ecmmvnrfish

Fisher information matrix for multivariate normal regression model

Syntax

Fisher = ecmmvnrfish(Data,Design,Covariance,Method,MatrixFormat,CovarFormat)

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 mvnrfish.)
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.
Covariance	NUMSERIES-by-NUMSERIES matrix of estimates for the covariance of the residuals of the regression.
Method	(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.
MatrixFormat	(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.
CovarFormat	(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.

Description

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',

NUMPARAMS = NUMSERIES * (NUMSERIES + 3)/2

If MatrixFormat = 'paramonly',

NUMPARAMS = NUMSERIES

Note

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

Examples

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