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


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



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.)


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 NUMSERIES1, 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.


NUMPARAMS-by-1 column vector of estimates for the parameters of the regression model.


(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.


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.


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 NUMSERIES1.

  • 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.


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

Version History

Introduced in R2006a