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Select model order for single-output ARX models

nn = selstruc(v) [nn,vmod] = selstruc(v,c)

**Note**

Use `selstruc`

for single-output systems only. `selstruc`

supports
both single-input and multiple-input systems.

`selstruc`

is a function to help choose a model
structure (order) from the information contained in the matrix `v`

obtained
as the output from `arxstruc`

or `ivstruc`

.

The default value of `c`

is `'plot'`

.
The plot shows the percentage of the output variance that is not explained
by the model as a function of the number of parameters used. Each
value shows the best fit for that number of parameters. By clicking
in the plot you can examine which orders are of interest. When you
click **Select**, the variable `nn`

is
exported to the workspace as the optimal model structure for your
choice of number of parameters. Several choices can be made.

`c = 'aic'`

gives no plots, but returns in `nn`

the
structure that minimizes

$$\begin{array}{c}{V}_{\mathrm{mod}}=\mathrm{log}\left(V\left(1+\frac{2d}{N}\right)\right)\\ =\mathrm{log}(V)+\frac{2d}{N},N\gg d\end{array}$$

where *V* is the loss function, *d* is
the total number of parameters in the structure in question, and *N* is
the number of data points used for the estimation. $$\mathrm{log}(V)+\frac{2d}{N}$$ is the Akaike's Information
Criterion (AIC). See `aic`

for
more details.

`c = 'mdl'`

returns in `nn`

the
structure that minimizes Rissanen's Minimum Description Length (MDL)
criterion.

$${V}_{\text{mod}}=V\left(1+\frac{d\mathrm{log}(N)}{N}\right)$$

When `c`

equals a numerical value, the structure
that minimizes $${V}_{\mathrm{mod}}=V\left(1+\frac{cd}{N}\right)$$

is selected.

The output argument `vmod`

has the same format
as `v`

, but it contains the logarithms of the accordingly
modified criteria.