R: Calculate Intermediate MVN Correlation for Continuous -...

intercorr_cont_pois2 {SimCorrMix}

R Documentation

Calculate Intermediate MVN Correlation for Continuous - Poisson Variables: Correlation Method 2

Description

This function calculates a k_cont x k_pois intermediate matrix of correlations for the k_cont continuous and k_pois Poisson variables. It extends the methods of Demirtas et al. (2012, doi: 10.1002/sim.5362) and Barbiero & Ferrari (2015, doi: 10.1002/asmb.2072) by:

1) including non-normal continuous and regular or zero-inflated Poisson variables

2) allowing the continuous variables to be generated via Fleishman's third-order or Headrick's fifth-order transformation, and

3) since the count variables are treated as ordinal, using the point-polyserial and polyserial correlations to calculate the intermediate correlations (similar to findintercorr_cont_cat) in
SimMultiCorrData).

Here, the intermediate correlation between Z1 and Z2 (where Z1 is the standard normal variable transformed using Headrick's fifth-order or Fleishman's third-order method to produce a continuous variable Y1, and Z2 is the standard normal variable used to generate a Poisson variable via the inverse CDF method) is calculated by dividing the target correlation by a correction factor. The correction factor is the product of the point-polyserial correlation between Y2 and Z2 (described in Olsson et al., 1982, doi: 10.1007/BF02294164) and the power method correlation (described in Headrick & Kowalchuk, 2007, doi: 10.1080/10629360600605065) between Y1 and Z1. After the maximum support value has been found using maxcount_support, the point-polyserial correlation is given by:

\rho_{Y2,Z2} = \frac{1}{\sigma_{Y2}} \sum_{j = 1}^{r-1} \phi(\tau_{j})(y2_{j+1} - y2_{j})

where

\phi(\tau) = (2\pi)^{-1/2} * exp(-0.5 \tau^2)

Here, y_{j} is the j-th support value and \tau_{j} is \Phi^{-1}(\sum_{i=1}^{j} Pr(Y = y_{i})). The power method correlation is given by:

\rho_{Y1, Z1} = c_1 + 3c_3 + 15c_5,

where c_5 = 0 if method = "Fleishman". The function is used in intercorr2 and corrvar2. This function would not ordinarily be called by the user.

Usage

intercorr_cont_pois2(method = c("Fleishman", "Polynomial"),
  constants = NULL, rho_cont_pois = NULL, pois_marg = list(),
  pois_support = list())

Arguments

`method`	the method used to generate the `k_cont` continuous variables. "Fleishman" uses Fleishman's third-order polynomial transformation and "Polynomial" uses Headrick's fifth-order transformation.
`constants`	a matrix with `k_cont` rows, each a vector of constants c0, c1, c2, c3 (if `method` = "Fleishman") or c0, c1, c2, c3, c4, c5 (if `method` = "Polynomial"), like that returned by `find_constants`
`rho_cont_pois`	a `k_cont x k_pois` matrix of target correlations among continuous and Poisson variables; the Poisson variables should be ordered 1st regular, 2nd zero-inflated
`pois_marg`	a list of length equal to `k_pois` ordered 1st regular and 2nd zero-inflated; the i-th element is a vector of the cumulative probabilities defining the marginal distribution of the i-th variable; if the variable can take r values, the vector will contain r - 1 probabilities (the r-th is assumed to be 1); this is created within `intercorr2` and `corrvar2`
`pois_support`	a list of length equal to `k_pois` ordered 1st regular and 2nd zero-inflated; the i-th element is a vector of containing the r ordered support values, with a minimum of 0 and maximum determined via `maxcount_support`

Value

a k_cont x k_pois matrix whose rows represent the k_cont continuous variables and columns represent the k_pois Poisson variables

References

Please see additional references in intercorr_cont_pois.