“Standard univariate linear models analyze traits separately and can fail to detect multivariate changes in body shape or somatic condition, including changes in mass-to-girth ratios.”

Studies that aim to describe the multivariate nature of body condition have used a variety of statistical methods (e.g. multiple regression, principal component analyses), which have limited flexibility and implicitly make specific assumptions that are not always recognized. … Multiple regression (MR) models have low flexibility in that they cannot handle variables that are simultaneously response and explanatory variables, which is resolved using stepwise modelling approaches that can potentially cause bias in the parameter estimates (Darlington & Smulders, 2001; Freckleton, 2002).

Previous published linear models have made univariate predictions (7 -11) . … The joint use of several segmental body compositions has been justified in some metabolic disease risk studies. … Compared with these published formulas, the originality and advantage of the proposed model consist in predicting simultaneously several segmental compartments (such as TF mass or APL mass) with a good accuracy

Most studies investigated single anthropometric traits in relation to BC risk, which might not adequately capture the complexity of body morphology, specifically among women who are similar in one trait but differ in others [10].

Compositional data, which are multivariate and constrained, behave differently than standard univariate data; thus, they require different statistical treatment.

While GWAS-meta-analyses have successfully revealed new loci, so far, all these studies have focused on one single anthropometric trait at a time and may not adequately capture differences in body shape between individuals who are similar in one trait but different in others.

This approximation provides a reasonably accurate predictor at the population level 3, 4 but is blind to many aspects of body shape and composition that may be critical to disease etiology.

Our findings highlight the value of using multiple traits to define complex phenotypes for discovery, which are not captured by single-trait analyses, and may shed light onto new pathways.

Animal bodies are multivariate and the many components that can change along with their interrelatedness complicate the interpretation of body condition indices and their ability to detect changes in any one aspect of animal body composition (e.g. lipid content; Speakman[2001](#fec12460-bib-0061)). … Multivariate response surfaces may be particularly useful for examining the relationships between external factors, body composition (e.g. lipid and protein contents) and fitness.

Generally speaking, ratio BCIs are correlated with size but by definition residual BCIs are not [1, 11]. … Measures of true body condition that accommodate allometry include scaled fat, where fat mass is scaled to length using the TL scaling model described above [27], and residual fat, where fat mass is regressed on length to calculate residuals [22]. Neither scaled fat nor residual fat are expected to change with body size [29, 36]. … Each of our measures of true body condition was associated with size (Table 3; Fig 1C–1E). Percent fat exhibited the strongest relationship with SVL, having a significant positive slope (p ≤ 0.001) and r2 values that suggest > 40% of the variation in percent fat is explained by SVL. Scaled fat exhibited a slight but significant negative relationship with SVL (p ≤ 0.05), and the r2 values suggest that approximately 7% of the variation in scaled fat is explained by SVL. Residual fat was similar, exhibiting a slightly negative but still significant relationship with SVL (p ≤ 0.05), and the r2 values suggest that 4–5% of the variation in residual fat is explained by SVL.

This study was designed to identify the body composition factors measured by skinfold fat (S), girth (G), and diameter (D) variables and to provide multivariate scaling models that measure fat (F) and lean body weight (LBW) factors.

Traditionally, researchers have tried to create strong biomarkers by combining together simpler ones through various hand-designed formulae 22, 30, 31; This is the case for ABSI 18 and RFM 19. In contrast, here we propose to combine multiple raw biomarkers together through joint, multi-dimensional statistical models.

Three-dimensional optical (3DO) body scanning has been proposed for automatic anthropometry. However, conventional measurements fail to capture detailed body shape.

The above premise may not hold if the model itself is too rigid, which is possible for a simple linear model (given that many adiposity formulas are non-linear and thus less rigid).

We analyzed scaling patterns in pooled and separate sexes with two methods: (1) bivariate log-log regression and (2) multivariate principal component analysis (PCA). … Our findings suggest that especially in sex-specific analyses, the pattern and magnitude of allometry are sensitive to statistical methodology.

A BW score to assess the likelihood of being overweight was developed by fitting a proportional odds logistic regression model on BCS using the difference between ideal and estimated BW, the neck to height ratio, and the girth to height ratio as predictors; this score was then standardized using the data from individuals with a BCS of 5.

Using data from three species of small mammals we show that, unlike the Scaled mass index, all six conventional methods fail to do this, and as a result they consistently lead to significant differences in CIs between age classes and sex that are a mere consequence of changes in body size. … all methods based on the principle of least squares in the*y*-plane (*R*i,ancova,*K*nand*W*r) were systematically biased towards larger individuals, despite the current acceptance of these methods in ecology or fisheries biology.

However, a one-way MANOVA, which uses Wilks's lambda as the test statistic, is the most powerful method of determining whether there are statistically significant differences between the somatotype means for two or more groups.

Simple ratios in which a measurement variable is divided by a size variable are commonly used but known to be inadequate for eliminating size correlations from morphometric data.

Stepwise[linear regressions](https://www.sciencedirect.com/topics/medicine-and-dentistry/linear-regression-analysis)were performed to derive linear models for each of the outcome body composition, blood marker, and strength variables. … Four different types of models were created:*1*) “3D PC-only” models that included the first fifteen 3D body shape model PCs as candidate variables;*2*) “Anthro-only” models that included height, weight, and linear circumference measurements extracted by the[3DO scanner](https://www.sciencedirect.com/topics/earth-and-planetary-sciences/optical-scanner)software along with ethnicity and age as candidate variables;*3*) “3D PC + Anthro” models that included both 3D PC and anthropometric candidate variables; and*4*) “Simple Anthro” models for body composition only that used the same variables as described by Ng et al. ([10](#bib10)).

We also compared the performance of these condition indices with the multiple regression of several morphometric variables on body fat mass, percent body fat and residual fat mass.

Most of the statistical analyses performed in geometric morphometric studies are the same analyses used in traditional morphometrics, such as general linear models or principal component analysis (Hotelling 1933).

Among these techniques, high-density geometric morphometric approaches provide a powerful and versatile framework to robustly characterize shape and phenotypic integration, the covariances among morphological traits.

Although body condition potentially encompasses a wide range of health state dimensions (nutritional, immune or hormonal status), in practice most studies operationalize body condition using a single (univariate) measure, such as fat storage.

Univariate metrics are not adequate to measure avian body size.

Third, the same set of distance measures could be obtained from two different shapes because the location of where the distances were made relative to one another was not included in the data. … For instance, if maximum length and maximum width were measured on both an oval and a teardrop, both objects could have the same height and width values, yet they are clearly different in shape Therefore, one expects the statistical power for distinguishing shapes to be much lower than it should be.

In this context, we highlight the problems of using indices when underlying statistical assumptions are not met (isometry, parallel slopes between treatments).

First method of morphometrics called Traditional morphometrics was done by measuring linear dis tances (such as length, width, and height) and multivariate statistical tools were used to describe patterns of shape variation within and among groups.