A comparative analysis of the reduced major axis technique of fitting lines to bivariate data

1987 ◽  
Vol 17 (12) ◽  
pp. 1630-1630 ◽  
Author(s):  
Daniel J. Leduc
Keyword(s):  
Comparative Analysis ◽  
Major Axis ◽  
Bivariate Data ◽  
Reduced Major Axis

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A comparative analysis of the reduced major axis technique of fitting lines to bivariate data

1987 ◽  
Vol 17 (7) ◽  
pp. 654-659 ◽  
Author(s):  
Daniel J. Leduc
Keyword(s):  
Comparative Analysis ◽  
Major Axis ◽  
Group Method ◽  
Least Squares Regression ◽  
Primary Interest ◽  
Conditional Mean ◽  
Bivariate Data ◽  
Functional Relations ◽  
Reduced Major Axis ◽  
The Relationship

There are many ways of estimating the parameters of an equation to represent the relationship between two variables. While least-squares regression is generally acknowledged to be the best method to use when estimating the conditional mean of one variable given a fixed value for another, it is not usually an appropriate method to use when your primary interest is in the values of the equation parameters themselves (functional relations). In this case there are many other techniques (Bartlett's three-group method, Schnute's trend line, the general structural relationship, major axis regression, and reduced major axis) that may provide better estimates of these values. When all of the above techniques are compared, it is found that reduced major axis is often the most applicable because of its desirable properties and ease of estimation.

Estimation of response slopes in respiratory control

1984 ◽  
Vol 56 (2) ◽  
pp. 536-539 ◽  
Author(s):  
D. L. Sherrill ◽  
G. D. Swanson
Keyword(s):  
Statistical Approach ◽  
Ventilatory Response ◽  
Respiratory Control ◽  
Major Axis ◽  
Bivariate Normal Distribution ◽  
Directional Statistics ◽  
Control Behavior ◽  
Slope Estimate ◽  
Partial Pressure Of Co2 ◽  
Reduced Major Axis

The ventilatory response to changes in alveolar (arterial) CO2 is widely used as an index of respiratory control behavior. Methods for estimating these response slopes should incorporate the possibility that there may be errors in both the independent (partial pressure of CO2) and dependent (ventilation) variables. In a recent paper Daubenspeck and Ogden (J. Appl. Physiol. Respirat. Environ. Exercise Physiol. 45:823–829, 1978) have suggested problems inherent in the traditional technique of reduced major axis and have suggested a more contemporary technique of directional statistics. We have previously analyzed both techniques and developed a method to overcome the problems of reduced major axis and problems inherent in the use of directional statistics. Under the assumption of a bivariate normal distribution, we demonstrate that our slope estimate is similar to the maximum likelihood estimate proposed by Mardia et al. (J. Appl. Physiol.: Respirat. Environ. Exercise Physiol. 54: 309–313, 1983) for this problem. In addition, we demonstrate a bootstrap statistical approach when the distributions are not normally distributed. These concepts are illustrated using O2-CO2 interaction data.

scholarly journals METABOLIC SCALING REGULARITY IN AQUATIC ECOSYSTEMS

2012 ◽  
Vol 27 (2) ◽  
pp. 13
Author(s):  
L. A. Salcido -Guevara ◽  
F. Arreguín -Sánchez ◽  
L. Palmeri ◽  
A. Barausse
Keyword(s):  
Aquatic Ecosystems ◽  
Major Axis ◽  
Ecosystem Metabolism ◽  
Power Scaling ◽  
Metabolic Scaling ◽  
Relevant Role ◽  
Geographic Differences ◽  
Reduced Major Axis ◽  
Distribución Geográfica ◽  
Trophic Models

We tested the hypothesis that ecosystem metabolism follows a quarter power scaling relation, analogous to organisms. Logarithm of Biomass/Production (B/P) to Trophic Level (TL) relationship was estimated to 98 trophic models of aquatic ecosystems. A normal distribution of the slopes gives a modal value of 0.64, which was significantly different of the theoretical value of 0.75 (p0.05). We also tested for error in both variables, Log (B/P) and TL, through a Reduced Major Axis regression with similar results, with a modal value of 0.756 (p>0.05). We also explored a geographic distribution showing no significant relation (p>0.05) to latitude and between different regions of the world. We conclude that: a) ecosystem metabolism follows the quarter-power scaling rule; b) transfer efficiency between TL plays a relevant role characterizing local attributes to ecosystem metabolism; and c) there is neither latitudinal nor geographic differences. These findings confirm the existence of a metabolic scaling regularity in aquatic ecosystems. Regularidad del escalamiento metabólico en ecosistemas acuáticos Se contrastó la hipótesis de que el metabolismo de un ecosistema sigue una relación de escalamiento análoga a la existente en los organismos. La relación entre el logaritmo de la razón Producción/Biomasa (B/P) y el nivel trófico (TL) se estimó para 98 modelos tróficos de los ecosistemas acuáticos. Una distribución normal de las pendientes de esta relación produjo un valor modal de 0.64 que es significativamente diferente del valor teórico de 0.75 (p0.05) similar al teórico esperado. También se contrastó la hipótesis de existencia de error en ambas variables, logaritmo (B/P) y TL, a través de la técnica de regresión denominada “Reduced Major Axis”, con resultados similares según el valor modal de 0.756, sin diferencia estadísticamente significativa (p>0.05) del valor teórico. Se exploró la existencia de algún patrón en la distribución geográfica, sin obtenerse relación significativa (p>0.05) con la latitud, o con diferentes regiones del mundo. Las conclusiones son: a) el metabolismo del ecosistema sigue la regla de escalamiento metabólico de 3/4; b) la eficiencia de la transferencia entre TL desempeña un papel relevante, representando los atributos locales del metabolismo del ecosistema; c) no hay una diferencias latitudinal o geográfica. Estos resultados confirman la existencia de una regularidad en el escalamiento metabólico en ecosistemas acuáticos.

scholarly journals On the Allometric Relationship Between Size and Composition of Avian Eggs: A Reassessment

The Condor ◽  
2007 ◽  
Vol 109 (3) ◽  
pp. 705-714 ◽  
Author(s):  
Todd W. Arnold ◽  
Andy J. Green
Keyword(s):  
Maternal Investment ◽  
Major Axis ◽  
Ordinary Least Squares ◽  
Egg Mass ◽  
Correlated Errors ◽  
Least Squares Regression ◽  
Inert Component ◽  
Female Component ◽  
Investment In Reproduction ◽  
Reduced Major Axis

AbstractAbstract. Numerous investigators have used allometric regression to characterize the relationship between proportional egg composition and egg size, which is a potentially important characterization for assessing maternal investment in reproduction. Herein, we document two important shortcomings of this approach. First, regressing log component mass against log egg mass involves regressing Y on itself, since each component (Y) is necessarily a part of the whole egg (X). This creates correlated errors, which leads to biased estimates of the regression slope. To circumvent this problem, we recommend regressing egg component masses on a relatively inert component like total water mass. Secondly, investigators routinely use ordinary least squares regression to estimate the slope of allometric relationships, which assumes that all error resides in Y. We demonstrate that this assumption is false, but so are the underlying error assumptions of commonly used alternatives such as reduced major axis and major axis regression. Because each egg is unique and determining composition involves destructive sampling, there is no obvious way to assess measurement error in Y versus X. As a solution, we recommend that investigators analyze multiple eggs per clutch whenever possible and fit a reduced major axis based on the among-female component of variability.

scholarly journals CONDUTIVIDADE ELÉTRICA DO EXTRATO DE SATURAÇÃO DO SOLO A PARTIR DE EXTRATOS 1:2 PELO MÉTODO DO EIXO PRINCIPAL REDUZIDO

Irriga ◽  
2005 ◽  
Vol 10 (4) ◽  
pp. 351-356
Author(s):  
Daniel Da Costa Dantas ◽  
José De Arimatea de Matos ◽  
José Francismar de Medeiros ◽  
Francisco De Queiroz Porto Filho ◽  
Neyton De Oliveira Miranda
Keyword(s):  
Electrical Conductivity ◽  
Linear Regression ◽  
Cucumis Melo ◽  
Major Axis ◽  
Soil Electrical Conductivity ◽  
Soil Extracts ◽  
Saturated Water ◽  
Different Depths ◽  
Reduced Major Axis ◽  
Soil And Water

CONDUTIVIDADE ELÉTRICA DO EXTRATO DE SATURAÇÃO DO SOLO A PARTIR DE EXTRATOS 1:2 PELO MÉTODO DO EIXO PRINCIPAL REDUZIDO  Daniel da Costa Dantas; José de Arimatea de Matos; José Francismar de Medeiros; Francisco de Queiroz Porto Filho; Neyton de Oliveira MirandaDepartamento de Ciências Ambientais, Universidade Federal Rural do Semi Árido, Mossoró, RN, [email protected]  1        RESUMO Com o objetivo de estimar a condutividade elétrica de extratos de saturação do solo (CEes) em função de extratos do solo 1:2 (CE1:2), procedeu-se o monitoramento da salinidade do solo em um experimento com melão irrigado com água de diferentes níveis de salinidade (S1 = 0,6; S2 = 1,9; S3 = 3,2 e S4 = 4,5 dS m-1), aplicada de forma incremental ao longo do ciclo. Coletaram-se amostras de solo para análise em três profundidades (0-15, 15-30 e 30-45 cm), durante dois ciclos de cultivo, aos 70 dias após a semeadura (DAS) no primeiro ciclo e aos 30 e 70 DAS no segundo. Determinou-se a CE1:2 e a CEes em amostras compostas, resultante de 15 tratamentos com três profundidades para cada tratamento. Os dados foram ajustados por profundidade e em conjunto, através de funções lineares de regressão e pelo método do eixo principal reduzido (EPR). A equação CEes = 8,094 CE1:2 + 0,0149 (R2 = 0,9112), desenvolvida através do eixo principal reduzido para todos os dados, apresentou nível de estimabilidade semelhante às equações obtidas para as diferentes profundidades e épocas e que a CE é inversamente proporcional a razão entre água:solo. UNITERMOS: Cucumis melo, salinidade.  DANTAS, D. da C.; MATOS, J. de. A. de; MEDEIROS, J. F. de; PORTO FILHO, F. de. Q.; MIRANDA, N. de. O.; ELECTRICAL CONDUCTIVITY OF SATURATED EXTRACTSDETERMINED BY THE REDUCED MAJOR AXIS METHOD USING MIXTURES OF SOIL AND WATER IN A 1:2 RATIO  2  ABSTRACT This experiment was carried out aiming to estimate electrical conductivity of saturated water soil extracts (CEes) using mixtures of soil and water in a 1:2 ratio (CE1:2). Soil salinity was monitored in a field where melon was irrigated with water which salinity level was increasing during the cycle (S1 = 0.6; S2 = 1.9; S3 = 3.2 and S4 = 4.5 dS m-¹). Samples were taken from two consecutive melon cycles at three depths (0-15, 15-30 and 30-45 cm). At 70 days after seeding (DAS) of the first cycle and at 30 and 70 DAS of the second CEes and CE1:2 were determined from compounded samples taken from 15 treatments with three depths each. Data were adjusted for all data and depth using linear regression and the reduced major axis method (RMA). The equation CEes = 8.094 CE1:2 + 0.0149 (R² = 0.9112) obtained using all data through RMA, showed a degree of predictability similar to the linear regression obtained for different depths and dates. Soil electrical conductivity was inversely correlated to the soil:water ratio. KEYWORDS: Cucumis melo, salinity

Measurement and distribution of zircons in some granitic rocks of magmatic origin

1957 ◽  
Vol 31 (238) ◽  
pp. 544-564 ◽  
Author(s):  
Leonard H. Larsen ◽  
Arie Poldervaart
Keyword(s):  
Major Axis ◽  
Morphological Characters ◽  
Granitic Rocks ◽  
Careful Study ◽  
Scatter Plot ◽  
Growth Trend ◽  
Small Bodies ◽  
Magmatic Origin ◽  
Quartz Monzonite ◽  
Reduced Major Axis

SummaryMorphological characters of zircons in concentrates have been studied by measurement of length along the c-axis and breadth along the a1- or a2-axis of 200 doubly terminated crystals for each sample. The sample is represented graphically by a line fitted mathematically to a scatter plot of the measurements. This line, the reduced major axis, is visualized as a growth trend, and samples are described and compared statistically.From a careful study of zircons in a tonalite it is concluded that zircon crystallized over a short range before crystallization of the main constituent minerals.The distribution of zircon in a batholith of magmatic origin has also been studied. The batholith grades from a core of granodiorite to a mantle of tonalite, but the zircons are uniform throughout. Small bodies of granodiorite and quartz monzonite have sharp contacts against the main batholithic rocks, and zircon samples from these intrusives differ from one another and from those of the batholith. It is concluded that the batholith represents a single intrusion which differentiated after emplacement, and that the later intrusives each crystallized under different conditions.

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