The Experts below are selected from a list of 312 Experts worldwide ranked by ideXlab platform
Gary C Packard - One of the best experts on this subject based on the ideXlab platform.
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misconceptions about Logarithmic Transformation and the traditional allometric method
Zoology, 2017Co-Authors: Gary C PackardAbstract:Logarithmic Transformation is often assumed to be necessary in allometry to accommodate the kind of variation that accompanies multiplicative growth by plants and animals; and the traditional approach to allometric analysis is commonly believed to have important application even when the bivariate distribution of interest is curvilinear on the Logarithmic scale. Here I examine four arguments that have been tendered in support of these perceptions. All the arguments are based on misunderstandings about the traditional method for allometric analysis and/or on a lack of familiarity with newer methods of nonlinear regression. Traditional allometry actually has limited utility because it can be used only to fit a two-parameter power equation that assumes lognormal, heteroscedastic error on the original scale. In contrast, nonlinear regression can fit two- and three-parameter power equations with differing assumptions about structure for error directly to untransformed data. Nonlinear regression should be preferred to the traditional method in future allometric analyses.
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multiplicative by nature Logarithmic Transformation in allometry
Journal of Experimental Zoology, 2014Co-Authors: Gary C PackardAbstract:The traditional allometric method, which is at the heart of research paradigms used by comparative biologists around the world, entails fitting a straight line to Logarithmic Transformations of the original bivariate data and then back-transforming the resulting equation to form a two-parameter power function in the arithmetic scale. The method has the dual advantages of enabling investigators to fit statistical models that describe multiplicative growth while simultaneously addressing the multiplicative nature of residual variation in response variables (heteroscedasticity). However, important assumptions of the traditional method seldom are assessed in contemporary practice. When the assumptions are not met, mean functions may fail to capture the dominant pattern in the original data and incorrect form for error may be imposed upon the fitted model. A worked example from metabolic allometry in doves and pigeons illustrates both the power of newer statistical procedures and limitations of the traditional allometric method. J. Exp. Zool. (Mol. Dev. Evol.) 322B: 202–207, 2014. © 2014 Wiley Periodicals, Inc.
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is Logarithmic Transformation necessary in allometry
Biological Journal of The Linnean Society, 2013Co-Authors: Gary C PackardAbstract:The Metabolic Theory of Ecology (MTE) transformed the field of biological allometry from a discipline that is focused on description to a discipline that is focused more on formulating and testing theory. However, much of the empirical research providing essential background for the MTE – as well as research to test predictions of the theory – is based on the ‘allometric method’, which is a simple procedure for estimating the parameters in a two-parameter power function by exponentiating the equation for a straight line fitted to Logarithmic Transformations of the original bivariate data. The allometric method has been in widespread use for so long that many investigators now apply the procedure mechanically and without due consideration for limitations of the approach. What has been missing from much of the contemporary research on allometric variation is exploratory analysis of untransformed data and graphical validation of the fitted model. I use two examples from the current literature: (1) to demonstrate the utility of exploratory analysis; (2) to illustrate how Transformation may lead investigators to conclusions that are not supported by their data; and (3) to show how nonlinear regression may obviate the putative need to transform. The MTE (and other theories pertaining to patterns of allometric variation) will benefit from greater awareness that the traditional allometric method is not well suited for fitting statistical models to data expressed in the arithmetic scale. © 2013 The Linnean Society of London, Biological Journal of the Linnean Society, 2013, 109, 476–486.
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unanticipated consequences of Logarithmic Transformation in bivariate allometry
Journal of Comparative Physiology B-biochemical Systemic and Environmental Physiology, 2011Co-Authors: Gary C PackardAbstract:Parameters in the two-parameter allometric equation are commonly estimated by fitting a straight line to Logarithmic Transformations of the original data and by back-transforming the resulting model to the arithmetic scale. However, log Transformation distorts the relationship between the predictor and response variables, and this distortion may be sufficient to lead unsuspecting investigators to analyze data that actually are unsuited for allometric research. Two data sets from the current literature are re-examined here to illustrate instances in which log Transformation caused ugly data to look deceptively good. One of the investigations focused on the scaling of metabolism to body mass in evolutionary transitions from prokaryotic to protistan to metazoan levels of organization whereas the other addressed the scaling of intestines to body size in rodents. In both instances investigators were led to conclusions that are not supported by the original data. Problems of the sort described here can readily be avoided simply by performing preliminary graphical analysis of observations expressed in the original units and by validating the final model in the arithmetic domain.
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model selection and Logarithmic Transformation in allometric analysis
Physiological and Biochemical Zoology, 2008Co-Authors: Gary C Packard, Thomas J BoardmanAbstract:Abstract The standard approach to most allometric research is to gather data on a biological function and a measure of body size, convert the data to logarithms, display the new values in a bivariate plot, and then fit a straight line to the Transformations by the method of least squares. The slope of the fitted line provides an estimate for the allometric (or scaling) exponent, which often is interpreted in the context of underlying principles of structural and functional design. However, interpretations of this sort are based on the implicit assumption that the original data conform with a power function having an intercept of 0 on a plot with arithmetic coordinates. Whenever this assumption is not satisfied, the resulting estimate for the allometric exponent may be seriously biased and misleading. The problem of identifying an appropriate function is compounded by the Logarithmic Transformations, which alter the relationship between the original variables and frequently conceal the presence of outliers...
John D Downie - One of the best experts on this subject based on the ideXlab platform.
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optical Logarithmic Transformation of speckle images with bacteriorhodopsin films
Optics Letters, 1995Co-Authors: John D DownieAbstract:The application of Logarithmic Transformations to speckle images is sometimes desirable in converting the speckle noise distribution into an additive, constant-variance noise distribution. The optical transmission properties of some bacteriorhodopsin films are well suited to implement such a Transformation optically in a parallel fashion. I present experimental results of the optical conversion of a speckle image into a transformed image with signal-independent noise statistics, using the real-time photochromic properties of bacteriorhodopsin. The original and transformed noise statistics are confirmed by histogram analysis.
Thomas J Boardman - One of the best experts on this subject based on the ideXlab platform.
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model selection and Logarithmic Transformation in allometric analysis
Physiological and Biochemical Zoology, 2008Co-Authors: Gary C Packard, Thomas J BoardmanAbstract:Abstract The standard approach to most allometric research is to gather data on a biological function and a measure of body size, convert the data to logarithms, display the new values in a bivariate plot, and then fit a straight line to the Transformations by the method of least squares. The slope of the fitted line provides an estimate for the allometric (or scaling) exponent, which often is interpreted in the context of underlying principles of structural and functional design. However, interpretations of this sort are based on the implicit assumption that the original data conform with a power function having an intercept of 0 on a plot with arithmetic coordinates. Whenever this assumption is not satisfied, the resulting estimate for the allometric exponent may be seriously biased and misleading. The problem of identifying an appropriate function is compounded by the Logarithmic Transformations, which alter the relationship between the original variables and frequently conceal the presence of outliers...
Joao Miguel Raposo Sanches - One of the best experts on this subject based on the ideXlab platform.
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Blind Inpainting Using $\ell _{0}$ and Total Variation Regularization
IEEE Transactions on Image Processing, 2015Co-Authors: Manya V. Afonso, Joao Miguel Raposo SanchesAbstract:In this paper, we address the problem of image reconstruction with missing pixels or corrupted with impulse noise, when the locations of the corrupted pixels are not known. A Logarithmic Transformation is applied to convert the multiplication between the image and binary mask into an additive problem. The image and mask terms are then estimated iteratively with total variation regularization applied on the image, and ℓ0 regularization on the mask term which imposes sparseness on the support set of the missing pixels. The resulting alternating minimization scheme simultaneously estimates the image and mask, in the same iterative process. The Logarithmic Transformation also allows the method to be extended to the Rayleigh multiplicative and Poisson observation models. The method can also be extended to impulse noise removal by relaxing the regularizer from the ℓ0 norm to the ℓ1 norm. Experimental results show that the proposed method can deal with a larger fraction of missing pixels than two phase methods, which first estimate the mask and then reconstruct the image.
I Klimes - One of the best experts on this subject based on the ideXlab platform.
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multimodal distribution versus Logarithmic Transformation of thyroid volumes in adolescents detection of subgroup with subclinical thyroid disorders and its impact on the assessment of the upper limit of normal thyroid volumes
Endocrine Journal, 2003Co-Authors: P Langer, Maria Tajtakova, J Koska, P Bohov, E Sebokova, I KlimesAbstract:Our objective was to evaluate whether there is a multimodal distribution of thyroid volume (ThV) in iodinereplete adolescents and to examine the relation between excessive ThV and the presence of thyroid hypoechogenicity (HE), serum thyroperoxidase antibodies (anti-TPO) and TSH levels >4.5 mU/l. ThV was measured by ultrasound in adolescents aged 13 yr (N = 1083) and 17 yr (N = 1089) from 22 schools in 6 districts of eastern Slovakia and expressed as ml and ml/m2 body surface area. For each age group the multimodal distribution of ThV values was tested by computing their frequency at intervals of 0.5 ml/m2 and plotting the cumulative frequency on a probability scale in which each segment with normal distribution should give a straight line. In all examined subjects the HE was evaluated by ultrasound; in 924 (42.5%) of those anti-TPO was estimated by radioimmunoassay and TSH by immuno-electrochemiluminiscent assay. The medians of urinary iodine found in 55-164 spot urine samples from each of 6 districts (total number = 1003) were 126-142 μg/l, indicating an iodine-replete status. There was a trimodal distribution of ThV in each group, 80-85% in the lowest, 10-15% in the middle, and 5-7% in the upper segments. In the 10th ThV decile of the 17-yr group the frequency of HE (33/109 = 30.3%), anti-TPO (13/62 = 21.0%) and TSH (6/62 = 9.7%) was significantly higher than that in the 1st-9th decile (71/980 = 7.2%, P 4.5 mU/l. Thus in the 10% of subjects with the highest ThV, the frequency of HE and anti-TPO was 4-5 times higher than in the remaining 90%. Our data indicate that an epidemiological evaluation of a large population of adolescents can detect a group with early signs of thyroid dysfunction (e.g. excessive ThV, increased frequency of HE, anti-TPO and TSH >4.5% mU/l), although such dysfunction may not be clinically apparent. This contrasts with numerous earlier reports which used a Logarithmic Transformation of the data in similar ThV sets, thus making the data appear homogeneous (unimodal) and with a normal distribution and obscuring the true multimodal distribution. This further prevents recognition of subjects with evidence of disordered thyroid status which thus become falsely included into a normal range.
