I know that if four parameters needed to be fitted, then we need at least 5 measured points to be able to apply the Fredlund particle size distribution model (Fredlund et al., 2000). But, I could fit their model by only three points of PSD for more than 100 measured data. And the performance of our approach was excellent. Now, I’m confused and can’t find any logical reason to interpret it.
By using reasonable assumptions it may be possible to reduce the number of minimum data points that would be necessary, in principle, to fully determine (estimate) the parameters of a modelling correlation. For instance, we may either take the «diameter of the minimum allowable size particle» as a fitting parameter, thus obtaining its estimate from the available experimental data, or we may accept (reasonable assumption) that it can be taken as null. This option reduces the number of degrees of freedom by one. Other assumption that can lead to one less degree of freedom is to accept that some kind of additional relationship can be established among two or more parameters (therefore not independent). Of course, such a previously accepted relationship will also decrease the number of degrees of freedom by one. The same occurs if one of the parameters is fixed at some 'reasonable value', thus not being fitted to the considered set of experimental data points. Of course, such assumptions restrain the generality of the correlation originally considered. The remaining number of degrees of freedom still requires at least the same number of independent data points for the corresponding parameters to be determined (estimated). We must be cautious to clearly distinguish modelling parameters from model assumptions.
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