R: Initialize and fit a mixed-scale Gaussian factor model, with...

bfa_mixed {bfa} | R Documentation

## Initialize and fit a mixed-scale Gaussian factor model, with probit specifications for the discrete margins

### Description

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.

### Usage

    bfa_mixed(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.iter = 500, imh.burn = 500,
      ...)

### Arguments

`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 all numeric variables if x is a formula.
`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 for ordinal variables (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.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)

### Details

Note: All the priors in use assume that the manifest Gaussian variables are on approximately the same scale.

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

- sigma2.a, sigma2.b: Gamma hyperparameters for error precisions (for numeric variables)

- gdp.alpha, gdp.beta: GDP prior parameters

- mu.mean, mu.var: (Scalar) prior mean and variance for mu[j] (where E(y) = mu). Defaults are 0 and 1e4.

### Value

A `bfa` object with posterior samples.

[Package bfa version 0.4 Index]