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Fisher information matrix for multivariate normal regression model


Fisher = ecmmvnrfish(Data,Design,Covariance,Method,MatrixFormat,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 mvnrfish.)


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 residuals of the regression.


(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 identifies parameters to be included in the Fisher information matrix:

  • full — Default format. Compute the full Fisher information matrix for both model and covariance parameter estimates.

  • paramonly — Compute only components of the Fisher information matrix associated with the model parameter estimates.


(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.


Fisher = ecmmvnrfish(Data,Design,Covariance,Method,MatrixFormat,CovarFormat) computes a Fisher information matrix based on current maximum likelihood or least-squares parameter estimates that account for missing data.

Fisher is a NUMPARAMS-by-NUMPARAMS Fisher information matrix or Hessian matrix. The size of NUMPARAMS depends on MatrixFormat and on current parameter estimates. If MatrixFormat = 'full',


If MatrixFormat = 'paramonly',



ecmmvnrfish operates slowly if you calculate the full Fisher information matrix.


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

Introduced in R2006a