Description Usage Arguments Value References See Also

View source: R/intercorr_cont_pois2.R

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:

*ρ_{Y2,Z2} = \frac{1}{σ_{Y2}} ∑_{j = 1}^{r-1} φ(τ_{j})(y2_{j+1} - y2_{j})*

where

*φ(τ) = (2π)^{-1/2} * exp(-0.5 τ^2)*

Here, *y_{j}* is the j-th support
value and *τ_{j}* is *Φ^{-1}(∑_{i=1}^{j} Pr(Y = y_{i}))*. The power method correlation is given by:

*ρ_{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.

1 2 3 |

`method` |
the method used to generate the |

`constants` |
a matrix with |

`rho_cont_pois` |
a |

`pois_marg` |
a list of length equal to |

`pois_support` |
a list of length equal to |

a `k_cont x k_pois`

matrix whose rows represent the `k_cont`

continuous variables and columns represent the
`k_pois`

Poisson variables

Please see additional references in `intercorr_cont_pois`

.

Barbiero A & Ferrari PA (2015). Simulation of correlated Poisson variables. Applied Stochastic Models in Business and Industry, 31:669-80. doi: 10.1002/asmb.2072.

`find_constants`

, `power_norm_corr`

,
`intercorr2`

, `corrvar2`

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