ecmmvnrobj

Log-likelihood function for multivariate normal regression with missing data

Syntax

Objective = ecmmvnrobj(Data,Design,Parameters,Covariance)

Objective = ecmmvnrobj(___,CovarFormat)

Description

Objective = ecmmvnrobj(Data,Design,Parameters,Covariance) computes a log-likelihood function based on current maximum likelihood parameter estimates with missing data. Objective is a scalar that contains the least-squares objective function.

Objective = ecmmvnrobj(___,CovarFormat) computes a log-likelihood function based on current maximum likelihood parameter estimates with missing data using an optional argument.

Input Arguments

Data — Data sample

matrix

Data sample, specified as an NUMSAMPLES-by-NUMSERIES matrix with NUMSAMPLES samples of a NUMSERIES-dimensional random vector. If a data sample has missing values, represented as NaNs. Only samples that are entirely NaNs are ignored. (To ignore samples with at least one NaN, use mvnrmle.)

Data Types: double

Design — Model design

matrix | cell array of character vectors

Model design, specified as 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.

Data Types: double | cell

Parameters — Estimates for the parameters of regression model

vector

Estimates for the parameters of regression model, specified as an NUMPARAMS-by-1 column vector.

Data Types: double

Covariance — Estimates for covariance matrix of residuals of the regression

matrix

Estimates for the covariance matrix of the residuals of the regression, specified as an NUMSERIES-by-NUMSERIES matrix.

Data Types: double

CovarFormat — Format for covariance matrix

'full' (default) | character vector with value 'full' or 'diagonal'

(Optional) Format for the covariance matrix, specified as a character vector. The choices are:

• 'full' — This is the default method that computes the full covariance matrix.

• 'diagonal' — This forces the covariance matrix to be a diagonal matrix.

Data Types: char

Output Arguments

Objective — Least-squares objective function

scalar

Least-squares objective function, returned as scalar.

Version History

Introduced in R2006a