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.

More About

Fisher Information Matrix

The Fisher information matrix is a key concept in statistics and information theory that measures the amount of information that an observable random variable carries about an unknown parameter upon which the probability of the random variable depends.

The Fisher information matrix is used to evaluate the efficiency of estimators and to derive confidence intervals.

Version History

Introduced in R2006a