mvnrstd

Evaluate standard errors for multivariate normal regression model

Syntax

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

Arguments

 `Data` `NUMSAMPLES`-by-`NUMSERIES` matrix with `NUMSAMPLES` samples of a `NUMSERIES`-dimensional random vector. If a data sample has missing values, represented as `NaN`s, the sample is ignored. (Use `ecmmvnrmle` to handle missing data.) `Design` 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. `Covariance` `NUMSERIES`-by-`NUMSERIES` matrix of estimates for the covariance of the regression residuals. `CovarFormat` (Optional) Character vector that specifies the format for the covariance matrix. The choices are: `'full'` — Default method. The covariance matrix is a full matrix.`'diagonal'` — The covariance matrix is a diagonal matrix.

Description

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

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

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`.

Notes

You can configure `Design` as a matrix if ```NUMSERIES = 1``` or as a cell array if `NUMSERIES `` 1`.

• If `Design` is a cell array and `NUMSERIES` = `1`, each cell contains a `NUMPARAMS` row vector.

• If `Design` is a cell array and `NUMSERIES` > `1`, each cell contains a `NUMSERIES`-by-`NUMPARAMS` matrix.

References

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

Introduced in R2006a