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

Runs the expectation maximization algorithm for Model A

fit_modelA(
  X,
  y,
  u = NULL,
  d,
  beta = NULL,
  alpha_00 = NULL,
  Gamma = NULL,
  P_00 = 1000 * diag(ncol(y) * d),
  Sigma = NULL,
  Omega = NULL,
  Omega_diagonal = FALSE,
  maxit = 100,
  silent = FALSE,
  tol_finish = 0.001,
  tol_EMstep = 0.001,
  return_covariances = FALSE,
  Gamma_rrr = "identity",
  initialize = "RRR"
)

`X`	predictors (t x q-dimensional)
`y`	target (t x p-dimensional)
`u`	additional predictors (t x q-dimensional)
`d`	latent dimension
`beta`	starting value for beta, default NULL (RRR)
`alpha_00`	starting value for the algorithm, 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).
`Gamma_rrr`	type of normalization for the starting values obtained from RRR
`initialize`	either `"RRR"` or `"random"`, applies if no starting values are handed over

An object of class tvRRR, that is a named list of lists with elements

`states`	The estimated states (i.e. coefficient matrices) 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-1` predicted 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 `u` additional predictors `Z` transition matrices (X_t'beta (x) I_p)
`parameters`	The parameters that have been fitted during the algorithm, that is `Sigma` the column covariance of the states `Omega` the error covariance `beta` (for model A) `alpha` (for model B)
`likelihoods`	list containing Q and data loglikelihood for each iteration
`convergence_information`	Message containing parameter stages at convergence