dtomogplot: Dynamic Tomography Plot

In MCMCpack: Markov Chain Monte Carlo (MCMC) Package

Dynamic Tomography Plot

Description

dtomogplot is used to produce a tomography plot (see King, 1997) for a series of temporally ordered, partially observed 2 x 2 contingency tables.

Usage

dtomogplot(
  r0,
  r1,
  c0,
  c1,
  time.vec = NA,
  delay = 0,
  xlab = "fraction of r0 in c0 (p0)",
  ylab = "fraction of r1 in c0 (p1)",
  color.palette = heat.colors,
  bgcol = "black",
  ...
)

Arguments

r0	An (ntables \times 1) vector of row sums from row 0.
r1	An (ntables \times 1) vector of row sums from row 1.
c0	An (ntables \times 1) vector of column sums from column 0.
c1	An (ntables \times 1) vector of column sums from column 1.
time.vec	Vector of time periods that correspond to the elements of r_0, r_1, c_0, and c_1.
delay	Time delay in seconds between the plotting of the tomography lines. Setting a positive delay is useful for visualizing temporal dependence.
xlab	The x axis label for the plot.
ylab	The y axis label for the plot.
color.palette	Color palette to be used to encode temporal patterns.
bgcol	The background color for the plot.
...	further arguments to be passed

Details

Consider the following partially observed 2 by 2 contingency table:

	| Y=0	| Y=1	|
---------	---------	---------	---------
X=0	| Y_0	|	| r_0
---------	---------	---------	---------
X=1	| Y_1	|	| r_1
---------	---------	---------	---------
	| c_0	| c_1	| N

where r_0, r_1, c_0, c_1, and N are non-negative integers that are observed. The interior cell entries are not observed. It is assumed that Y_0|r_0 \sim \mathcal{B}inomial(r_0, p_0) and Y_1|r_1 \sim \mathcal{B}inomial(r_1, p_1).

This function plots the bounds on the maximum likelihood estimates for (p0, p1) and color codes them by the elements of time.vec.

References

Gary King, 1997. A Solution to the Ecological Inference Problem. Princeton: Princeton University Press.

Jonathan C. Wakefield. 2004. “Ecological Inference for 2 x 2 Tables.” Journal of the Royal Statistical Society, Series A. 167(3): 385445.

Kevin Quinn. 2004. “Ecological Inference in the Presence of Temporal Dependence." In Ecological Inference: New Methodological Strategies. Gary King, Ori Rosen, and Martin A. Tanner (eds.). New York: Cambridge University Press.

See Also

MCMChierEI, MCMCdynamicEI,tomogplot

Examples

## Not run: 
## simulated data example 1
set.seed(3920)
n <- 100
r0 <- rpois(n, 2000)
r1 <- round(runif(n, 100, 4000))
p0.true <- pnorm(-1.5 + 1:n/(n/2))
p1.true <- pnorm(1.0 - 1:n/(n/4))
y0 <- rbinom(n, r0, p0.true)
y1 <- rbinom(n, r1, p1.true)
c0 <- y0 + y1
c1 <- (r0+r1) - c0

## plot data
dtomogplot(r0, r1, c0, c1, delay=0.1)

## simulated data example 2
set.seed(8722)
n <- 100
r0 <- rpois(n, 2000)
r1 <- round(runif(n, 100, 4000))
p0.true <- pnorm(-1.0 + sin(1:n/(n/4)))
p1.true <- pnorm(0.0 - 2*cos(1:n/(n/9)))
y0 <- rbinom(n, r0, p0.true)
y1 <- rbinom(n, r1, p1.true)
c0 <- y0 + y1
c1 <- (r0+r1) - c0

## plot data
dtomogplot(r0, r1, c0, c1, delay=0.1)

## End(Not run)

MCMCpack documentation built on Sept. 11, 2024, 8:13 p.m.