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.
ppi_cW(cW, ...)ppi_cW_auto(cW, Y)
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.
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.
A matrix of observations
The Windham robustifying method involves weighting observations by a function of the proposed model density windham1995roscorematchingad. scealy2024ro;textualscorematchingad 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. scealy2024ro;textualscorematchingad set the remaining tuning exponents to a constant.
Y <- rppi_egmodel(100)$sample
ppi_cW_auto(0.01, Y)
ppi_cW(0.01, TRUE, TRUE, FALSE)
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