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Evaluate standard errors for multivariate normal regression model


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



NUMSAMPLES-by-NUMSERIES matrix with NUMSAMPLES samples of a NUMSERIES-dimensional random vector. If a data sample has missing values, represented as NaNs, the sample is ignored. (Use ecmmvnrmle to handle missing data.)


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 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] = mvnrstd(Data,Design,Covariance,CovarFormat) evaluates standard errors for a multivariate normal regression model without missing data. The model has the form


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

mvnrstd 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.


    mvnrstd 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.

Version History

Introduced in R2006a