::FixedPoint() for the fixed point iteration.

Details

ppi_robust_alrgengamma(): must fit a PPI model via additive-log ratio transform of the simplex with b_L=0 fixed and the final element of \beta fixed. The default convergence metric and threshold are different to the default for ppi_robust() to match the implementation in (Scealy et al. 2024): convergence is measured by the change in the first element of \beta, and convergence is reached when the change is smaller than 1E-6. Override this behaviour by specifying the elements ConvergenceMetric and ConvergenceMetricThreshold in a list passed as fpcontrol. Windham() is called with alternative_populationinverse = TRUE.

Value

A list:

• est The estimated parameters in vector form (paramvec) and as AL, bL and beta.

• SE "Not calculated." Returned for consistency with other estimators.

• info Information returned in the optim slot of Windham(). Includes the final weights in finalweights.

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.

See Also

Other PPI model tools: dppi(), ppi_param_tools, ppi(), rppi()

Other Windham robustness functions: Windham(), vMF_robust()

Examples

set.seed(7)
model <- rppi_egmodel(100)
estsqrt <- ppi_robust(model$sample,
  cW = ppi_cW_auto(0.01, model$sample),
  paramvec_start = model$theta,
  trans = "sqrt", bdryw = "minsq", acut = 0.1)
set.seed(14)
model <- rppi_egmodel(100)
ppi_robust_alrgengamma(model$sample,
   cW = ppi_cW_auto(0.01, model$sample),
   paramvec = ppi_paramvec(betap = -0.5, p = ncol(model$sample)))