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.

More About

Multivariate Normal Regression

Multivariate normal regression is a statistical modeling approach that extends traditional regression techniques to situations where the dependent variable is multivariate, meaning it consists of multiple correlated outcomes.

Multivariate normal regression is particularly useful in fields where researchers are interested in understanding the relationships between several response variables and one or more predictor variables.

Version History

Introduced in R2006a