bfa_copula: Initialize and fit a Gaussian copula factor model
In bfa: Bayesian Factor Analysis

Description Usage Arguments Details Value Examples

This function performs a specified number of MCMC iterations and returns an object containing summary statistics from the MCMC samples as well as the actual samples of factor scores if keep.scores is TRUE. Default behavior is to save only samples of the loadings.

bfa_copula(x, data = NULL, num.factor = 1, restrict = NA,
  normal.dist = NA, nsim = 10000, nburn = 1000, thin = 1,
  print.status = 500, keep.scores = FALSE, loading.prior = c("gdp",
  "pointmass", "normal"), factor.scales = FALSE, px = TRUE,
  coda = "loadings", coda.scale = TRUE, imh = FALSE, imh.iter = 500,
  imh.burn = 500, ...)

`x`	A formula or bfa object.
`data`	The data if x is a formula
`num.factor`	Number of factors
`restrict`	A matrix or list giving restrictions on factor loadings. A matrix should be the same size as the loadings matrix. Acceptable values are 0 (identically 0), 1 (unrestricted), or 2 (strictly positive). List elements should be character vectors of the form c('variable',1, ">0") where 'variable' is the manifest variable, 1 is the factor, and ">0" is the restriction. Acceptable restrictions are ">0" or "0".
`normal.dist`	A character vector specifying which variables should be treated as observed Gaussian. Defaults to none (a completely semiparametric copula model)
`nsim`	Number of iterations past burn-in
`nburn`	Number of initial (burn-in) iterations to discard
`thin`	Keep every thin'th MCMC sample (i.e. save nsim/thin samples)
`print.status`	How often to print status messages to console
`keep.scores`	Save samples of factor scores
`loading.prior`	Specify GDP ("gdp", default) point mass ("pointmass") or normal priors ("normal")
`factor.scales`	Include a separate scale parameter for each factor
`px`	Use parameter expansion (strongly recommended!)
`coda`	Create `mcmc` objects to allow use of functions from the `coda` package: "all" for loadings and scores, "loadings" or "scores" for one or the other, or "none" for neither
`coda.scale`	Put the loadings on the correlation scale when creating `mcmc` objects
`imh`	Use Independence Metropolis-Hastings step for discrete margins. If FALSE, use the semiparametric extended rank likelihood. If TRUE, uses a uniform prior on the cutpoints
`imh.iter`	Iterations used to build IMH proposal
`imh.burn`	Burn-in before collecting samples used to build IMH proposal (total burn-in is nburn+imh.iter+imh.burn)
`...`	Prior parameters and other (experimental) arguments (see details)

Additional parameters:

loadings.var: Factor loading prior variance
tau.a, tau.b: Gamma hyperparameters (scale=1/b) for factor precisions (if factor.scales=T). Default is a=b=1 (MV t w/ df=2)
rho.a, rho.b: Beta hyperparameters for point mass prior
gdp.alpha, gdp.beta: GDP prior parameters

A bfa object with posterior samples.

## Not run: 
require(MASS)
data(UScereal)
UScereal$shelf = factor(UScereal$shelf, ordered=TRUE)
UScereal$vitamins = factor(UScereal$vitamins, ordered=TRUE,
                           levels=c("none", "enriched", "100%"))
obj = bfa_copula(~., data=UScereal[,-1], num.factor=2, nsim=10000, nburn=1000, thin=4,
                     rest=list(c("sugars", 2, "0")), loading.prior="gdp", keep.scores=T,
                     print.status=2500)
biplot(obj, cex=c(0.8, 0.8))
plot(get_coda(obj))
plot(get_coda(obj, loadings=F, scores=T))
hpd.int = HPDinterval(obj, scores=T)

#sample from posterior predictive
ps = predict(obj)

m=ggplot(UScereal, aes(x=calories, y=sugars))+geom_point(position='jitter', alpha=0.5)
m=m+stat_density2d(data=ps, aes(x=calories, y=sugars, color = ..level..), geom='contour')
print(m)

m=ggplot(UScereal, aes(x=calories))+geom_histogram()
m=m+stat_density(data=ps, aes(x=calories, y=..count..), color='red',fill=NA, adjust=1.3)
m=m+facet_grid(shelf~.)
print(m)

#we can compute conditional dist'n estimates directly as well by supplying cond.vars
cond.vars=list(shelf=1)
out = predict(obj, resp.var="calories", cond.vars=cond.vars)
plot(sort(unique(UScereal$calories)), apply(out, 2,mean), type='s')
lines(sort(unique(UScereal$calories)), apply(out, 2, quantile, 0.05), type='s', lty=2)
lines(sort(unique(UScereal$calories)), apply(out, 2,quantile, 0.95), type='s', lt=2)
lines(ecdf(UScereal$calories[UScereal$shelf==1]), col='blue')
text(400, 0.1, paste("n =", sum(UScereal$shelf==1)))

out2 = predict(obj, resp.var="calories", cond.vars=list(shelf=2))
out3 = predict(obj, resp.var="calories", cond.vars=list(shelf=3))
plot(sort(unique(UScereal$calories)), apply(out, 2,mean), type='s')
lines(sort(unique(UScereal$calories)), apply(out2, 2,mean), type='s', lty=2)
lines(sort(unique(UScereal$calories)), apply(out3, 2,mean), type='s', lty=3)

## End(Not run)