fit_modelB: Runs the expectation maximization algorithm for Model B...
In b-brune/tvRRR: Time-varying reduced-rank regression using state-space models

Runs the expectation maximization algorithm for Model B Input:

fit_modelB(
  X,
  y,
  u = NULL,
  d,
  alpha = NULL,
  beta_00 = NULL,
  Gamma = NULL,
  P_00 = 1000 * diag(ncol(X) * d),
  Sigma = NULL,
  Omega = NULL,
  Omega_diagonal = FALSE,
  maxit = 100,
  silent = FALSE,
  tol_finish = 0.001,
  tol_EMstep = 0.001,
  return_covariances = FALSE,
  initialize = "RRR",
  Gamma_rrr = "identity"
)

`X`	predictors (t x q-dimensional)
`y`	target (t x p-dimensional)
`u`	additional predictors (t x q-dimensional)
`d`	latent dimension
`alpha`	starting value for the algorithm, default NULL (RRR)
`beta_00`	starting value for beta', default NULL (RRR)
`Gamma`	starting value for the fixed full-rank coefficient matrix, default NULL (RRR)
`P_00`	starting state covariance (default 1000 * diag(p x d))
`Sigma`	column covariance of states (default 0.01 * diag(d))
`Omega`	error covariance (defaults to residual covariance from RRR, or respective starting values)
`Omega_diagonal`	logical, indicates whether Omega is assumed to be a diagonal matrix (advisable if p is large)
`maxit`	maximum number of iterations for the EM algorithm
`silent`	logical, indicates whether progress should be printed during model fitting
`tol_finish`	tolerance for stopping the EM algorithm
`tol_EMstep`	tolerance for iterative estimation during EM step Output:
`return_covariances`	logical, indicates whether the state covariances should be returned (might be necessary for evaluation of the likelihood).
`initialize`	either `"RRR"` or `"random"`, applies if no starting values are handed over
`Gamma_rrr`	type of normalization for the starting values obtained from RRR

A named list of lists with elements

states: filtered (the filtered states) smoothed (the smoothed states)
covariances: the filtered and smoothed covariances and lag-1 covariances (if return_covariances = TRUE) P_t^t filtered covariances P_t^t-1predicted covariances P_t^T smoothed covariances P_t-1t-2^T smoothed lag-1 covariances
data: the data handed over to the algorithms X predictors y responses Z transition matrices (X_t'beta (x) I_p)
parameters used during filtering: Sigma, Omega, beta
likelihoods: list containing Q and data loglikelihood for each iteration
convergence_information: Message containing parameter stages at convergence