Milne’s Argument for the Log‐Ratio Measure*

Survival analysis is commonly conducted in medical and public health research to assess the association of an exposure or intervention with a hard end outcome such as mortality. The Cox (proportional hazards) regression model is probably the most popular statistical tool used in this context. However, when the exposure includes compositional covariables (that is, variables representing a relative makeup such as a nutritional or physical activity behaviour composition), some basic assumptions of the Cox regression model and associated significance tests are violated. Compositional variables involve an intrinsic interplay between one another which precludes results and conclusions based on considering them in isolation as is ordinarily done. In this work, we introduce a formulation of the Cox regression model in terms of log-ratio coordinates which suitably deals with the constraints of compositional covariates, facilitates the use of common statistical inference methods, and allows for scientifically meaningful interpretations. We illustrate its practical application to a public health problem: the estimation of the mortality hazard associated with the composition of daily activity behaviour (physical activity, sitting time and sleep) using data from the U.S. National Health and Nutrition Examination Survey (NHANES).

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Independent Tests and the Log-Likelihood-Ratio Measure of Confirmation

Thought A Journal of Philosophy ◽

10.1002/tht3.120 ◽

2014 ◽

Vol 3 (2) ◽

pp. 124-135

Author(s):

Alexander R. Pruss

Keyword(s):

Likelihood Ratio ◽

Log Likelihood ◽

Log Likelihood Ratio ◽

Ratio Measure

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Digital soil mapping of compositional particle-size fractions using proximal and remotely sensed ancillary data

Geophysics ◽

10.1190/geo2012-0053.1 ◽

2012 ◽

Vol 77 (4) ◽

pp. WB201-WB211 ◽

Cited By ~ 40

Author(s):

S. Buchanan ◽

J. Triantafilis ◽

I. O. A. Odeh ◽

R. Subansinghe

Keyword(s):

Particle Size ◽

High Resolution ◽

Soil Mapping ◽

Additive Models ◽

Digital Soil Mapping ◽

Unbiased Estimation ◽

Ancillary Data ◽

Size Fractions ◽

Particle Size Fractions ◽

Log Ratio

The soil particle-size fractions (PSFs) are one of the most important attributes to influence soil physical (e.g., soil hydraulic properties) and chemical (e.g., cation exchange) processes. There is an increasing need, therefore, for high-resolution digital prediction of PSFs to improve our ability to manage agricultural land. Consequently, use of ancillary data to make cheaper high-resolution predictions of soil properties is becoming popular. This approach is known as “digital soil mapping.” However, most commonly employed techniques (e.g., multiple linear regression or MLR) do not consider the special requirements of a regionalized composition, namely PSF; (1) should be nonnegative (2) should sum to a constant at each location, and (3) estimation should be constrained to produce an unbiased estimation, to avoid false interpretation. Previous studies have shown that the use of the additive log-ratio transformation (ALR) is an appropriate technique to meet the requirements of a composition. In this study, we investigated the use of ancillary data (i.e., electromagnetic (EM), gamma-ray spectrometry, Landsat TM, and a digital elevation model to predict soil PSF using MLR and generalized additive models (GAM) in a standard form and with an ALR transformation applied to the optimal method (GAM-ALR). The results show that the use of ancillary data improved prediction precision by around 30% for clay, 30% for sand, and 7% for silt for all techniques (MLR, GAM, and GAM-ALR) when compared to ordinary kriging. However, the ALR technique had the advantage of adhering to the special requirements of a composition, with all predicted values nonnegative and PSFs summing to unity at each prediction point and giving more accurate textural prediction.

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Standardizing sablefish (Anoplopoma fimbria) long-line survey abundance indices by modeling the log-ratio of paired comparative fishing cpues

ICES Journal of Marine Science ◽

10.1006/jmsc.1996.0181 ◽

1997 ◽

Vol 54 (1) ◽

pp. 48-59 ◽

Cited By ~ 7

Author(s):

D Kimura

Keyword(s):

Anoplopoma Fimbria ◽

Long Line ◽

Abundance Indices ◽

Line Survey ◽

Log Ratio

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Mineral exploration in the glaciated terrain using upper soil horizon geochemistry and compositional statistical data analysis

10.5194/egusphere-egu21-10191 ◽

2021 ◽

Author(s):

Pertti Sarala ◽

Solveig Pospiech ◽

Maarit Middleton ◽

Anne Taivalkoski ◽

Helena Hulkki ◽

...

Keyword(s):

Data Analysis ◽

Statistical Data ◽

Mineral Exploration ◽

Environmentally Friendly ◽

Soil Horizon ◽

Geochemical Data ◽

Elemental Distribution ◽

Statistical Data Analysis ◽

Aqua Regia ◽

Log Ratio

Vulnerable nature in northernmost Europe requires development of new, environmentally friendly sampling and analyses techniques for mineral exploration. Those areas are typically covered by transported glaciogenic sediments where the glacial till is most dominant. To offer an alternative for conventional basal till and bedrock sampling with heavy machines, the use of different surface geochemical sampling media and techniques which are quick and cost-effective have been actively applied during the last decade. Particularly, the development of selective and weak leach techniques for the upper soil (Ah and B) horizons&#8217; geochemistry has been intensive, but the reliability needs to be improved and testing is required in different glaciogenic environments.In this research, carried out under the project New Exploration Technologies (NEXT), funded by the European Union&#8217;s Horizon 2020 research and innovation programme under grant agreement No 776804, we used stratified random sampling strategy for choosing sampling locations and developed novel compositional statistical data analysis for the interpretation of geochemical data obtained by surface geochemical techniques. The test area is located in the Rajapalot area, Ylitornio, northern Finland, where an active project is carried out by Mawson Oy for Au-Co exploration. The thickness of till cover varies from some metres to 5 m and the glacial morphology is composed of the ribbed moraine ridges with peatlands in between. A sampling network for the Ah and B horizon samples was comprised of 89 routine samples and 10 field replicates acquired of mineral Podsol-type soils. The chemical analyses methods used were Ultratrace 1:1:1 Aqua Regia leach and 0.1 M sodium pyrophosphate leach for the Ah horizon samples, and Ionic leach and Super Trace Aqua Regia leach methods for the B horizon samples. The laboratory analyses were supported by the portable X-Ray Fluorescence (pXRF) analyses done directly in the field. The statistical analysis was based on log-ratio transformations of the geochemical compositions to avoid spurious results. In addition, the response ratios were calculated to measure the degree of enrichment in each element per sample.The preliminary results of the soil geochemistry show a significant response to many elements (e.g. Au, Co, Cu, Mo, Sc, Te and W) with known mineralized bedrock targets observed in the drill core data. Elemental distribution is also reflecting the lithological variations of the rock units in the bedrock. Based on the results, it is obvious that a) there is good or moderate correlation for several elements between the surface geochemical data and underlying bedrock, and b) soil analysis method using certain soil sampling procedure and selective extraction is an effective, environmentally friendly geochemical exploration technique in the glaciated terrains.

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Heterogeneous calcium flux in peripheral T cell subsets revealed by five-color flow cytometry using log-ratio circuitry

Cytometry ◽

10.1002/cyto.990210211 ◽

1995 ◽

Vol 21 (2) ◽

pp. 187-196 ◽

Cited By ~ 22

Author(s):

M. Roederer ◽

M. Bigos ◽

T. Nozaki ◽

R. T. Stovel ◽

D. R. Parks ◽

...

Keyword(s):

Flow Cytometry ◽

T Cell ◽

T Cell Subsets ◽

Calcium Flux ◽

Color Flow ◽

Log Ratio

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data a; * significance level; a=0.05; * variance of difference of two observations on the log scale; * sigmaW = within-subjects standard deviation; sigmaW=0.355; s=sqrt(2)sigmaW; total number of subjects (needs to be a multiple of 2); n=58; * error degrees of freedom for AB/BA cross-over with n subjects in total; n2=n-2; * ratio = mu_T/mu_R; ratio=1.00; run; data b; set a; * calculate power; t1=tinv(1-a,n-2); t2=-t1; nc1=(sqrt(n))((log(ratio)-log(0.8))/s); nc2=(sqrt(n))((log(ratio)-log(1.25))/s); df=(sqrt(n-2))((nc1-nc2)/(2t1)); prob1=probt(t1,df,nc1); prob2=probt(t2,df,nc2); answer=prob2-prob1; power=answer*100; run; proc print data=b; run; As an example of using this SAS code, suppose µ = 1, σ = 0.355, α = 0.05 and n = 58. The power (as a percentage) is calculated as 90.4. The required number of subjects to achieve a given power can easily be obtained by trial and error using a selection of values of n. An alternative approach is to use trial and error directly on the sample size n for a given power. For more on this see Phillips (1990) and Diletti et al. (1991), for example. 7.4 Individual bioequivalence As noted in Section 7.1, individual bioequivalence (IBE) is a criterion for deciding if a patient who is currently being treated with R can be

Design and Analysis of Cross-Over Trials ◽

10.1201/9781420036091-17 ◽

2003 ◽

pp. 362-362

Keyword(s):

Standard Deviation ◽

Sample Size ◽

Degrees Of Freedom ◽

Trial And Error ◽

Significance Level ◽

Individual Bioequivalence ◽

Alternative Approach ◽

Within Subjects ◽

Log Ratio ◽

Selection Of

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Chemical markers in the aroma profiles of South Moravian red wine distillates

Czech Journal of Food Sciences ◽

10.17221/208/2011-cjfs ◽

2012 ◽

Vol 30 (No. 4) ◽

pp. 369-376 ◽

Cited By ~ 2

Author(s):

L. Veverka ◽

M. Jelínková ◽

K. Hron ◽

J. Balík ◽

J. Stávek ◽

...

Keyword(s):

Red Wine ◽

Pinot Noir ◽

The Other ◽

Cabernet Sauvignon ◽

Chemical Markers ◽

The Czech Republic ◽

Linalool Oxide ◽

South Moravia ◽

Log Ratio ◽

Grape Cultivars

HSSPME-GC/MS method was used to investigate the volatile compounds responsible for varietal character in the aroma of wine distillates made from 16 different red wine grape cultivars: Andre, Blue Frankish, Merlot, Cabernet Moravia, Rubinet, Pinot Noir, Ariana, Alibernet, Laurot, Dornfelder, Blauer Portugieser, Agni, Neronet, Zweigeltrebe, Cabernet Sauvignon, and Domina. The grapes were all grown in the same vineyard in South Moravia, an important viticultural region in the south of the Czech Republic bordering Austria. The isometric log-ratio transformation was used to compute variances prior to statistical analysis, and a compositional biplot was used to interpret the data and identify the main chemical markers. A comparison of the key terpenoids present in the aroma profiles indicated that these were consistent with the known relationships between the cultivars based on their parentage. There were similarities in the terpenoid elements of the aroma profiles of Blue Frankish and its relatives Andre, Laurot, Agni, and Zweigeltrebe, which are dominated by (Z)-linalool oxide, linalool, isoborneol, terpinen-4-ol and α-terpineol. On the other hand, the aroma profiles of Pinot Noir, Blauer Portugieser, Cabernet Sauvignon and their related hybrids are dominated by o-cymene, limonene, (E)-sabinyl acetate, and (E)-calamenene.  

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