margMLE {poisDoubleSamp}

Compute the marginal MLE of phi

Description

Compute the marginal MLE of the ratio of two Poisson rates in a two-sample Poisson rate problem with misclassified data given fallible and infallible datasets.

Usage

margMLE(data, N1, N2, N01, N02, l = 0.001, u = 1000, out = c("par", "all"))

Arguments

data

the vector of counts of the fallible data (z11, z12, z21, z22) followed by the infallible data (m011, m012, m021, m022, y01, y02)

N1

the opportunity size of group 1 for the fallible data

N2

the opportunity size of group 2 for the fallible data

N01

the opportunity size of group 1 for the infallible data

N02

the opportunity size of group 2 for the infallible data

l

the lower end of the range of possible phi's (for optim)

u

the upper end of the range of possible phi's (for optim)

out

"par" or "all" (for the output of optim)

Value

a named vector containing the marginal mle of phi

References

Kahle, D., P. Young, B. Greer, and D. Young (2016). "Confidence Intervals for the Ratio of Two Poisson Rates Under One-Way Differential Misclassification Using Double Sampling." Computational Statistics & Data Analysis, 95:122–132.

Examples

# small example
z11 <- 34; z12 <- 35; N1 <- 10;
z21 <- 22; z22 <- 31; N2 <- 10;
m011 <- 9; m012 <- 1; y01 <- 3; N01 <- 3;
m021 <- 8; m022 <- 8; y02 <- 2; N02 <- 3;
data <- c(z11, z12, z21, z22, m011, m012, m021, m022, y01, y02)

fullMLE(data, N1, N2, N01, N02)
margMLE(data, N1, N2, N01, N02)


## Not run: 

# big example :
z11 <- 477; z12 <- 1025; N1 <- 16186;
z21 <- 255; z22 <- 1450; N2 <- 18811;
m011 <- 38;  m012 <- 90; y01 <- 15; N01 <- 1500;
m021 <- 41; m022 <- 200; y02 <-  9; N02 <- 2500;
data <- c(z11, z12, z21, z22, m011, m012, m021, m022, y01, y02)

fullMLE(data, N1, N2, N01, N02)
margMLE(data, N1, N2, N01, N02)





## End(Not run)