factorQR: A Bayesian factor model for quantile regression
In factorQR: Bayesian quantile regression factor models

Description Arguments Value Author(s)

factorQR is an MCMC sampler to fit a Bayesian factor model for quantile regression.

`factorForm`	A formula of the form `factorForm = Y ~ X1 + X2`, where `Y` is the response and variables on the right-hand side are manifest variables related to the latent factors on which we are regressing `Y`. The right-hand side variables will be centered automatically, though they are not scaled.
`nonFactorForm`	An optional formula of the form `nonFactorForm = ~ X3 + X4`. These covariates are used to model `Y`, but they do not relate to any of the latent factors.
`dataSet`	An optional data frame, list, or environment containing the variables in the model.
`pQuant`	Response quantile to model. Defaults to `pQuant=0.5`.
`whichFactor`	Vector of indicators to show factor grouping. E.g., if `whichFactor=c(1,1,1,2,2,2)`, it would mean the first three variables in the right-hand side of `factorForm` group and the last three group together in two factors. If `whichFactor = NULL`, a single latent factor will be assumed.
`nSamp`	Number of MCMC iterations, with a default of `5000`.
`burn`	Iterations of burn-in, with a default of `0`.
`thin`	Number of iterations to skip between stored values in the chain, with a default of `0`.
`cTau0`	Prior shape for τ, which is the inverse scale of the response. Defaults to `1`.
`dTau0`	Prior scale for τ.
`cPsi0`	Prior shape for Ψ, the inverse scale of the manifest variables related to the factors. Defaults to `1`.
`dPsi0`	Prior rate for Ψ. Defaults to `1`.
`sig0`	Hyperparameter for scale of free Λ_{-s} variables, which is rows of the factor loading matrix that do not correspond to the response. Defaults to `1`.
`mu0`	Prior mean for Λ_{-s} components. Defaults to `1`.
`R0`	Prior scale of Φ^{-1}. If not specified, defaults to the identity matrix.
`nu0`	Prior degrees of freedom for inverse Wishart associated with Φ. Must be an integer greater than or equal to the dimension of Φ, but defaults to one greater than that dimension.
`B0s`	Prior precision (i.e., inverse variance) for Λ_{s}. Default is a diagonal matrix with non-zero values of `0.01`. May be left at NULL, or changed to a non-negative scalar, a vector with length equal to the number of latent factors, or a symmetric, positive definite matrix with dimension equal to the number of latent factors.
`B0Beta`	Prior precision for regression coefficients related to `nonFactorForm`. Default is a diagonal matrix with non-zero values of `0.01`. May be left at NULL, or changed to a non-negative scalar, a vector with length equal to the number of covariates not related to the latent factors, or a symmetric, positive definite matrix with that dimension.
`betaZero`	Starting value for β.
`PhiZero`	Initial value of Φ.
`invPsiZero`	initial value of Ψ^{-1}.
`LambdaZero`	Initial value of Λ_{-s}. Must be a scalar or vector with length equal to the number of manifest variables in the right-hand side of `factorForm`. Will be expanded to its matrix form internally, and elements that should be fixed at `1` will be adjusted if necessary, with warning.
`LambdaSZero`	Initial value of last row of Λ, i.e. the part that models the left-hand side of `factorForm`. If specified, must either be a scalar or vector with length equal to the number of latent factors being modeled. Defaults to `0.1`
`OmegaZero`	Initial value for latent Ω.
`verbose`	If `TRUE`, prints progress updates in Gibbs sampler.
`storeOmega`	If `TRUE`, stores the sampled Ω values.
`latentInteract`	If `TRUE`, interacts the first two latent factors. More latent/latent interactions are not currently supported.
`interactX`	If supplied, a matrix of variables with which to interact the latent factors. Repeated columns are allowed.
`whichFactorInteract`	A vector that indicates which factors to interact with the columns of `interactX`. For example, `whichFactorInteract = c(1,1)` would indicate that the two columns of `interactX` are to be interacted with the first latent factor.

Returns an item of the class factorQR composed of the following components:

`param`	Matrix of sampled parameter values.
`call`	The matched call.
`nReg`	The number of regression parameters.
`betLen`	The number of β components.
`nObs`	The number of observations.
`burn`	The number of Gibbs iterations before samples were stored.
`thin`	The number of Gibbs iterations between stored values.
`nSamp`	The total number of Gibbs iterations.
`nFact`	The number of modeled latent factors.
`nFactorX`	The number of manifest variables related to the factors.
`omega`	Sampled Ω values, if `storeOmega` is `TRUE`.
`nFactInt`	Number of factor/manifest variable interactions.