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The position of the filament tip, per line in the kymograph, was estimated by fitting an error function as previously described (Demchouk et al., 2011).
The position of each end of the filament was then determined by fitting an error function (Demchouk et al., 2011) to each line of the kymograph (see 'Materials and methods' and Figure 1 figure supplement 1 for details).
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The calculation of the concentration-dependent diffusion coefficients was performed by fitting a modified error function on the measured concentration profiles assuming the nonmetal diffusivity being an exponential function of the nonmetal concentration.
To avoid error induced by fitting an exponential function, the PCHIP (piecewise cubic hermite interpolating polynomial) procedure is used to interpolate between the points (MathWorks 2015).
By fitting an ordinary ORM with robust standard errors for clustered data instead of fitting a variance components model (a multilevel model for ordinal responses), we were treating the within-cluster dependence as a "nuisance" and not as a phenomenon that we were interested in [36].
Fold changes and standard errors were obtained by fitting a linear model to each gene and standard errors were smoothed by empirical Bayes.
Further, we estimated the fold change and standard errors by fitting a linear model (using the lmFit function) for each gene given the groups of arrays and then compute a moderated t-statistics of differential expression by applying empirical Bayes at a level of 0.05.
Fold changes and standard errors were obtained by fitting a linear model to each gene expression values and standard errors were smoothed based on the empirical Bayes method.
The experimental error bars were derived by fitting a linear function to the backward events and reading deviations of the data from the fitting function (Fig. 6(c)).
Measurement error from breast density was assessed by fitting a linear mixed-effects model by restricted maximum likelihood and corresponding intraclass correlation coefficient [ 26].
The vertical distribution of error patterns of temperature and water vapor, and ozone mixing ratios are determined by fitting the simulated error covariance matrix to the observations.
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