Abstract
Background: Novel models for the assessment of non-linear data are being developed for the benefit of making better predictions from the data. Objective: To review traditional and modern models. Results, and Conclusions: 1) Logit and probit transformations are often successfully used to mimic a linear model. Logistic regression, Cox regression, Poisson regression, and Markow modeling are examples of logit transformation; 2) Either the x- or y-axis or both of them can be logarithmically transformed. Also Box Cox transformation equations and ACE (alternating conditional expectations) or AVAS (additive and variance stabilization for regression) packages are simple empirical methods often successful for linearly remodeling of non-linear data; 3) Data that are sinusoidal, can, generally, be successfully modeled using polynomial regression or Fourier analysis; 4) For exponential patterns like plasma concentration time relationships exponential modeling with or without Laplace transformations is a possibility. Spline and Loess are computationally intensive modern methods, suitable for smoothing data patterns, if the data plot leaves you with no idea of the relationship between the y- and x-values. There are no statistical tests to assess the goodness of fit of these methods, but it is always better than that of traditional models.
Highlights
Non-linear relationships like the smooth shapes of airplanes, boats, and motor cars were constructed from scale models using stretched thin wooden strips, otherwise called splines, producing smooth curves, assuming a minimum of strain in the materials used
Spline and Loess are computationally intensive modern methods, suitable for smoothing data patterns, if the data plot leaves you with no idea of the relationship between the y- and x-values
Suitable for smoothing data patterns, if the data plot leaves you with no idea of the relationship between the y- and x-values
Summary
Non-linear relationships like the smooth shapes of airplanes, boats, and motor cars were constructed from scale models using stretched thin wooden strips, otherwise called splines, producing smooth curves, assuming a minimum of strain in the materials used. Many non-linear data patterns can be developed mathematically, and this paper reviews some of them. Novel models for the assessment of non-linear data are being developed for the benefit of making better predictions from the data. Box Cox transformation equations and ACE (alternating conditional expectations) or AVAS (additive and variance stabilization for regression) packages are simple empirical methods often successful for linearly remodeling of non-linear data; 3) Data that are sinusoidal, can, generally, be successfully modeled using polynomial regression or Fourier analysis; 4) For exponential patterns like plasma concentration time relationships exponential modeling with or without Laplace transformations is a possibility. There are no statistical tests to assess the goodness of fit of these methods, but it is always better than that of traditional models
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