nullModelFitting: Fit base model

In RestoreNet: Random-Effects Stochastic Reaction Networks

Fit base model

Description

Fit the base (null) model to the given data using a maximum likelihood approach.

Usage

nullModelFitting(
  theta_start,
  M,
  y,
  V,
  psiLB,
  psiUB,
  maxit,
  factr,
  pgtol,
  lmm,
  VCNs,
  nObs,
  trace = TRUE
)

Arguments

theta_start	p-dimensional vector parameter used as initial guess in the inference procedure.
M	A n \times K dimensional (design) matrix.
y	n-dimensional vector of the time-adjacent cellular increments
V	A p \times K dimensional net-effect matrix.
psiLB	p-dimensional vector of lower bound values for theta.
psiUB	p-dimensional vector of upper bound values for theta.
maxit	maximum number of iterations for the optimization step. This argument is passed to optim() function. Details on "maxit" can be found in "optim()" documentation page.
factr	controls the convergence of the "L-BFGS-B" method. Convergence occurs when the reduction in the objective is within this factor of the machine tolerance. Default is 1e7, that is a tolerance of about 1e-8. This argument is passed to optim() function.
pgtol	helps control the convergence of the "L-BFGS-B" method. It is a tolerance on the projected gradient in the current search direction. This defaults to zero, when the check is suppressed. This argument is passed to optim() function.
lmm	is an integer giving the number of BFGS updates retained in the "L-BFGS-B" method, It defaults to 5. This argument is passed to optim() function.
VCNs	A n-dimensional vector including values of the vector copy number corresponding to the cell counts of y.
nObs	A K-dimensional vector including the frequencies of each clone k (k = 1,\dots,K).
trace	Non-negative integer. If positive, tracing information on the progress of the optimization is produced. This parameter is also passed to the optim() function. Higher values may produce more tracing information: for method "L-BFGS-B" there are six levels of tracing. (To understand exactly what these do see the source code: higher levels give more detail.)

Value

A 3-length list. First element is the output returned by optim() function (see optim() documentation for details). Second element is a vector of statistics associated to the fitted null model:

nPar	number of parameters of the base(null) model
cll	value of the conditional log-likelihood, in this case just the log-likelihood
mll	value of the marginal log-likelihood, in this case just the log-likelihood
cAIC	conditional Akaike Information Criterion (cAIC), in this case simply the AIC.
mAIC	marginal Akaike Information Criterion (mAIC), in this case simply the AIC.
Chi2	value of the \chi^2 statistic (y - M\theta)'S^{-1}(y - M\theta).
p-value	p-value of the \chi^2 test for the null hypothesis that Chi2 follows a \chi^2 distribution with n - nPar degrees of freedom.

The third element, called design, is a list including:

M	A n \times K dimensional (design) matrix.
V	A p \times K dimensional net-effect matrix.

RestoreNet documentation built on May 29, 2024, 4 a.m.