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Evaluate standard errors for multivariate normal regression model


[StdParameters, StdCovariance] = ecmmvnrstd(Data,Design,Covariance,Method,CovarFormat)



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 mvnrstd.)


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.


NUMSERIES-by-NUMSERIES matrix of estimates for the covariance of the regression residuals.


(Optional) Character vector that identifies method of calculation for the information matrix:

  • hessian — Default method. Use the expected Hessian matrix of the observed log-likelihood function. This method is recommended since the resultant standard errors incorporate the increased uncertainties due to missing data.

  • fisher — Use the Fisher information matrix.


(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.


[StdParameters,StdCovariance] = ecmmvnrstd(Data,Design,Covariance,Method,CovarFormat) evaluates standard errors for a multivariate normal regression model with missing data. The model has the form


for samples k = 1, ... , NUMSAMPLES.

ecmmvnrstd computes two outputs:

  • StdParameters is a NUMPARAMS-by-1 column vector of standard errors for each element of Parameters, the vector of estimated model parameters.

  • StdCovariance is a NUMSERIES-by-NUMSERIES matrix of standard errors for each element of Covariance, the matrix of estimated covariance parameters.


    ecmmvnrstd operates slowly when you calculate the standard errors associated with the covariance matrix Covariance.


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.


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


Roderick J. A. Little and Donald B. Rubin. Statistical Analysis with Missing Data. 2nd edition, John Wiley & Sons, Inc., 2002.

Introduced in R2006a