MCMCpack (version 1.7-1)

tomogplot: Tomography Plot

Description

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

Usage

tomogplot(
  r0,
  r1,
  c0,
  c1,
  xlab = "fraction of r0 in c0 (p0)",
  ylab = "fraction of r1 in c0 (p1)",
  bgcol = "white",
  ...
)

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.

xlab

The x axis label for the plot.

ylab

The y axis label for the plot.

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 estimatess for (p0, p1).

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.

See Also

MCMChierEI, MCMCdynamicEI, dtomogplot

Examples

r0 <- rpois(100, 500)
r1 <- rpois(100, 200)
c0 <- rpois(100, 100)
c1 <- (r0 + r1) - c0
tomogplot(r0, r1, c0, c1)