selstruc (System Identification Toolbox)

Select model order (structure).

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

Description

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'. This graphs the values of the loss functions in v against the total number of parameters in the corresponding model structure. If v was generated by ivstruc, so that it also contains the condition numbers of the IV matrices, then these are also graphed against the number of parameters. Based on inspection of these plots, you can choose a suitable number of parameters, and nn returns the best structure with this number of parameters.

If c = 'log', the logarithms of the loss functions are graphed instead.

c = 'aic' gives no plots, but returns in nn the structure that minimizes Akaike's Information Theoretic Criterion (AIC),

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.

c = 'mdl' returns in nn the structure that minimizes Rissanen's Minimum Description Length (MDL) criterion.

When c equals a numerical value, the structure that minimizes

is selected.

The output argument vmod has the same format as v, but it contains the logarithms of the accordingly modified criteria.

The formal grounds for applying AIC or MDL require that v be generated by arxstruc with ze = zv. When cross-validation is used (ze different from zv), the logical choice is c = 0.

When selecting model structures, it is important to assess carefully whether the benefit of a better fit is worth the additional complexity of a higher order model. See Chapter 3, "Tutorial" for more information.

Examples

Here is a typical sequence of commands for finding a suitable model structure:

NN = struc(2,2,1:8); 
v = arxstruc(z(1:200,:),z(201:400,:),NN);
nn = selstruc(v,0);
nk = nn(3);
NN = struc(1:4,1:4,nk);
va = arxstruc(z(1:200,:),z(201:400,:),NN);
vi = ivstruc(z(1:200,:),z(201:400,:),NN);
nna = selstruc(va);
nni = selstruc(vi);