ecmlsrobj

Log-likelihood function for least-squares regression with missing data

Syntax

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

Arguments

Data	NUMSAMPLES-by-NUMSERIES matrix with NUMSAMPLES samples of a NUMSERIES-dimensional random vector. Missing values are represented as NaNs. Only samples that are entirely NaNs are ignored. (To ignore samples with at least one NaN, use mvnrmle.)
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	(Optional) NUMSERIES-by-NUMSERIES matrix that contains a user-supplied estimate for the covariance matrix of the residuals of the regression. Default is an identity matrix.

Description

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

Notes

ecmlsrobj requires that Covariance be positive-definite.

Note that

ecmlsrobj(Data, Design, Parameters) = ecmmvnrobj(Data, ... 
Design, Parameters, IdentityMatrix)

where IdentityMatrix is a NUMSERIES-by-NUMSERIES identity matrix.

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.

Examples

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