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For linear regression to perform properly, data underwent log-log (power law fitting) or log-linear (exponential fitting) transformation prior to performing the piecewise fit.
Because curvatures were detected, an rLowess curve fitting transformation [ 105] was applied to all arrays.
Because curvatures were detected in a few of the arrays, an rLowess curve fitting transformation [ 57] was applied to the data.
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We identified best fitting transformations by comparison of model deviances using a χ2 distribution with 1 degree of freedom.
Firstly, the fact that the best-fitting transformation matrices remain similar across consecutive trials shows that the algorithm is correcting a stable source of noise in the data and not just providing a random over-fitting of the fixations.
Continuous variables were evaluated for nonlinearity by applying simple log transformations followed by more complex fractional polynomials, and the best-fitting transformation was applied as assessed by the change in Akaike's information criterion between univariate Cox proportional hazard models of transformed and untransformed data (Collett, 1994).
The best fitting polynomial transformation that captured this change was determined using a modification of a SAS macro from Sauerbrei [ 24].
The Cahn model leads to erroneous results on fitting to simulated transformation curves.
where f QLCP ( T, δ ) is the transformation fitting criterion described in Section 4.4 and ν is a positive constant.
The traditional fitting procedure consists of transformation of natural data into logarithms and fitting logarithmic data to a Pearson type III distribution by the method of moments.
As described in Zitova et al. [ 22], our registration algorithm pipeline consists of four steps: (1) feature detection and extraction, (2) feature matching, (3) transformation function fitting and (4) image transformation and image resampling.
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