eco | R Documentation |
eco
is used to fit the parametric Bayesian model (based on a
Normal/Inverse-Wishart prior) for ecological inference in 2 \times 2
tables via Markov chain Monte Carlo. It gives the in-sample predictions as
well as the estimates of the model parameters. The model and algorithm are
described in Imai, Lu and Strauss (2008, 2011).
eco( formula, data = parent.frame(), N = NULL, supplement = NULL, context = FALSE, mu0 = 0, tau0 = 2, nu0 = 4, S0 = 10, mu.start = 0, Sigma.start = 10, parameter = TRUE, grid = FALSE, n.draws = 5000, burnin = 0, thin = 0, verbose = FALSE )
formula |
A symbolic description of the model to be fit, specifying the
column and row margins of 2 \times 2 ecological tables. |
data |
An optional data frame in which to interpret the variables in
|
N |
An optional variable representing the size of the unit; e.g., the
total number of voters. |
supplement |
An optional matrix of supplemental data. The matrix has
two columns, which contain additional individual-level data such as survey
data for W_1 and W_2, respectively. If |
context |
Logical. If |
mu0 |
A scalar or a numeric vector that specifies the prior mean for
the mean parameter μ for (W_1,W_2) (or for (W_1, W_2, X)
if |
tau0 |
A positive integer representing the scale parameter of the
Normal-Inverse Wishart prior for the mean and variance parameter (μ,
Σ). The default is |
nu0 |
A positive integer representing the prior degrees of freedom of
the Normal-Inverse Wishart prior for the mean and variance parameter
(μ, Σ). The default is |
S0 |
A positive scalar or a positive definite matrix that specifies the
prior scale matrix of the Normal-Inverse Wishart prior for the mean and
variance parameter (μ, Σ) . If it is a scalar, then the prior
scale matrix will be a diagonal matrix with the same dimensions as
Σ and the diagonal elements all take value of |
mu.start |
A scalar or a numeric vector that specifies the starting
values of the mean parameter μ. If it is a scalar, then its value
will be repeated to yield a vector of the length of μ, otherwise, it
needs to be a vector of same length as μ. When
|
Sigma.start |
A scalar or a positive definite matrix that specified the
starting value of the variance matrix Σ. If it is a scalar, then
the prior scale matrix will be a diagonal matrix with the same dimensions as
Σ and the diagonal elements all take value of |
parameter |
Logical. If |
grid |
Logical. If |
n.draws |
A positive integer. The number of MCMC draws. The default is
|
burnin |
A positive integer. The burnin interval for the Markov chain;
i.e. the number of initial draws that should not be stored. The default is
|
thin |
A positive integer. The thinning interval for the Markov chain;
i.e. the number of Gibbs draws between the recorded values that are skipped.
The default is |
verbose |
Logical. If |
An example of 2 \times 2 ecological table for racial voting is given below:
black voters | white voters | |||
vote | W_{1i} | W_{2i} | Y_i | |
not vote | 1-W_{1i} | 1-W_{2i} | 1-Y_i | |
X_i | 1-X_i |
where Y_i and X_i represent the observed margins, and W_1 and W_2 are unknown variables. In this exmaple, Y_i is the turnout rate in the ith precint, X_i is the proproption of African American in the ith precinct. The unknowns W_{1i} an dW_{2i} are the black and white turnout, respectively. All variables are proportions and hence bounded between 0 and 1. For each i, the following deterministic relationship holds, Y_i=X_i W_{1i}+(1-X_i)W_{2i}.
An object of class eco
containing the following elements:
call |
The matched call. |
X |
The row margin, X. |
Y |
The column margin, Y. |
N |
The size of each table, N. |
burnin |
The number of initial burnin draws. |
thin |
The thinning interval. |
nu0 |
The prior degrees of freedom. |
tau0 |
The prior scale parameter. |
mu0 |
The prior mean. |
S0 |
The prior scale matrix. |
W |
A three dimensional array storing the posterior in-sample predictions of W. The first dimension indexes the Monte Carlo draws, the second dimension indexes the columns of the table, and the third dimension represents the observations. |
Wmin |
A numeric matrix storing the lower bounds of W. |
Wmax |
A numeric matrix storing the upper bounds of W. |
The
following additional elements are included in the output when
parameter = TRUE
.
mu |
The posterior draws of the population mean parameter, μ. |
Sigma |
The posterior draws of the population variance matrix, Σ. |
Imai, Kosuke, Ying Lu and Aaron Strauss. (2011). “eco: R Package for Ecological Inference in 2x2 Tables” Journal of Statistical Software, Vol. 42, No. 5, pp. 1-23.
Imai, Kosuke, Ying Lu and Aaron Strauss. (2008). “Bayesian and Likelihood Inference for 2 x 2 Ecological Tables: An Incomplete Data Approach” Political Analysis, Vol. 16, No. 1 (Winter), pp. 41-69.
ecoML
, ecoNP
, predict.eco
, summary.eco
## load the registration data ## Not run: data(reg) ## NOTE: convergence has not been properly assessed for the following ## examples. See Imai, Lu and Strauss (2008, 2011) for more ## complete analyses. ## fit the parametric model with the default prior specification res <- eco(Y ~ X, data = reg, verbose = TRUE) ## summarize the results summary(res) ## obtain out-of-sample prediction out <- predict(res, verbose = TRUE) ## summarize the results summary(out) ## load the Robinson's census data data(census) ## fit the parametric model with contextual effects and N ## using the default prior specification res1 <- eco(Y ~ X, N = N, context = TRUE, data = census, verbose = TRUE) ## summarize the results summary(res1) ## obtain out-of-sample prediction out1 <- predict(res1, verbose = TRUE) ## summarize the results summary(out1) ## End(Not run)
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