# Dynamic Tomography Plot dtomogplot is used to produce a tomography plot (see King, 1997) for a series of temporally ordered, partially observed 2 x 2 contingency tables. ```r 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 c("$Y_0|r_0 \\sim\n$", "$\\mathcal{B}inomial(r_0, p_0)$") 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. ## Examples ```r ## 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) ``` ## 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`

dtomogplot function