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Negative log-likelihood for multivariate regression


nlogL = mvregresslike(X,Y,b,SIGMA,alg)
[nlogL,COVB] = mvregresslike(...)
[nlogL,COVB] = mvregresslike(...,type,format)


nlogL = mvregresslike(X,Y,b,SIGMA,alg) computes the negative log-likelihood nlogL for a multivariate regression of the d-dimensional multivariate observations in the n-by-d matrix Y on the predictor variables in the matrix or cell array X, evaluated for the p-by-1 column vector b of coefficient estimates and the d-by-d matrix SIGMA specifying the covariance of a row of Y. If d = 1, X can be an n-by-p design matrix of predictor variables. For any value of d, X can also be a cell array of length n, with each cell containing a d-by-p design matrix for one multivariate observation. If all observations have the same d-by-p design matrix, X can be a single cell.

NaN values in X or Y are taken as missing. Observations with missing values in X are ignored. Treatment of missing values in Y depends on the algorithm specified by alg.

alg should match the algorithm used by mvregress to obtain the coefficient estimates b, and must be one of the following:

  • 'ecm' — ECM algorithm

  • 'cwls' — Least squares conditionally weighted by SIGMA

  • 'mvn' — Multivariate normal estimates computed after omitting rows with any missing values in Y

[nlogL,COVB] = mvregresslike(...) also returns an estimated covariance matrix COVB of the parameter estimates b.

[nlogL,COVB] = mvregresslike(...,type,format) specifies the type and format of COVB.

type is either:

  • 'hessian' — To use the Hessian or observed information. This method takes into account the increased uncertainties due to missing data. This is the default.

  • 'fisher' — To use the Fisher or expected information. This method uses the complete data expected information, and does not include uncertainty due to missing data.

format is either:

  • 'beta' — To compute COVB for b only. This is the default.

  • 'full' — To compute COVB for both b and SIGMA.

Version History

Introduced in R2007a