mvnrobj

Log-likelihood function for multivariate normal regression without missing data

Syntax

Objective = mvnrobj(Data,Design,Parameters,Covariance,CovarFormat)

Arguments

Data	NUMSAMPLES-by-NUMSERIES matrix with NUMSAMPLES samples of a NUMSERIES-dimensional random vector. If a data sample has missing values, represented as NaNs, the sample is ignored. (Use ecmmvnrmle to handle missing data.)
Design	A matrix or a cell array that handles two model structures: If NUMSERIES = 1, Design is a NUMSAMPLES-by-NUMPARAMS matrix with known values. This structure is the standard form for regression on a single series. If NUMSERIES ≥ 1, Design is a cell array. The cell array contains either one or NUMSAMPLES cells. Each cell contains a NUMSERIES-by-NUMPARAMS matrix of known values. If Design has a single cell, it is assumed to have the same Design matrix for each sample. If Design has more than one cell, each cell contains a Design matrix for each sample.
Parameters	NUMPARAMS-by-1 column vector of estimates for the parameters of the regression model.
Covariance	NUMSERIES-by-NUMSERIES matrix of estimates for the covariance of the residuals of the regression.
CovarFormat	(Optional) Character vector that specifies the format for the covariance matrix. The choices are: 'full' — Default method. The covariance matrix is a full matrix. 'diagonal' — The covariance matrix is a diagonal matrix.

Description

Objective = mvnrobj(Data,Design,Parameters,Covariance,CovarFormat) computes the log-likelihood function based on current maximum likelihood parameter estimates without missing data. Objective is a scalar that contains the log-likelihood function.

Notes

You can configure Design as a matrix if NUMSERIES = 1 or as a cell array if NUMSERIES ≥ 1.

• If Design is a cell array and NUMSERIES = 1, each cell contains a NUMPARAMS row vector.

• If Design is a cell array and NUMSERIES > 1, each cell contains a NUMSERIES-by-NUMPARAMS matrix.

Although Design should not have NaN values, ignored samples due to NaN values in Data are also ignored in the corresponding Design array.

Examples

See Multivariate Normal Regression, Least-Squares Regression, Covariance-Weighted Least Squares, Feasible Generalized Least Squares, and Seemingly Unrelated Regression.