analyze2x2 {SimpleTable} | R Documentation |
analyze2x2
performs a causal Bayesian analysis of
a 2 x 2 table in which it is assumed that unmeasured confounding is
present. The binary treatment variable is denoted X =
0 (control), 1 (treatment); and the binary outcome variable
is denoted Y = 0 (failure), 1 (success). The
notation and terminology are from Quinn (2008).
analyze2x2(C00, C01, C10, C11, a00, a01, a10, a11, b00, b01, b10, b11, c00, c01, c10, c11, nsamp = 50000)
C00 |
The number of observations in (X=0, Y=0) cell of the table. In other words, the number of observations that received control and failed. |
C01 |
The number of observations in (X=0, Y=1) cell of the table. In other words, the number of observations that received control and succeeded. |
C10 |
The number of observations in (X=1, Y=0) cell of the table. In other words, the number of observations that received treatment and failed. |
C11 |
The number of observations in (X=1, Y=1) cell of the table. In other words, the number of observations that received treatment and succeeded. |
a00 |
One of four parameters (with a01 , a10 , and
a11 governing the Dirichlet prior for theta
(the joint probabilities of X and Y). This prior has the
effect of adding a00 - 1 observations to the (X=0, Y=0)
cell of the table. |
a01 |
One of four parameters (with a00 , a10 , and
a11 governing the Dirichlet prior for theta
(the joint probabilities of X and Y). This prior has the
effect of adding a01 - 1 observations to the (X=0, Y=1)
cell of the table. |
a10 |
One of four parameters (with a00 , a01 , and
a11 governing the Dirichlet prior for theta
(the joint probabilities of X and Y). This prior has the
effect of adding a10 - 1 observations to the (X=1, Y=0)
cell of the table. |
a11 |
One of four parameters (with a00 , a01 , and
a10 governing the Dirichlet prior for theta
(the joint probabilities of X and Y). This prior has the
effect of adding a11 - 1 observations to the (X=1, Y=1)
cell of the table. |
b00 |
One of two parameters (with c00 ) governing the
beta prior for the distribution of potential outcome types within
the (X=0, Y=0) cell of the table. This prior adds the same
information as would be gained from observing b00 - 1 Helped
units in the (X=0, Y=0) cell of the table. |
b01 |
One of two parameters (with c01 ) governing the
beta prior for the distribution of potential outcome types within
the (X=0, Y=1) cell of the table. This prior adds the same
information as would be gained from observing b01 - 1 Always Succeed
units in the (X=0, Y=1) cell of the table. |
b10 |
One of two parameters (with c10 ) governing the
beta prior for the distribution of potential outcome types within
the (X=1, Y=0) cell of the table. This prior adds the same
information as would be gained from observing b10 - 1 Hurt
units in the (X=1, Y=0) cell of the table. |
b11 |
One of two parameters (with c11 ) governing the
beta prior for the distribution of potential outcome types within
the (X=1, Y=1) cell of the table. This prior adds the same
information as would be gained from observing b11 - 1 Always Succeed
units in the (X=1, Y=1) cell of the table. |
c00 |
One of two parameters (with b00 ) governing the
beta prior for the distribution of potential outcome types within
the (X=0, Y=0) cell of the table. This prior adds the same
information as would be gained from observing b00 - 1 Never Succeed
units in the (X=0, Y=0) cell of the table. |
c01 |
One of two parameters (with b01 ) governing the
beta prior for the distribution of potential outcome types within
the (X=0, Y=1) cell of the table. This prior adds the same
information as would be gained from observing c01 - 1 Hurt
units in the (X=0, Y=1) cell of the table. |
c10 |
One of two parameters (with b10 ) governing the
beta prior for the distribution of potential outcome types within
the (X=1, Y=0) cell of the table. This prior adds the same
information as would be gained from observing c10 - 1 Never Succeed
units in the (X=1, Y=0) cell of the table. |
c11 |
One of two parameters (with b11 ) governing the
beta prior for the distribution of potential outcome types within
the (X=1, Y=1) cell of the table. This prior adds the same
information as would be gained from observing b11 - 1 Helped
units in the (X=1, Y=1) cell of the table. |
nsamp |
Size of the Monte Carlo sample used to summarize the posterior. |
analyze2x2
performs the Bayesian analysis of a 2 x 2
table described in Quinn (2008). summary
and plot
methods can be used to examine the output.
An object of class SimpleTable
.
Kevin M. Quinn
Quinn, Kevin M. 2008. ``What Can Be Learned from a Simple Table: Bayesian Inference and Sensitivity Analysis for Causal Effects from 2 x 2 and 2 x 2 x K Tables in the Presence of Unmeasured Confounding.'' Working Paper.
ConfoundingPlot
, analyze2x2xK
, ElicitPsi
, summary.SimpleTable
, plot.SimpleTable
## Not run: ## Example from Quinn (2008) ## (original data from Oliver and Wolfinger. 1999. ## ``Jury Aversion and Voter Registration.'' ## American Political Science Review. 93: 147-152.) ## ## Y=0 Y=1 ## X=0 19 143 ## X=1 114 473 ## ## uniform prior on the potential outcome distributions S.unif <- analyze2x2(C00=19, C01=143, C10=114, C11=473, a00=.25, a01=.25, a10=.25, a11=.25, b00=1, c00=1, b01=1, c01=1, b10=1, c10=1, b11=1, c11=1) summary(S.unif) plot(S.unif) ## a prior belief in an essentially negative monotonic treatment effect S.mono <- analyze2x2(C00=19, C01=143, C10=114, C11=473, a00=.25, a01=.25, a10=.25, a11=.25, b00=0.02, c00=10, b01=25, c01=3, b10=3, c10=25, b11=10, c11=0.02) summary(S.mono) plot(S.mono) ## End(Not run)