MCMCpack (version 1.4-4)

dtomogplot: 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:

	| \(Y=0\)	| \(Y=1\)	|
---------	---------	---------	---------
\(X=0\)	| \(Y_0\)	|	| \(r_0\)
---------	---------	---------	---------
\(X=1\)	| \(Y_1\)	|	| \(r_1\)
---------	---------	---------	---------

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 {
# }
# 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)
# }
# NOT RUN {
# }