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.

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.

Improved Comparison of ILI Data and Field Excavations

2012 ◽  
Author(s):  
William V. Harper ◽  
David J. Stucki ◽  
Thomas A. Bubenik ◽  
Clifford J. Maier ◽  
David A. R. Shanks ◽  
...  
Keyword(s):  
Regression Analysis ◽  
Regression Line ◽  
Cost Savings ◽  
Major Axis ◽  
Least Squares Regression ◽  
Text Book ◽  
Probability Of Exceedance ◽  
Management Plans ◽  
Independent Variable ◽  
Reduced Major Axis

The importance of comparing in-line inspection (ILI) calls to excavation data should not be underestimated. Neither should it be undertaken without a solid understanding of the methodologies being employed. Such a comparison is not only a key part of assessing how well the tool performed, but also for an API 1163 evaluation and any subsequent use of the ILI data. The development of unity (1-1) plots and the associated regression analysis are commonly used to provide the basis for predicting the likelihood of leaks or failures from unexcavated ILI calls. Combining such analysis with statistically active corrosion methods into perhaps a probability of exceedance (POE) study helps develop an integrity maintenance plan for the years ahead. The theoretical underpinnings of standard regression analysis are based on the assumption that the independent variable (often thought of as x) is measured without error as a design variable. The dependent variable (often labeled y) is modeled as having uncertainty or error. Pipeline companies may run their regressions differently, but ILI to field excavation regressions often use the ILI depth as the x variable and field depth as the y variable. This is especially the case in which a probability of exceedance analysis is desired involving transforming ILI calls to predicted depths for a comparison to a threshold of interest such as 80% wall thickness. However, in ILI to field depth regressions, both the measured depths can have error. Thus, the underlying least squares regression assumptions are violated. Often one common result is a regression line that has a slope much less than the ideal 1-1 relationship. Reduced Major Axis (RMA) Regression is specifically formulated to handle errors in both the x and y variables. It is not commonly found in the standard literature but has a long pedigree including the 1995 text book Biometry by Sokal and Rohlf in which it appears under the title of Model II regression. In this paper we demonstrate the potential improvements brought about by RMA regression. Building on a solid comparison between ILI data and excavations provides the foundation for more accurate predictions and management plans that reliably provide longer range planning. This may also result in cost savings as the time between ILI runs might be lengthened due to a better analysis of such important data.

scholarly journals Empirical Estimation of Accumulation-Induced Change in Gill Net Catchability: Mind the Observation Errors

2015 ◽  
Vol 8 (1) ◽  
pp. 13-22 ◽  
Author(s):  
Timo J. Marjomäki ◽  
Marko Paloniemi ◽  
Tapio Keskinen ◽  
Jonna Kuha ◽  
Juha Karjalainen
Keyword(s):  
Functional Relationship ◽  
Major Axis ◽  
Error Variance ◽  
Ordinary Least Squares ◽  
Observation Error ◽  
Least Squares Regression ◽  
Empirical Estimation ◽  
Gill Net ◽  
Negative Effect ◽  
The Relationship

We analyzed cumulative catches for 24 h gill net exposures divided into 4*6 h, 2*12 h and 1*24 h soak time treatments to estimate the reduction in its catchability due to accumulation of fish. The effects of loss of catch during net lifting, disturbance effect and fouling were eliminated as far as possible to reveal the true effect of accumulation. First we applied simple nonparametric and parametric tests in comparison of treatments. As expected, considerable reduction in catchability took place along with the increase in soak time, indicated by significantly lower total 24 h catches from longer soaks in comparison with shorter ones. The reduction was more pronounced for roach than for perch. Further, we compared a functional relationship regression (FRR), admitting correctly observation error variance also in the x-axis variable, with ordinary least squares regression (OLS) in modelling the relationship between cumulative 24 h catches for different treatments. We estimated the between-replicates proportional observation error variance within a treatment and found it to be similar in different treatments. Therefore the variance ratio could be assumed to be close to 1 enabling the use of major axis solution FRR. In this particular case the incorrect use of OLS obviously gives a seriously biased result, exacerbating the negative effect of accumulation for high x-axis values in comparison with FRR. We recommend the use of FRR for any analysis comparing different notoriously low precision fish abundance proxies.

scholarly journals Rensch's rule is not verified in melanopline grasshoppers (Acrididae)

2013 ◽  
Vol 1 (12) ◽  
pp. 1 ◽  
Author(s):  
Claudio J. Bidau ◽  
Dardo A. Marti ◽  
Elio R. Castillo
Keyword(s):  
Body Size ◽  
Body Length ◽  
Major Axis ◽  
Evolutionary Trend ◽  
Male Body ◽  
Rensch’S Rule ◽  
Rensch's Rule ◽  
First Case ◽  
Reduced Major Axis ◽  
The Relationship

Sexual size dimorphism (SSD) is almost universal in animals. Rensch’s rule proposes that SSD increases with increasing average body size in taxa where males are larger than females (male- biased SSD; MBSSD) and decreases when females are larger (female-biased SSD; FBSSD). Although it was proposed that both patterns are part of the same evolutionary trend, there is more evidence for Rensch’s rule in the first case. We analysed SSD in the acridid subfamily Melanoplinae in a sample of 718 species and subspecies covering all tribes and representative genera. As in all Orthopera, SSD is female/biased. Body length was used as a proxy for body size. Mean body size within the subfamily varied between 9 and 34.5 mm in males (N= 812) and 12.75 and 44.0 mm in females (N= 735). Except for five species (0.7%) all taxa (from subfamily to subspecies) showed moderate to strong FBSSD (mean= 1.27). The lowest SSD was observed in Melanoplus chumasch (SSD= 1.01), and the highest in Phaedrotettix aptera coquinae (SSD= 1.83). To test Rensch’s rule we performed reduced major axis (RMA) regressions between log10 (male body length) and log10 (female body length). In no case RMA slopes were significantly higher than 1.0 which would signal Rensch’s rule. Thus, Melanoplinae represents a new case of FBSSD where Rensch’s rule is not verified. The proximate causes of FBSSD and the non-occurrence of Rensch’s rule in the Orthoptera are discussed as well as the relationship between SSD patterns at the intra- and supraspecific levels.

The number of employed as a macroeconomic indicator of working time dynamics

2020 ◽  
Vol 16 (5) ◽  
pp. 935-945
Author(s):  
I.A. Zaikova
Keyword(s):  
Comparative Analysis ◽  
Manufacturing Sector ◽  
Working Hours ◽  
Working Time ◽  
Labor Costs ◽  
Factors Affecting ◽  
Time Dynamics ◽  
Developed Economies ◽  
The Relationship ◽  
Macroeconomic Indicator

Subject. The working time of workers at any stage of economic development is a value reflecting the level of labor productivity. Any progress in productivity contributes to changes in the volume of labor costs and the number of employed. Depending on the relationship between the total volume of labor costs and the number of employed, the duration of working time per one worker may change (it may increase, decrease, or remain unchanged). Objectives. The study aims to confirm the importance of such a macroeconomic indicator as the number of employed in varying working hours. Methods. The study rests on the comparative analysis of countries with developed economies based on some indicators like dynamics of the working time fund, dynamics of the number of employed, average number of hours worked during the year per employee, etc. The analyzed timespan is 25 years (from 1991 to 2016). Results. The comparative analysis revealed that in the non-production sphere and the economy as a whole the macroeconomic determinants correlate so that the length of working time per worker reduces. When considering the analysis results for the manufacturing sector, no single trend was identified. Conclusions. One of the key factors affecting the change in working hours is the number of employed. The relationship between the working time fund and the number of employed directly determines the dynamics of working time per worker.

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 Research on the Relationship between Shared Leadership and Individual Creativity-Qualitative Comparative Analysis on the Basis of Clear Set

2021 ◽  
Vol 13 (10) ◽  
pp. 5445
Author(s):  
Muyun Sun ◽  
Jigan Wang ◽  
Ting Wen
Keyword(s):  
Comparative Analysis ◽  
Environmental Factors ◽  
Shared Leadership ◽  
Management Practices ◽  
Qualitative Comparative Analysis ◽  
Necessary Condition ◽  
The Individual ◽  
The Impact ◽  
The Relationship ◽  
Sufficient And Necessary Condition

Creativity is the key to obtaining and maintaining competitiveness of modern organizations, and it has attracted much attention from academic circles and management practices. Shared leadership is believed to effectively influence team output. However, research on the impact of individual creativity is still in its infancy. This study adopts the qualitative comparative analysis method, taking 1584 individuals as the research objects, underpinned by a questionnaire-based survey. It investigates the influence of the team’s shared leadership network elements and organizational environmental factors on the individual creativity. We have found that there are six combination of conditions of shared leadership and organizational environmental factors constituting sufficient combination of conditions to increase or decrease individual creativity. Moreover, we have noticed that the low network density of shared leadership is a sufficient and necessary condition of reducing individual creativity. Our results also provide management suggestions for practical activities during the team management.

scholarly journals Including distorted specimens in allometric studies: linear mixed models account for deformation

2021 ◽  
Author(s):  
Brenen M Wynd ◽  
Josef C Uyeda ◽  
Sterling J Nesbitt
Keyword(s):  
Mixed Model ◽  
Linear Mixed Model ◽  
Major Axis ◽  
Ordinary Least Squares ◽  
Evolutionary Constraint ◽  
Body Parts ◽  
Least Squares Regression ◽  
Full Dataset ◽  
Residual Variation ◽  
Cranial Measurements

Abstract Allometry—patterns of relative change in body parts—is a staple for examining how clades exhibit scaling patterns representative of evolutionary constraint on phenotype, or quantifying patterns of ontogenetic growth within a species. Reconstructing allometries from ontogenetic series is one of the few methods available to reconstruct growth in fossil specimens. However, many fossil specimens are deformed (twisted, flattened, displaced bones) during fossilization, changing their original morphology in unpredictable and sometimes undecipherable ways. To mitigate against post burial changes, paleontologists typically remove clearly distorted measurements from analyses. However, this can potentially remove evidence of individual variation and limits the number of samples amenable to study, which can negatively impact allometric reconstructions. Ordinary least squares regression (OLS) and major axis regression are common methods for estimating allometry, but they assume constant levels of residual variation across specimens, which is unlikely to be true when including both distorted and undistorted specimens. Alternatively, a generalized linear mixed model (GLMM) can attribute additional variation in a model (e.g., fixed or random effects). We performed a simulation study based on a empirical analysis of the extinct cynodont, Exaeretodon argentinus, to test the efficacy of a GLMM on allometric data. We found that GLMMs estimate the allometry using a full dataset better than simply using only non-distorted data. We apply our approach on two empirical datasets, cranial measurements of actual specimens of E. argentinus (n = 16) and femoral measurements of the dinosaur Tawa hallae (n = 26). Taken together, our study suggests that a GLMM is better able to reconstruct patterns of allometry over an OLS in datasets comprised of extinct forms and should be standard protocol for anyone using distorted specimens.

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