fosr: MCMC Sampling Algorithm for the Function-on-Scalars...
In drkowal/dfosr: Dynamic Function-on-Scalars Regression

Description Usage Arguments Value Note Examples

Runs the MCMC for the function-on-scalars regression model based on a reduced-rank expansion. Here we assume the factor regression has independent errors, which allows for subject-specific random effects, as well as some additional default conditions.

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fosr(Y, tau, X = NULL, K = NULL, nsave = 1000, nburn = 1000,
  nskip = 3, mcmc_params = list("beta", "fk", "alpha", "sigma_e",
  "sigma_g"), Con_mat = NULL)

`Y`	the `T x m` data observation matrix, where `T` is the number of time points and `m` is the number of observation points (`NA`s allowed)
`tau`	the `m x d` matrix of coordinates of observation points
`X`	the `T x p` matrix of predictors; if NULL, only include an intercept
`K`	the number of factors; if NULL, use SVD-based proportion of variability explained
`nsave`	number of MCMC iterations to record
`nburn`	number of MCMC iterations to discard (burin-in)
`nskip`	number of MCMC iterations to skip between saving iterations, i.e., save every (nskip + 1)th draw
`mcmc_params`	named list of parameters for which we store the MCMC output; must be one or more of "beta" (factors) "fk" (loading curves) "alpha" (regression coefficients) "mu_k" (intercept term for factor k) "sigma_e" (observation error SD) "sigma_g" (random effects SD) "Yhat" (fitted values) "Ypred" (posterior predictive values)
`Con_mat`	a `Jc x m` matrix of constraints for the loading curves such that `Con_mat*fk = 0` for each loading curve `fk`; default is NULL for no constraints.

A named list of the nsave MCMC samples for the parameters named in mcmc_params

If Tm is large, then storing all posterior samples for Yhat or Ypred, which are nsave x T x m, may be inefficient

## Not run: 
# Simulate some data (w/ NAs):
sim_data = simulate_dfosr(T = 100, m = 20,
                          p_0 = 2, p_1 = 2,
                          use_dynamic_reg = FALSE,
                          prop_missing = 0.5)
Y = sim_data$Y; X = sim_data$X; tau = sim_data$tau
T = nrow(Y); m = ncol(Y); p = ncol(X) # Dimensions

# Run the MCMC w/ K = 6:
out = fosr(Y = Y, tau = tau, X = X, K = 6,
           mcmc_params = list("beta", "fk", "alpha", "Yhat", "Ypred"))

# Plot a regression coefficient function (Note: these are non-dynamic)
j = 3 # choose a predictor
post_alpha_tilde_j = get_post_alpha_tilde(out$fk, out$alpha[,j,])
plot_curve(post_f = post_alpha_tilde_j,
           tau = tau,
           main = paste('Posterior Mean and Credible bands, j =',j))
# Add the true regression coefficient function:
lines(tau, sim_data$alpha_tilde_true[1,j,], lwd=8, col='black', lty=6)

# Plot the factors:
plot_factors(post_beta = out$beta)

# Plot the loading curves:
plot_flc(post_fk = out$fk, tau = tau)

# Plot a fitted value w/ posterior predictive credible intervals:
i = sample(1:T, 1); # Select a random time i
plot_fitted(y = Y[i,],
            mu = colMeans(out$Yhat)[i,],
            postY = out$Ypred[,i,],
            y_true = sim_data$Y_true[i,],
            t01 = tau)

## End(Not run)