Bayesian Factor Analysis
a symbolic representation of the model to be
estimated, in the form ~ Y1 + Y2 + Y3, where Y1, Y2, and Y3 are variables
of interest in factor analysis (manifest variables), assumed to be
normally distributed. The model requires a minimum of three manifest
variables contained in the
same dataset. The + symbol means ``inclusion'' not
``addition.''
number of the factors to be fitted (defaults to 2).
the name of a statistical model to estimate. For a list of other supported models and their documentation see: http://docs.zeligproject.org/articles/.
the name of a data frame containing the variables
referenced in the formula or a list of multiply imputed data frames
each having the same variable names and row numbers (created by
Amelia or to_zelig_mi).
additional arguments passed to zelig,
relevant for the model to be estimated.
a factor variable contained in data. If supplied,
zelig will subset
the data frame based on the levels in the by variable, and
estimate a model for each subset. This can save a considerable amount of
effort. You may also use by to run models using MatchIt
subclasses.
If is set to 'TRUE' (default), the model citation will be printed to the console.
Depending on the class of model selected, zelig will return
an object with elements including coefficients, residuals,
and formula which may be summarized using
summary(z.out) or individually extracted using, for example,
coef(z.out). See
http://docs.zeligproject.org/articles/getters.html for a list of
functions to extract model components. You can also extract whole fitted
model objects using from_zelig_model.
zelig(formula, data, model = NULL, ..., weights = NULL, by, bootstrap = FALSE)The zelig function estimates a variety of statistical models
In addition, zelig() accepts the following additional arguments for model specification:
lambda.constraints: list containing the equality or
inequality constraints on the factor loadings. Choose from one of the following forms:
varname = list(): by default, no constraints are imposed.
varname = list(d, c): constrains the dth loading for the
variable named varname to be equal to c.
varname = list(d, +): constrains the dth loading for the variable named varname to be positive;
varname = list(d, -): constrains the dth loading for the variable named varname to be negative.
std.var: defaults to FALSE (manifest variables are rescaled to
zero mean, but retain observed variance). If TRUE, the manifest
variables are rescaled to be mean zero and unit variance.
In addition, zelig() accepts the following additional inputs for bayes.factor:
burnin: number of the initial MCMC iterations to be discarded (defaults to 1,000).
mcmc: number of the MCMC iterations after burnin (defaults to 20,000).
thin: thinning interval for the Markov chain. Only every thin-th
draw from the Markov chain is kept. The value of mcmc must be divisible
by this value. The default value is 1.
verbose: defaults to FALSE. If TRUE, the
progress of the sampler (every 10
seed: seed for the random number generator. The default is NA which
corresponds to a random seed 12345.
Lambda.start: starting values of the factor loading matrix \(\Lambda\), either a
scalar (all unconstrained loadings are set to that value), or a matrix with
compatible dimensions. The default is NA, where the start value are set to
be 0 for unconstrained factor loadings, and 0.5 or - 0.5 for constrained
factor loadings (depending on the nature of the constraints).
Psi.start: starting values for the uniquenesses, either a scalar
(the starting values for all diagonal elements of \(\Psi\) are set to be this value),
or a vector with length equal to the number of manifest variables. In the latter
case, the starting values of the diagonal elements of \(\Psi\) take the values of
Psi.start. The default value is NA where the starting values of the all the
uniquenesses are set to be 0.5.
store.lambda: defaults to TRUE, which stores the posterior draws of the factor loadings.
store.scores: defaults to FALSE. If TRUE, stores the posterior draws of the
factor scores. (Storing factor scores may take large amount of memory for a large
number of draws or observations.)
The model also accepts the following additional arguments to specify prior parameters:
l0: mean of the Normal prior for the factor loadings, either a scalar or a
matrix with the same dimensions as \(\Lambda\). If a scalar value, that value will be the
prior mean for all the factor loadings. Defaults to 0.
L0: precision parameter of the Normal prior for the factor loadings, either
a scalar or a matrix with the same dimensions as \(\Lambda\). If L0 takes a scalar value,
then the precision matrix will be a diagonal matrix with the diagonal elements
set to that value. The default value is 0, which leads to an improper prior.
a0: the shape parameter of the Inverse Gamma prior for the uniquenesses
is a0/2. It can take a scalar value or a vector. The default value is 0.001.
b0: the scale parameter of the Inverse Gamma prior for the uniquenesses
is b0/2. It can take a scalar value or a vector. The default value is 0.001.
Additional parameters avaialable to this model include:
weights: vector of weight values or a name of a variable in the dataset
by which to weight the model. For more information see:
http://docs.zeligproject.org/articles/weights.html.
Vignette: http://docs.zeligproject.org/articles/zelig_factorbayes.html
# NOT RUN {
data(swiss)
names(swiss) <- c("Fert", "Agr", "Exam", "Educ", "Cath", "InfMort")
z.out <- zelig(~ Agr + Exam + Educ + Cath + InfMort,
model = "factor.bayes", data = swiss,
factors = 2, verbose = FALSE,
a0 = 1, b0 = 0.15, burnin = 500, mcmc = 5000)
z.out$geweke.diag()
z.out <- zelig(~ Agr + Exam + Educ + Cath + InfMort,
model = "factor.bayes", data = swiss, factors = 2,
lambda.constraints =
list(Exam = list(1,"+"),
Exam = list(2,"-"),
Educ = c(2, 0),
InfMort = c(1, 0)),
verbose = FALSE, a0 = 1, b0 = 0.15,
burnin = 500, mcmc = 5000)
z.out$geweke.diag()
z.out$heidel.diag()
z.out$raftery.diag()
summary(z.out)
# }
# NOT RUN {
# }
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