TestDimorph: An R package for analysis of interpopulation sexual dimorphism differences using summary statistics.

OBJECTIVE: The degree of sexual dimorphism in certain traits between males and females differ from one sample to another. Although trait differences by sex are often reported in bioanthropological research, few studies test for statistical significance or make raw data available. TestDimorph is the first R package dedicated to testing and comparing the degree of sexual dimorphism among different samples by leveraging summary statistics. MATERIALS AND METHODS: We provide two approaches of analysis of inter-sample differences in degree of sexual dimorphism: univariate and multivariate for two or more samples. The methods follow upon publications primarily from the AJBA. Within-sex size variability between samples is compared using one-way ANOVA followed by control for multiple pairwise comparisons. In addition, we compute the overlapping area between the density functions of two normal distributions from the mixture intersection index or the non-overlapping area using the dissimilarity index as well as Hedges' g with inferential support using the 95% confidence interval. Finally, we use a multivariate analysis of differences in patterning of sexual dimorphism between samples. RESULTS: We demonstrate various results from applying TestDimorph functions to data supplied with the package. DISCUSSION: The package has many features including functionality for working with summary statistics, simulating data from summary statistics, and the extraction of summary statistics from raw data, so that the entire analysis can be performed through the package.

Allometric scaling and growth: Evaluation and applications in subadult body mass estimation.

OBJECTIVES: Previously developed methods in subadult body mass estimation have not been tested in populations other than European-American or African-American. This study uses a contemporary Taiwanese sample to test these methods. Through evaluating their accuracy and bias, we addressed whether the allometric relationships between body mass and skeletal traits commonly used in subadult body mass estimation are conserved among different populations. MATERIALS AND METHODS: Computed tomography scans of lower limbs from individuals aged 0-17 years old of both sexes were collected from National Taiwan University Hospital along with documented body weight. Polar second moment of area, distal femoral metaphyseal breadth, and maximum superior/inferior femoral head diameter were collected either directly from the scans or from reconstructed 3D models. Estimated body mass was compared with documented body mass to assess the performance of the equations. RESULTS: Current methods provided good body mass estimates in Taiwanese individuals, with accuracy and bias similar to those reported in other validation studies. A tendency for increasing error with increasing age was observed for all methods. Reduced major axis regression showed the allometric relationships between different skeletal traits and body mass across different age categories can all be summarized using a common fitted line. A revised, maximum likelihood-based approach was proposed for all skeletal traits. DISCUSSION: The results suggested that the allometric relationships between body mass and different skeletal traits are largely conserved among populations. The revised method provided improved applicability with strong underlying theoretical justifications, and potential for future improvements.

Scaling of linear anthropometric dimensions in living humans.

OBJECTIVES: Some previous studies suggest that humans do not conform to geometric similarity (isometry) in anthropometric dimensions of the upper and lower limbs. Researchers often rely on a single statistical approach to the study of scaling patterns, and it is unclear whether these methods produce similar results and are equally robust. This study used one bivariate and one multivariate method to examine how linear anthropometric dimensions scale in a sample of adult humans. MATERIALS AND METHODS: Motion capture marker data from 104 adults of varying height and mass were used to calculate anthropometric dimensions. We analyzed scaling patterns in pooled and separate sexes with two methods: (1) bivariate log-log regression and (2) multivariate principal component analysis (PCA). We calculated 95% highest density/confidence intervals for each method and defined positive/negative allometry as estimates lying outside those intervals. RESULTS: Results identified isometric scaling of the upper arm, thigh, and shoulder, positive allometry of the forearm and shank, and negative allometry of the pelvis in the pooled sample using both statistical methods. Patterns of allometry in the pooled sample were similar between methods but differed in magnitude. Sex-specific results differed in both pattern and magnitude between log-log regression and PCA. Only one measurement (shoulder width) departed from isometry in the sex-specific log-log regressions. DISCUSSION: Our findings suggest that especially in sex-specific analyses, the pattern and magnitude of allometry are sensitive to statistical methodology. When body mass was selected as the size variable, most human linear anthropometric dimensions in this sample scaled isometrically and were therefore geometrically similar within sexes.

Prior Probabilities and the Age Threshold Problem: First and Second Molar Development.

Dental development has been used to assess whether an individual may be below or above an age that serves as a legal threshold. This study used development of the first and second mandibular molars from a large sample of individuals (N = 2,676) to examine the age threshold for minimum age of criminal responsibility. A bivariate ordered probit model was applied to dental scores following the Moorrees et al. (1963) system, with the addition of a crypt-absent/present stage. Then a 10-fold cross-validation within each of the sexes showed that the bivariate models produce unbiased estimates of age but are heteroskedastic (with increasing spread of the estimates against actual age). To address the age threshold problem, a normal prior centered on the threshold is assumed, and the product of the prior and the likelihood is integrated up to the age threshold and again starting at the age threshold. The ratio of these two integrals is a Bayes factor, which because the prior is symmetric around the threshold, can also be interpreted as the posterior odds that an individual is over versus under the age threshold. It was necessary to assume an unreasonably high standard deviation of age in the prior to achieve posterior odds that were well above "evens." These results indicate that dental developmental evidence from the first and second molars is of limited use in examining the question of whether an individual is below or over the minimum age of criminal responsibility. As the third molar is more variable in its development than the first two molars, the question of dental evidence regarding the age of majority (generally 18 years) remains problematic.

The Use of Roche, Wainer, and Thissen's Skeletal Maturity of the Knee.

The Roche, Wainer, and Thissen (RWT) knee method was designed to assess maturity in living individuals, but is infrequently cited in studies of skeletal measures for legal age thresholds or estimation of age-at-death for forensic cases. We implement the RWT method using R scripts and analyze its utility in establishing an age threshold of 18 years. We fit the RWT model and verify its accuracy in estimating skeletal age against results and known age data provided by RWT. We also found the transition distribution for full skeletal maturity. Agreement between the RWT method and our implementation was good, with a maximum deviation of 0.03 years. The modes of transition to full skeletal maturity are 18.37 and 17.16 years for males and females. The corresponding Bayes factors are 5.73 and 1.77, indicating that complete skeletal maturity of the knee does not provide conclusive evidence of attainment of 18 years of age.

Timing of Development of the Permanent Mandibular Dentition: New Reference Values from the Fels Longitudinal Study.

Estimating chronological age or assessing the rate of maturation in immature individuals is an important task in biological anthropology and clinical practice. One of the most reliable ways of doing this is by evaluating one's dental development, specifically tooth mineralization. However, few chronologies include reference values for very young children, and few provide an extensive documentation of the range of variation surrounding the reported reference values. We present a new chronology of development of permanent mandibular canine and postcanine teeth from birth through age 28 years, based on over 6,000 radiographs of 590 participants of the Fels Longitudinal Study, recorded between 1940 and 1982. Tooth mineralization was scored following the 14-stage system of Moorrees, Fanning, and Hunt (Moorrees et al., 1963a) with an additional crypt stage. We calculated ages of attainment, as well as average age in stage, using transition analysis. We find that variation increases throughout ontogeny for all teeth, though it is generally comparable between girls and boys. The tempo of dental development tends to be faster in girls. Compared to the classic chronology of Moorrees et al. (1963a), partly based on Fels radiographs, in our sample the development of crowns tends to occur at earlier, and development of roots at increasingly later ages. Our results are more similar to chronologies based on more recent, clinical samples (Liversidge, 2009), though the development of tooth roots in our sample occurs at older ages. Anat Rec, 302:1733-1753, 2019. © 2019 American Association for Anatomy.

Status of Mandibular Third Molar Development as Evidence in Legal Age Threshold Cases.

The completion of the third molar roots has played an important role in ascertaining whether individuals may be at or over a legal threshold of age, often taken as 18 years. This study demonstrates that root apex completion in the third molar is relatively uninformative regarding the threshold of age 18 years in a sample of 1184 males, where mean age-of-attainment of root apex completion for third mandibular molars is about 19.4 years. This paper also considers the legal age threshold problem for cases where the third mandibular molar is not completely formed, and outlines the use of parametric models and Bayes' factors to evaluate dental evidence in statistically appropriate ways. It attempts to resolve confusion over age-within-stage versus age-of-attainment, likelihood ratios versus other diagnostic tests, and prior odds for a case versus the prior density for an age distribution.

Typicality and Predictive Distributions in Discriminant Function Analysis.

While discriminant function analysis is an inherently Bayesian method, researchers attempting to estimate ancestry in human skeletal samples often follow discriminant function analysis with the calculation of frequentist-based typicalities for assigning group membership. Such an approach is problematic because it fails to account for admixture and for variation in why individuals may be classified as outliers or nonmembers of particular groups. This article presents an argument and methodology for employing a fully Bayesian approach in discriminant function analysis applied to cases of ancestry estimation. The approach requires adding the calculation, or estimation, of predictive distributions as the final step in ancestry-focused discriminant analyses. The methods for a fully Bayesian multivariate discriminant analysis are illustrated using craniometrics from identified population samples within the Howells published data. The article also presents ways to visualize predictive distributions calculated in more than three dimensions, explains the limitations of typicality measures, and suggests an analytical route for future studies of ancestry and admixture based in discriminant function analysis.

Univariate and Linear Composite Asymmetry Statistics for the "Pair-Matching" of Bone Antimeres.

This paper examines the distributional properties of univariate and linear composite measures of long bone asymmetry. The goal of this paper is to examine models that best fit the distribution of asymmetries with implications for the improvement of forensic pair-matching techniques. We use the software R to model reference data (N = 2343) and test data (N = 71) as normal distributions, an exponential power distribution, and a skew exponential power distribution-the latter two include the normal as a special case. Our results indicate that the data best fit the latter two distributions because the data are nonnormal. We also show how asymmetry statistics that use absolute values of side differences can be fit as folded distributions. This obviates the need for empirical distributions or for transformations that attempt to convert nonnormal distributions to normal distributions. The results of this study lay the framework for improving pair-matching methods that use comparative reference data.

Population Identifiability from Forensic Genetic Markers: Ancestry Variation in Latin America.

The Combined DNA Index System (CODIS) loci comprise a standard microsatellite marker set widely used for distinguishing among individuals in forensic DNA identity testing for medicolegal casework in the United States and in other countries. In anthropological genetic research, CODIS markers have become an important tool for uses extending beyond case investigations to quantify ancestry proportions, reveals patterns of admixture, and trace population histories. These investigations are especially prevalent in studies of Latin American population structure. Nevertheless, the accuracy of the ancestry estimates computed from the CODIS loci for highly admixed Latino populations has not been formally tested. Longstanding arguments have been made that small ancestry panels, including the CODIS loci specifically, are not suitable for ancestry inference in admixed populations, due to high heterozygosity and limited number of loci used. Recent studies on ancestry inference using the CODIS loci suggest that these do confer more information of population-level identifiability than recognized in forensic genetic scholarship and by the medicolegal community. Here, we formally test the ability of CODIS and CODIS-proxy (e.g., high-heterozygosity and individual-identifiability loci) marker panels to accurately estimate admixture proportions of individuals, including a sample of Latinos with a wide range of ancestry proportions. Using the same individuals to make direct comparisons of the outcomes, the authors produced ancestry estimates from (a) a small CODIS/CODIS-proxy locus panel and (b) a robust and validated microsatellite ancestry-informative panel. They found evidence (e.g., ρ = 0.80-0.88) that supports the use of CODIS/ CODIS-proxy loci to capture the general ancestry estimation trends of a sample. This finding is in line with results of studies using CODIS on Latin American populations: the ancestry estimations generated by CODIS present trends supported by documented population histories (e.g., colonialism and population movements) and microevolutionary events (e.g., gene flow) in Latin America. However, this study also highlights the limitations of CODIS for making individual-level inferences of ancestry: the associated estimates for an acceptable level of statistical confidence (95%) are too broad to make any nuanced inferences regarding an individual's actual ancestry composition.

Optimal trait scoring for age estimation.

OBJECTIVES: Little attention has been paid to questions about the applicability of parametric models to age estimation data and the related problem of how to adjust trait scoring in light of potential deviations from particular parametric models. This article addresses this deficit. METHODS: A Lagrange multiplier goodness-of-fit test is applied to two datasets to address the question of whether or not attainment ages for stages are log-normally distributed. The first dataset used in this article consists of scores of the Todd ten-phase system for the pubic symphysis obtained from 938 individuals with known ages. The second dataset consists of scores for 15 stages of formation for the second mandibular molar scored in 2,304 individuals of known age. RESULTS: For the Todd ten-phase system there is a significant departure from log-normally distributed ages of attainment. To obtain an acceptable goodness-of-fit statistic, Todd scores consequently are collapsed into an eight-phase system that maintains scores I through VII as individual scores but combines phases VIII through X into one phase. The 15-stage scoring system for the second mandibular molar has an acceptable fit to the log-normal distribution for ages of attainment. CONCLUSIONS: The results from the analysis of the Todd pubic symphysis scores show that researchers should use goodness-of-fit tests for parametric models before deciding to collapse scores. Further, such goodness-of-fit tests are an essential tool in answering questions concerning the suitability of various parametric models. For the 15-stage scoring of the second mandibular molar, the log-normal model is appropriate for attainment ages.

Multivariate cumulative probit for age estimation using ordinal categorical data.

BACKGROUND: Multivariate ordinal categorical data have figured prominently in the age estimation literature. Unfortunately, the osteological and dental age estimation literature is often disconnected from the statistical literature that provides the underpinnings for rationale analyses. AIM: The aim of the study is to provide an analytical basis for age estimation using multiple ordinal categorical traits. SUBJECTS AND METHODS: Data on ectocranial suture closure from 1152 individuals are analysed in a multivariate cumulative probit model fit using a Markov Chain Monte Carlo (MCMC) method. RESULTS: Twenty-six parameters in a five variable analysis are estimated, including the 10 unique elements of the five × five correlation matrix. The correlation matrix differs substantially from the identity matrix one would assume under conditional independence among the sutures. CONCLUSION: While the assumption of conditional independence between traits greatly simplifies the use of parametric models in age estimation, this assumption is not a necessary step. Further, in the analysis discussed here there are considerable residual correlations between ectocranial suture closure scores even after 'regressing out' the effect of age.

Bayes in biological anthropology.

In this article, we both contend and illustrate that biological anthropologists, particularly in the Americas, often think like Bayesians but act like frequentists when it comes to analyzing a wide variety of data. In other words, while our research goals and perspectives are rooted in probabilistic thinking and rest on prior knowledge, we often proceed to use statistical hypothesis tests and confidence interval methods unrelated (or tenuously related) to the research questions of interest. We advocate for applying Bayesian analyses to a number of different bioanthropological questions, especially since many of the programming and computational challenges to doing so have been overcome in the past two decades. To facilitate such applications, this article explains Bayesian principles and concepts, and provides concrete examples of Bayesian computer simulations and statistics that address questions relevant to biological anthropology, focusing particularly on bioarchaeology and forensic anthropology. It also simultaneously reviews the use of Bayesian methods and inference within the discipline to date. This article is intended to act as primer to Bayesian methods and inference in biological anthropology, explaining the relationships of various methods to likelihoods or probabilities and to classical statistical models. Our contention is not that traditional frequentist statistics should be rejected outright, but that there are many situations where biological anthropology is better served by taking a Bayesian approach. To this end it is hoped that the examples provided in this article will assist researchers in choosing from among the broad array of statistical methods currently available.