A command in the Candidates menu of the FormantPathEditor window.

Coefficients by track

determines how many coefficients will be used in the modelling of a formant track. The second number determines the number of coefficients for the modelling of formant 2, and so on. For example, if you specify "4 3 3", the first three formants will be modelled. Formant 1 will be modelled with 4 coefficients which means that a third order polynomial is used for modelling. Formant 2 and formant 3 are modelled with 3 coefficients which means that their tracks will be modelled as parabolas.

Variance exponent

determines the power of the first term in the overall stress criterion S. The best model is the one with the lowest value for the stress S.

The stress criterion S is defined in Weenink (2015) as

where s² is the sum of the squares of the standard errors of all the coefficients of the modelled formant tracks within one Formant object, k is the total number of coefficients of these tracks, in the example given above k is 10 (= 4 + 3 + 3), χ² is the sum of the chi squares of each track, d is the sum of the degrees of freedom of each track. Because the standard error s is proportional to bandwidth and χ² is inversely proportional to bandwidth, the expression for S grows approximately as 2·varianceExponent-2 with bandwidth. Setting the varianceExponent somewhat larger than one guarantees that for two tracks whose formants only differ in their bandwidths, the track with the larger bandwidths obtains a larger value for the stress value S.