intercorr: Calculate Intermediate MVN Correlation for Ordinal,...

In AFialkowski/SimCorrMix: Simulation of Correlated Data with Multiple Variable Types Including Continuous and Count Mixture Distributions

Description

This function calculates a k x k intermediate matrix of correlations, where k = k_cat + k_cont + k_pois + k_nb, to be used in simulating variables with corrvar. The k_cont includes regular continuous variables and components of continuous mixture variables. The ordering of the variables must be ordinal, continuous non-mixture, components of continuous mixture variables, regular Poisson, zero-inflated Poisson, regular Negative Binomial (NB), and zero-inflated NB (note that it is possible for k_cat, k_cont, k_pois, and/or k_nb to be 0). There are no parameter input checks in order to decrease simulation time. All inputs should be checked prior to simulation with validpar. There is a message given if the calculated intermediate correlation matrix Sigma is not positive-definite because it may not be possible to find a MVN correlation matrix that will produce the desired marginal distributions. This function is called by the simulation function corrvar, and would only be used separately if the user wants to first find the intermediate correlation matrix. This matrix Sigma can be used as an input to corrvar.

Please see the Comparison of Correlation Methods 1 and 2 vignette for information about calculations by variable pair type and the differences between this function and intercorr2.

Usage

intercorr(k_cat = 0, k_cont = 0, k_pois = 0, k_nb = 0,
  method = c("Fleishman", "Polynomial"), constants = NULL,
  marginal = list(), support = list(), lam = NULL, p_zip = 0,
  size = NULL, prob = NULL, mu = NULL, p_zinb = 0, rho = NULL,
  seed = 1234, epsilon = 0.001, maxit = 1000, nrand = 1e+05,
  quiet = FALSE)

Arguments

k_cat	the number of ordinal (r >= 2 categories) variables (default = 0)
k_cont	the number of continuous non-mixture variables and components of continuous mixture variables (default = 0)
k_pois	the number of regular and zero-inflated Poisson variables (default = 0)
k_nb	the number of regular and zero-inflated Negative Binomial variables (default = 0)
method	the method used to generate the k_cont continuous variables. "Fleishman" uses a 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
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; default = list())
support	a list of length equal to k_cat; the i-th element is a vector of containing the r ordered support values; if not provided (i.e. support = list()), the default is for the i-th element to be the vector 1, ..., r
lam	a vector of lambda (mean > 0) constants for the regular and zero-inflated Poisson variables (see stats::dpois); the order should be 1st regular Poisson variables, 2nd zero-inflated Poisson variables
p_zip	a vector of probabilities of structural zeros (not including zeros from the Poisson distribution) for the zero-inflated Poisson variables (see VGAM::dzipois); if p_zip = 0, Y_{pois} has a regular Poisson distribution; if p_zip is in (0, 1), Y_{pois} has a zero-inflated Poisson distribution; if p_zip is in (-(exp(lam) - 1)^(-1), 0), Y_{pois} has a zero-deflated Poisson distribution and p_zip is not a probability; if p_zip = -(exp(lam) - 1)^(-1), Y_{pois} has a positive-Poisson distribution (see VGAM::dpospois); if length(p_zip) < length(lam), the missing values are set to 0 (and ordered 1st)
size	a vector of size parameters for the Negative Binomial variables (see stats::dnbinom); the order should be 1st regular NB variables, 2nd zero-inflated NB variables
prob	a vector of success probability parameters for the NB variables; order the same as in size
mu	a vector of mean parameters for the NB variables (*Note: either prob or mu should be supplied for all Negative Binomial variables, not a mixture; default = NULL); order the same as in size; for zero-inflated NB this refers to the mean of the NB distribution (see VGAM::dzinegbin)
p_zinb	a vector of probabilities of structural zeros (not including zeros from the NB distribution) for the zero-inflated NB variables (see VGAM::dzinegbin); if p_zinb = 0, Y_{nb} has a regular NB distribution; if p_zinb is in (-prob^size/(1 - prob^size), 0), Y_{nb} has a zero-deflated NB distribution and p_zinb is not a probability; if p_zinb = -prob^size/(1 - prob^size), Y_{nb} has a positive-NB distribution (see VGAM::dposnegbin); if length(p_zinb) < length(size), the missing values are set to 0 (and ordered 1st)
rho	the target correlation matrix which must be ordered 1st ordinal, 2nd continuous non-mixture, 3rd components of continuous mixtures, 4th regular Poisson, 5th zero-inflated Poisson, 6th regular NB, 7th zero-inflated NB; note that rho is specified in terms of the components of Y_{mix}
seed	the seed value for random number generation (default = 1234)
epsilon	the maximum acceptable error between the pairwise correlations (default = 0.001) in the calculation of ordinal intermediate correlations with ord_norm
maxit	the maximum number of iterations to use (default = 1000) in the calculation of ordinal intermediate correlations with ord_norm
nrand	the number of random numbers to generate in calculating intermediate correlations (default = 10000)
quiet	if FALSE prints simulation messages, if TRUE suppresses message printing

Value

the intermediate MVN correlation matrix

References

Please see references for SimCorrMix.

See Also

corrvar

Examples

Sigma1 <- intercorr(k_cat = 1, k_cont = 1, method = "Polynomial",
  constants = matrix(c(0, 1, 0, 0, 0, 0), 1, 6), marginal = list(0.3),
  support = list(c(0, 1)), rho = matrix(c(1, 0.4, 0.4, 1), 2, 2),
  quiet = TRUE)
## Not run: 
# 1 continuous mixture, 1 binary, 1 zero-inflated Poisson, and
# 1 zero-inflated NB variable
seed <- 1234

# Mixture of N(-2, 1) and N(2, 1)
constants <- rbind(c(0, 1, 0, 0, 0, 0), c(0, 1, 0, 0, 0, 0))

marginal <- list(0.3)
support <- list(c(0, 1))
lam <- 0.5
p_zip <- 0.1
size <- 2
prob <- 0.75
p_zinb <- 0.2

k_cat <- k_pois <- k_nb <- 1
k_cont <- 2
Rey <- matrix(0.35, 5, 5)
diag(Rey) <- 1
rownames(Rey) <- colnames(Rey) <- c("O1", "M1_1", "M1_2", "P1", "NB1")

# set correlation between components of the same mixture variable to 0
Rey["M1_1", "M1_2"] <- Rey["M1_2", "M1_1"] <- 0

Sigma2 <- intercorr(k_cat, k_cont, k_pois, k_nb, "Polynomial", constants,
  marginal, support, lam, p_zip, size, prob, mu = NULL, p_zinb, Rey, seed)

## End(Not run)

AFialkowski/SimCorrMix documentation built on May 30, 2019, 3:47 p.m.