selectmodel

Selection of an optimal parametric model

Syntax

opt = selectmodel(models,V,r,K,'method')
[opt,f,param,paramcis] = selectmodel(models,V,r,K,'method')
[opt,f,param,paramcis] = selectmodel(models,{V1,V2,___},r,{K1,K2,___},'method')
[opt,f,param,paramcis] = selectmodel(models,V,r,K,{'method1','method2',___})
[opt,f,param,paramcis] = selectmodel(models,V,r,K,'method',param0)
[opt,f,param,paramcis] = selectmodel(models,V,t,'method')
[opt,f,param,paramcis] = selectmodel(models,{V1,V2,___},{t1,t2,___},'method')
[opt,f,param,paramcis] = selectmodel(models,V,t,'method',param0)
[opt,f,param,paramcis] = selectmodel(___,'Property',Value)
Parameters
  • models - Input parametric models (cell array of function handles)
  • V - Input signal (N-element array)
  • r - Distance axis (N-element array), in nanometers
  • K - Dipolar kernel (NxM-element array)
  • t - Time axis (N-array), in microseconds
  • method - Model selection type(s) (string or cell array of strings)
  • param0 - Initial parameter values for each model (cell array of numerical vectors)
Returns
  • opt - Index of optimal parametric model (scalar)
  • f - Evaluated model selection functionals (cell array)
  • param - Fitted parameters for each evaluated model (cell array)
  • paramcis - Confidence intervals for the fitted parameters for each evaluated model (cell array)

Description

opt = selectmodel({@model1,@model2,___,@modelN},V,r,K,{'aic',___})

Fits the distance distribution models model1, …, modelN to a signal V, using the dipolar kernel K and distance axis r. The models must be passed as a cell array of function handles. The fits are then evaluated according to the model selection criteria specified in the last input argument:

  • 'aic' - Akaike information criterion
  • 'aicc' - Corrected Akaike information criterion
  • 'bic' - Bayesian information criterion
  • 'rmsd' - Root mean square deviation

The function returns an array containing the optimal model for each selection method.

opt = selectmodel({@model1,@model2,___,@modelN},V,t,{'aic',___})

Fits the time-domain parametric models model1, …, modelN to a signal V defined over the time axis t.

opt = selectmodel(models,{V1,V2,___},r,{K1,K2,___})
opt = selectmodel(models,{V1,V2,___},r,{K1,K2,___},param0)

Passing multiple signals/kernels enables distance-domain global fitting of the parametric models to single distributions. The global fit weights are automatically computed according to their contribution to ill-posedness. The multiple signals are passed as a cell array of arrays of sizes N1, N2,… and a cell array of kernel matrices with sizes N1xM, N2xM, … must be passed as well.

opt = selectmodel(models,{V1,V2,___},{t1,t2,___})
opt = selectmodel(models,{V1,V2,___},{t1,t2,___},param0)

Similarly, time-domain global fitting can be used when passing time-domain models and the model time axes {t1,t2,___} of the corresponding signals.

opt = selectmodel(models,V,r,K,{'aic',___},{par1,___,parN})
opt = selectmodel(models,V,t,{'aic',___},{par1,___,parN})

The initial guess values for the parameters of each model can be passed as a cell array {par1,___,parN} of value vectors.

[opt,f,param,paramcis] = selectmodel(___)

Additional outputs include: the evaluated method selection functionals f for the different methods, a cell array params with the fitted parameters for each of the evaluated models, as well as their confidence intervals paramcis.

Additional Settings

Additional settings can be specified via name-value pairs. All property names are case insensitive and the property-value pairs can be passed in any order after the required input arguments have been passed.

opt = selectmodel(___,'Property1',Value1,'Property2',Value2,___)
  • 'Upper' - Parameter upper bound constraints

    Cell array containing the upper bound values for the parameters of the evaluated parametric models.

    Default: [empty] - Uses the model’s default upper bound values

    Example:

    opt = selectmodel({@dd_gauss,@dd_rice},V,r,K,'aicc','Upper',{[10 1],[10 2]})
  • 'Lower' - Parameter lower bound constraints

    Cell array containing the lower bound values for the parameters of the evaluated parametric models.

    Default: [empty] - Uses the model’s default lower bound values

    Example:

    opt = selectmodel({@dd_gauss,@dd_rice},V,r,K,'aicc','Lower',{[1 0.1],[10 0.2]})

See fitparamodel for a detailed list of other name-value pairs accepted by the function.