findintercorr_cat_pois: Calculate Intermediate MVN Correlation for Ordinal - Poisson...
In SimMultiCorrData: Simulation of Correlated Data with Multiple Variable Types

Description Usage Arguments Value References See Also

This function calculates a k_cat x k_pois intermediate matrix of correlations for the k_cat ordinal (r >= 2 categories) and k_pois Poisson variables. It extends the method of Amatya & Demirtas (2015, doi: 10.1080/00949655.2014.953534) to ordinal - Poisson pairs. Here, the intermediate correlation between Z1 and Z2 (where Z1 is the standard normal variable discretized to produce an ordinal 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 upper Frechet-Hoeffding bound on the correlation between a Poisson variable and the normal variable used to generate it (see chat_pois) and a simulated GSC upper bound on the correlation between an ordinal variable and the normal variable used to generate it (see Demirtas & Hedeker, 2011, doi: 10.1198/tast.2011.10090). The function is used in findintercorr and rcorrvar. This function would not ordinarily be called by the user.

1 2	findintercorr_cat_pois(rho_cat_pois, marginal, lam, nrand = 100000, seed = 1234)

`rho_cat_pois`	a `k_cat x k_pois` matrix of target correlations among ordinal and Poisson variables
`marginal`	a list of length equal to `k_cat`; 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)
`lam`	a vector of lambda (> 0) constants for the Poisson variables (see `Poisson`)
`nrand`	the number of random numbers to generate in calculating the bound (default = 10000)
`seed`	the seed used in random number generation (default = 1234)

a k_cat x k_pois matrix whose rows represent the k_cat ordinal variables and columns represent the k_pois Poisson variables

Amatya A & Demirtas H (2015). Simultaneous generation of multivariate mixed data with Poisson and normal marginals. Journal of Statistical Computation and Simulation, 85(15): 3129-39. doi: 10.1080/00949655.2014.953534.

Demirtas H & Hedeker D (2011). A practical way for computing approximate lower and upper correlation bounds. American Statistician, 65(2): 104-109. doi: 10.1198/tast.2011.10090.

Frechet M. Sur les tableaux de correlation dont les marges sont donnees. Ann. l'Univ. Lyon SectA. 1951;14:53-77.

Hoeffding W. Scale-invariant correlation theory. In: Fisher NI, Sen PK, editors. The collected works of Wassily Hoeffding. New York: Springer-Verlag; 1994. p. 57-107.

Yahav I & Shmueli G (2012). On Generating Multivariate Poisson Data in Management Science Applications. Applied Stochastic Models in Business and Industry, 28(1): 91-102. doi: 10.1002/asmb.901.

chat_pois, findintercorr, rcorrvar

SimMultiCorrData documentation built on May 2, 2019, 9:50 a.m.