boral (version 0.4)

create.life: Simulate a Multivariate Response Matrix

Description

Simulate a multivariate response matrix, given parameters such as but not necessarily all of: family, number of latent variables and related coefficients, an matrix of explanatory variables and related coefficients, row effects, cutoffs for proportional odds regression of ordinal responses.

Usage

create.life(true.lv = NULL, lv.coefs, X = NULL, X.coefs = NULL, 
     family, site.coefs = NULL, trial.size = NULL, 
     cutoffs = NULL, powerparam = NULL, manual.dim = NULL)

Arguments

true.lv

A matrix of true latent variables. With multivariate abundance data in ecology for instance, each row corresponds to the true site ordination coordinates. Defaults to NULL, in which case no latent variables are included.

lv.coefs

The column-specific intercepts, regression coefficients relating to the latent variables true.lv, and dispersion parameters.

X

An model matrix of covariates, which can be included as part of the data generation. Defaults to NULL, in which case no model matrix is used. No intercept column should be included in X.

X.coefs

The coefficients relating to the model matrix X.

family

Either a single element, or a vector of length equal to the number of columns in $y$. The former assumes all columns of $y$ come from this distribution. The latter option allows for different distributions for each column of $y$. Elements can be one of "b

site.coefs

Row effects. Defaults to NULL, in which case it is assumed there are no row effects.

trial.size

Either equal to NULL, a single element, or a vector of length equal to the number of columns in $y$. If a single element, then all columns assumed to be binomially distributed will have trial size set to this. If a vector, different trial sizes are allowe

cutoffs

A vector of common common cutoffs for proportional odds regression when any of family is ordinal. They should be increasing order. Defaults to NULL.

powerparam

A common power parameter for tweedie regression when any of family is tweedie. Defaults to NULL.

manual.dim

A vector of length 2, containing the number of rows ($n$) and columns ($p$) for the multivariate response matrix. This is a "backup" argument only required when create.life can not determine how many rows or columns the multivariate response

Value

• A multivariate response matrix of dimension $n$ times $p$.

See Also

boral for the default function for fitting a boral (Bayesian Ordination and Regression AnaLysis) model.

Examples

## Let's simulate a multivariate response matrix of normally distributed data
## (normal data doesn't occur too often in ecology!)
library(mvtnorm)

true.lv <- rbind(rmvnorm(n=15,mean=c(1,2)),rmvnorm(n=15,mean=c(-3,-1))) 
## 30 rows (sites) with two latent variables 
lv.coefs <- cbind(matrix(runif(30*3),30,3),1)
## 30 columns (species)

X <- matrix(rnorm(30*4),30,4) 
## 4 explanatory variables
X.coefs <- matrix(rnorm(30*4),30,4)

sim.y <- create.life(true.lv, lv.coefs, X, X.coefs, family = "normal")

fit.boral <- boral(sim.y, X = X, family = "normal", num.lv = 2, 
     site.eff = FALSE, save.model = FALSE)

lvsplot(fit.boral)

## Simulate a multivariate response matrix of ordinal data

true.lv <- rbind(rmvnorm(10,mean=c(-2,-2)),rmvnorm(10,mean=c(2,2)))
## 20 rows (sites) with two latent variables 
true.lv.coefs <- rmvnorm(30,mean = rep(0,3)); 
## 30 columns (species)
true.lv.coefs[nrow(true.lv.coefs),1] <- -sum(true.lv.coefs[-nrow(true.lv.coefs),1])
## Impose a sum-to-zero constraint on the column effects
true.ordinal.cutoffs <- seq(-2,10,length=10-1)
## Cutoffs for proportional odds regression (must be in increasing order)

sim.y <- create.life(true.lv = true.lv, lv.coefs = true.lv.coefs, 
     family = "ordinal", cutoffs = true.ordinal.cutoffs) 

fit.boral <- boral(y = sim.y, family = "ordinal", num.lv = 2, site.eff = F, 
     n.thin = 5, save.model = FALSE, calc.ics = TRUE)