ecmlsrobj

Log-likelihood function for least-squares regression with missing data

Syntax

Objective = ecmlsrobj(Data,Design,Parameters)

Objective = ecmlsrobj(___,Covariance)

Description

Objective = ecmlsrobj(Data,Design,Parameters) computes a least-squares objective function based on current parameter estimates with missing data. Objective is a scalar that contains the least-squares objective function.

Objective = ecmlsrobj(___,Covariance) computes a least-squares objective function based on current parameter estimates with 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. Only samples that are entirely NaNs are ignored. (To ignore samples with at least one NaN, use mvnrmle.)

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

Parameters — Estimates for the parameters of regression model

vector

Estimates for the parameters of regression model, specified as an NUMPARAMS-by-1 column vector.

Data Types: double

Covariance — User-supplied estimate for covariance matrix of residuals of the regression

vector

(Optional) User-supplied estimate for the covariance matrix of the residuals of the regression, specified as an NUMPARAMS-by-1 column vector.

ecmlsrobj requires that Covariance be positive-definite.

Note that

ecmlsrobj(Data, Design, Parameters) = ecmmvnrobj(Data, Design, Parameters, IdentityMatrix)

where IdentityMatrix is a NUMSERIES-by-NUMSERIES identity matrix.

Data Types: double

Output Arguments

Objective — Least-squares objective function

scalar

Least-squares objective function, returned as scalar.

More About

Least Squares Regression

Least squares regression is a statistical method used to estimate the relationships between variables.

Least squares regression is commonly employed in linear regression analysis to find the best-fitting line through a set of data points. The goal is to minimize the sum of the squares of the differences (residuals) between the observed values and the values predicted by the model.

Version History

Introduced in R2006a