# ecmlsrmle

Least-squares regression with missing data

## Syntax

## Description

`[`

estimates a least-squares regression model with missing data. The model has the
form`Parameters`

,`Covariance`

,`Resid`

,`Info`

] = ecmlsrmle(`Data`

,`Design`

)

$$Dat{a}_{k}\sim N\left(Desig{n}_{k}\times Parameters,\text{\hspace{0.17em}}Covariance\right)$$

for samples *k* = 1, ... , `NUMSAMPLES`

.

`ecmlsrmle`

estimates a
`NUMPARAMS`

-by-`1`

column vector of model
parameters called `Parameters`

, and a
`NUMSERIES`

-by-`NUMSERIES`

matrix of
covariance parameters called `Covariance`

.

`ecmlsrmle(Data,Design)`

with no output arguments plots the
log-likelihood function for each iteration of the algorithm.

`[`

estimates a least-squares regression model with missing data using optional
arguments.`Parameters`

,`Covariance`

,`Resid`

,`Info`

] = ecmlsrmle(___,`MaxIterations`

,`TolParam`

,`TolObj`

,`Param0`

,`Covar0`

,`CovarFormat`

)

## Input Arguments

## Output Arguments

## References

[1] Dempster A, P., N.M. Laird,
and D. B. Rubin. “Maximum Likelihood from Incomplete Data via the EM
Algorithm.” *Journal of the Royal Statistical Society.*
Series B, Vol. 39, No. 1, 1977, pp. 1–37.

[2] Roderick J., A. Little, and
Donald B. Rubin. *Statistical Analysis with Missing Data.*, 2nd
Edition. John Wiley & Sons, Inc., 2002.

[3] Sexton J. and Anders Rygh
Swensen. “ECM Algorithms that Converge at the Rate of EM.”
*Biometrika.* Vol. 87, No. 3, 2000, pp. 651–662.

[4] Xiao-Li Meng and Donald B.
Rubin. “Maximum Likelihood Estimation via the ECM Algorithm.”
*Biometrika.* Vol. 80, No. 2, 1993, pp. 267–278.

## Version History

**Introduced in R2006a**