mvnrstd

Evaluate standard errors for multivariate normal regression model

Syntax

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

[StdParameters,StdCovariance] = mvnrstd(___,CovarFormat)

Description

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

$$Dat{a}_k\sim N\left(Desig{n}_k\times Parameters,Covariance\right)$$

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.

  Note

  mvnrstd operates slowly when you calculate the standard errors associated with the covariance matrix Covariance.

[StdParameters,StdCovariance] = mvnrstd(___,CovarFormat) computes the log-likelihood function based on current maximum likelihood parameter estimates without missing data using an optional argument.

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 ecmmvnrmle 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

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

StdParameters — standard errors for each element of Parameters, the vector of estimated model parameters

vector

Standard errors for each element of Parameters, the vector of estimated model parameters, returned as an NUMPARAMS-by-1 column vector.

StdCovariance — standard errors for each element of Covariance, the matrix of estimated covariance parameters

matrix

Standard errors for each element of Covariance, the matrix of estimated covariance parameters, returned as an NUMSERIES-by-NUMSERIES matrix.

More About

Multivariate Normal Regression

Multivariate normal regression is a statistical modeling approach that extends traditional regression techniques to situations where the dependent variable is multivariate, meaning it consists of multiple correlated outcomes.

Multivariate normal regression is particularly useful in fields where researchers are interested in understanding the relationships between several response variables and one or more predictor variables.

References

[1] 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