Description Usage Arguments Details Value Author(s) References See Also Examples
eco
is used to fit the parametric Bayesian model (based on a
Normal/InverseWishart prior) for ecological inference in 2 \times 2
tables via Markov chain Monte Carlo. It gives the insample predictions as
well as the estimates of the model parameters. The model and algorithm are
described in Imai, Lu and Strauss (2008, 2011).
1 2 3 4 
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 individuallevel 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
NormalInverse 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 NormalInverse 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 NormalInverse 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  1W_{1i}  1W_{2i}  1Y_i  
X_i  1X_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}+(1X_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 insample 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. 
Kosuke Imai, Department of Politics, Princeton University, kimai@Princeton.Edu, http://imai.princeton.edu; Ying Lu,Center for Promoting Research Involving Innovative Statistical Methodology (PRIISM), New York University, ying.lu@nyu.Edu
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. 123. available at http://imai.princeton.edu/software/eco.html
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. 4169. available at http://imai.princeton.edu/research/eiall.html
ecoML
, ecoNP
, predict.eco
, summary.eco
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32  ## 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 outofsample 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 outofsample prediction
out1 < predict(res1, verbose = TRUE)
## summarize the results
summary(out1)
## End(Not run)

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