interactionDL: Factor regression model with interactions using the...

In poworoznek/infinitefactor: Bayesian Infinite Factor Models

Description

Perform a regression of y onto X and all 2 way interactions in X using the latent factor model introduced in Ferrari and Dunson (2020). This version uses the Dirichlet-Laplace shrinkage prior as in the original paper.

Usage

interactionDL(y, X, nrun, burn = 0, thin = 1, 
              delta_rw = 0.0526749, a = 1/2, k = NULL, 
              output = c("covMean", "covSamples", "factSamples", 
              "sigSamples", "coefSamples","errSamples"), 
              verbose = TRUE, dump = FALSE, filename = "samps.Rds", 
              buffer = 10000, adapt = "burn", augment = NULL)

Arguments

y	response vector.
X	predictor matrix (n x p).
nrun	number of iterations.
burn	burn-in period.
thin	thinning interval.
delta_rw	metropolis-hastings proposal variance.
a	shrinkage hyperparameter.
k	number of factors.
output	output type, a vector including some of: c("covMean", "covSamples", "factSamples", "sigSamples", "coefSamples", "numFactors", "errSamples").
verbose	logical. Show progress bar?
dump	logical. Save samples to a file during sampling?
filename	if dump: filename to address list of posterior samples
buffer	if dump: how often to save samples
adapt	logical or "burn". Adapt proposal variance in metropolis hastings step? if "burn", will adapt during burn in and not after.
augment	additional sampling steps as an expression

Value

some of:

covMean	X covariance posterior mean
omegaSamps	X covariance posterior samples
lambdaSamps	Posterior factor loadings samples (rotationally ambiguous)
etaSamps	Posterior factor samples (rotationally ambiguous)
sigmaSamps	Posterior marginal variance samples (see notation in Bhattacharya and Dunson (2011))
phiSamps	Posterior main effect coefficient samples in factor form (rotationally ambiguous)
PsiSamps	Posterior interaction effect coefficient samples in factor form (rotationally ambiguous)
interceptSamps	Posterior induced intercept samples
mainEffectSamps	Posterior induced main effect coefficient samples
interactionSamps	Posterior induced interaction coefficient samples
ssySamps	Posterior irreducible error samples

Author(s)

Evan Poworoznek

Federico Ferrari

References

Ferrari, Federico, and David B. Dunson. "Bayesian Factor Analysis for Inference on Interactions." arXiv preprint arXiv:1904.11603 (2019).

See Also

interactionMGSP

Examples

k0 = 5
p = 20
n = 50

lambda = matrix(rnorm(p*k0, 0, 0.01), ncol = k0)
lambda[sample.int(p, 40, replace = TRUE) +
         p*(sample.int(k0, 40, replace = TRUE)-1)] = rnorm(40, 0, 1)
lambda[1:7, 1] = rnorm(7, 2, 0.5)
lambda[8:14, 2] = rnorm(7, -2, 0.5)
lambda[15:20, 3] = rnorm(6, 2, 0.5)
lambda[,4] = rnorm(p, 0, 0.5)
lambda[,5] = rnorm(p, 0, 0.5)
plotmat(varimax(lambda)[[1]])

X = matrix(rnorm(n*k0),n,k0)%*%t(lambda) + matrix(rnorm(n*p), n, p)

beta_true = numeric(p); beta_true[c(1,3,6,8,10,11)] =c(1,1,0.5,-1,-2,-0.5)
Omega_true = matrix(0,p,p)
Omega_true[1,2] = 1; Omega_true[5,2] = -1; Omega_true[10,8] = 1; 
Omega_true[11,5] = -2; Omega_true[1,1] = 0.5; 
Omega_true[2,3] = 0.5; 
Omega_true = Omega_true + t(Omega_true)
y = X%*%beta_true + diag(X%*%Omega_true%*%t(X)) +  rnorm(n,0.5)

intdl = interactionDL(y, X, 1000, 500, k = 5)

poworoznek/infinitefactor documentation built on April 7, 2020, 1:10 p.m.