sandwich2: Generate Time Series with Negative Binomial Distribution and...

In spass: Study Planning and Adaptation of Sample Size

Description

rnbinom.inar1 generates one or more independent time series following the NB-INAR(1) model. The generated data has negative binomial marginal distribution and an autoregressive covariance structure.

Usage

sandwich2(sigma, rho, theta, k, Time, dropout, Model)

Arguments

sigma	assymptotic standard deviation for Full and subpupulation
rho	correlation coefficient of the underlying autoregressive correlation structure. Must be between 0 and 1.
theta	correlation absorption coefficient if tinepoints are farther appart
k	sample size allocation factor between groups: see 'Details'.
Time	vector of measured timepoints
dropout	vector describing the percentage of dropout in every timepoint
Model	either 1 or 2, describing if 4-regressor or 3-regressor model was used.

Details

The generated marginal negative binomial distribution with mean mu = μ and size = η has density

(μ/(μ+η))^x Γ(x + η)/(Γ(x+1)Γ(η)) (η/(μ+η))^η

for 0 < μ, 0 < η and x=0, 1, 2, ....

Within the NB-INAR(1) model, the correlation between two time points t and s for rho = ρ is given through

ρ^|t-s|

for 0 ≤ ρ ≤ 1.

Value

rnbinom.inar1 returns a matrix of dimension n x tp with marginal negative binomial distribution with mean mu and dispersion parameter size, and an autoregressive correlation structure between time points.

Source

rnbinom.inar1 computes a reparametrization of the NB-INAR(1) model by McKenzie 1986 using code contributed by Thomas Asendorf.

References

McKenzie Ed (1986), Autoregressive Moving-Average Processes with Negative-Binomial and Geometric Marginal Distributions. Advances in Applied Probability Vol. 18, No. 3, pp. 679-705.

Examples

set.seed(8)
random<-rnbinom.inar1(n=1000, size=0.6, mu=2, rho=0.8, tp=6)
cor(random)

#Check the marginal distribution of time point 3
plot(table(random[,3])/1000, xlab="Probability", ylab="Observation")
lines(0:26, dnbinom(0:26, mu=2, size=0.6), col="red")
legend("topright",legend=c("Theoretical Marginal Distribution", "Observed Distribution"), 
col=c("red", "black"), lty=1, lwd=c(1,2))

spass documentation built on Jan. 13, 2021, 7:57 p.m.