ecmmvnrfish

Fisher information matrix for multivariate normal regression model

Syntax

Fisher] = ecmmvnrfish(Data,Design,Covariance)

Fisher = ecmmvnrfish(___,Method,MatrixFormat,CovarFormat)

Description

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

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

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.

Input Arguments

Data — Data sample

matrix

Data sample, specified as an 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 mvnrmle to handle missing data.)

Data Types: double

Design — Model design

matrix | cell array of character vectors

Model design, specified as 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.

Data Types: double | cell

Covariance — Estimates for the covariance of the residuals of the regression

matrix

Estimates for the covariance of the residuals of the regression, specified as an NUMSERIES-by-NUMSERIES matrix.

Data Types: double

Method — Method of calculation for information matrix

'hessian' (default) | character vector with value 'hessian' or 'fisher'

(Optional) Method of calculation for the information matrix, specified as a character vector. The choices are:

• 'hessian' — This is the default method using 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' — This computes using the Fisher information matrix.

Data Types: char

MatrixFormat — Parameters to be included in Fisher information matrix

'full' (default) | character vector with value 'full' or 'paramonly'

(Optional) Parameters to be included in the Fisher information matrix, specified as a character vector. The choices are:

• 'full' — This is the default method that computes the full Fisher information matrix for both model and covariance parameter estimates.

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

Data Types: char

CovarFormat — Format for covariance matrix

'full' (default) | character vector with value 'full' or 'diagonal'

(Optional) Format for the covariance matrix, specified as a character vector. The choices are:

• 'full' — This is the default method that computes the full covariance matrix.

• 'diagonal' — This forces the covariance matrix to be a diagonal matrix.

Data Types: char

Output Arguments

Fisher — Fisher information matrix

matrix

Fisher information matrix, returned as an NUMPARAMS-by-NUMPARAMS Fisher information matrix or Hessian matrix, depending on the optional input argument Method.

Version History

Introduced in R2006a