Linear Mixed Model Framework Research Articles

A graphical model for skewed matrix-variate non-randomly missing data.

Epidemiological studies on periodontal disease (PD) collect relevant bio-markers, such as the clinical attachment level (CAL) and the probed pocket depth (PPD), at pre-specified tooth sites clustered within a subject's mouth, along with various other demographic and biological risk factors. Routine cross-sectional evaluation are conducted under a linear mixed model (LMM) framework with underlying normality assumptions on the random terms. However, a careful investigation reveals considerable non-normality manifested in those random terms, in the form of skewness and tail behavior. In addition, PD progression is hypothesized to be spatially-referenced, i.e. disease status at proximal tooth-sites may be different from distally located sites, and tooth missingness is non-random (or informative), given that the number and location of missing teeth informs about the periodontal health in that region. To mitigate these complexities, we consider a matrix-variate skew-$t$ formulation of the LMM with a Markov graphical embedding to handle the site-level spatial associations of the bivariate (PPD and CAL) responses. Within the same framework, the non-randomly missing responses are imputed via a latent probit regression of the missingness indicator over the responses. Our hierarchical Bayesian framework powered by relevant Markov chain Monte Carlo steps addresses the aforementioned complexities within an unified paradigm, and estimates model parameters with seamless sharing of information across various stages of the hierarchy. Using both synthetic and real clinical data assessing PD status, we demonstrate a significantly improved fit of our proposition over various other alternative models.

A linear mixed model framework for gene‐based gene–environment interaction tests in twin studies

Interaction between genes and environments (G×E) can be well investigated in families due to the shared genes and environment among family members. However, the majority of the current tests of G×E interaction between a set of variants and an environment are only suitable for studies with unrelated subjects. In this paper, we extend several G×E interaction tests to a linear mixed model framework to study interaction between a set of correlated environments and a candidate gene in families. The correlated environments can either be modeled separately or jointly in one model. We demonstrate theoretically that the tests developed by modeling correlated environments separately are valid and present a computationally fast alternative to detect G×E interaction in families. For either strategy, we propose treating the genetic main effects as a random effect to reduce the number of main-effect parameters and thus improve the power to detect interactions. Additionally, we propose a generalization of a test of interaction that adaptively sums the interactions using a sequential algorithm. This generalized set of tests, referred to as the sequential algorithm for the sum of powered score (Seq-SPU) family of tests, can be expressed as a weighted version of the SPU. We find that the adaptive version of our test, Seq-aSPU, can outperform aSPU in cases where the interactions effects are in opposite directions. We applied these methods to the Minnesota Center for Twin and Family Research data set and found one significant gene in interaction with four psychosocial environmental factors affecting the alcohol consumption among the twins.

Method for short-term prediction of milk yield at the quarter level to improve udder health monitoring

Udder health problems are often associated with milk losses. These losses are different between quarters, as infected quarters are affected both by systemic and pathogen-specific local effects, whereas noninfected quarters are only subject to systemic effects. To gain insight in these losses and the milk yield dynamics during disease, it is essential to have a reliable reference for quarter-level milk yield in an unperturbed state, mimicking its potential yield. We developed a novel methodology to predict this quarter milk yield per milking session, using an historical data set of 504 lactations collected on a test farm by an automated milking system from DeLaval (Tumba, Sweden). Using a linear mixed model framework in which covariates associated with the linearized Wood model and the milking interval are included, we were able to describe quarter-level yield per milking session with a proportional error below 10%. Applying this model enables us to predict the milk yield of individual quarters 1 to 50 d ahead with a mean prediction error ranging between 8 and 20%, depending on the amount of historical data available to estimate the random effect covariates for the predicted lactation. The developed methodology was illustrated using 2 examples for which quarter-level milk losses are calculated during clinical mastitis. These showed that the quarter-level mixed model allows us to gain insight in quarter lactation dynamics and enables to calculate milk losses in different situations.

An adaptive gene-level association test for pedigree data

BackgroundWe propose a gene-level association test that accounts for individual relatedness and population structures in pedigree data in the framework of linear mixed models (LMMs). Our method data-adaptively combines the results across a class of score-based tests, only requiring fitting a single null model (under the null hypothesis) for the whole genome, thereby being computationally efficient.ResultsWe applied our approach to test for association with the high-density lipoprotein (HDL) ratio of post- and pretreatments in GAW20 data. Using the LMM similar to that used by Aslibekyan et al. (PLos One, 7:48663, 2012), our method identified 2 nearly significant genes (APOA5 and ZNF259) near rs964184, whereas neither the other gene-level tests nor the standard test on each individual single-nucleotide polymorphism (SNP) detected any significant gene in a genome-wide scan.ConclusionsGene-level association testing can be a complementary approach to the SNP-level association testing and our method is adaptive and efficient compared to several other existing gene-level association tests.

Shifts in functional trait-species abundance relationships over secondary subalpine meadow succession in the Qinghai-Tibetan Plateau.

Although trait-based processes of community assembly during secondary succession invokes multiple factors that ultimately determine the presence or absence of a species, little is known regarding the impacts of functional traits on species abundance in successional plant communities. Here in species-rich subalpine secondary successional meadows of the Qinghai-Tibetan Plateau, we measured photosynthesis rate and leaf proline content that are related to plant growth and abiotic stress resistance, respectively, and seed germination rate that is closely correlated with plant germination strategy to test their influence on species abundance during succession. We used a linear mixed effects model framework to examine the shifts in trait-abundance relationships and the correlations among these three traits in successional communities. We observed significant shifts in trait-abundance relationships during succession, e.g., abundant species in early-successional meadows exhibited relatively high photosynthesis rates and leaf proline content, but showed low seed germination rates, whereas the converse were true in late successional communities. However, the correlations among the three traits were insignificant in most meadow communities. Our results show that functional traits associated with plant growth, stress resistance, and reproduction impose strong influence on species abundance during secondary subalpine meadow succession in the Qinghai-Tibetan Plateau.

Heritability estimation and differential analysis of count data with generalized linear mixed models in genomic sequencing studies.

Genomic sequencing studies, including RNA sequencing and bisulfite sequencing studies, are becoming increasingly common and increasingly large. Large genomic sequencing studies open doors for accurate molecular trait heritability estimation and powerful differential analysis. Heritability estimation and differential analysis in sequencing studies requires the development of statistical methods that can properly account for the count nature of the sequencing data and that are computationally efficient for large datasets. Here, we develop such a method, PQLseq (Penalized Quasi-Likelihood for sequencing count data), to enable effective and efficient heritability estimation and differential analysis using the generalized linear mixed model framework. With extensive simulations and comparisons to previous methods, we show that PQLseq is the only method currently available that can produce unbiased heritability estimates for sequencing count data. In addition, we show that PQLseq is well suited for differential analysis in large sequencing studies, providing calibrated type I error control and more power compared to the standard linear mixed model methods. Finally, we apply PQLseq to perform gene expression heritability estimation and differential expression analysis in a large RNA sequencing study in the Hutterites. PQLseq is implemented as an R package with source code freely available at www.xzlab.org/software.html and https://cran.r-project.org/web/packages/PQLseq/index.html. Supplementary data are available at Bioinformatics online.

Fitting an optimal variance-covariance structure for longitudinal data under linear mixed effects models framework: simulation based analysis

Dans la presente etude, (i) la performance de 5 criteres d’information statistique (AIC, BIC, HQIC, CAIC et AICC) dans la determination de la matrice de covariance entre mesures repetees dans l’analyse des donnees longitudinales et (ii) les consequences d’une mauvaise specification de la matrice de covariance entre mesures repetees ont ete evaluees. Premierement, une simulation a ete realisee dans 192 situations determinees par les caracteristiques de l'echantillon de donnees (taille de l’echantillon, nombre de mesures repetees, parametre de croissance, taille de la matrice G, matrice de covariance entre mesures repetees et la distribution des erreurs entre mesures repetees). Pour chaque combinaison de ces parametres, le taux de succes de chaque critere d’information statistique est calcule dans le but de comparer les performances des 5 criteres d’information statistique. Deuxiemement, sur la base de 32 situations restreintes determinees par les caracteristiques de l’echantillon de donnees, l’effet d’une mauvaise specification de la matrice de covariance entre mesures repetees a ete evalue par la determination des ecarts et biais relatifs moyens des effets fixes et aleatoires estimes. Les resultats obtenus de la simulation montrent de meilleures performances globales pour HQIC, BIC and CAIC dans l’identification des matrices de covariance autoregressive de premier ordre [AR(1)] et de moyenne mobile de premier ordre [MA(1)]. Concernant la matrice de covariance autoregressive a moyenne mobile de premier ordre [ARMA(1,1)], les criteres AIC, AICC et HQIC presentent les meilleures performances globales. Les resultats obtenus montrent egalement que, quelle que soit la situation de simulation consideree, les effets fixes etaient bien estimes avec cependant, une tendance au biais lorsque le parametre de croissance tend a devenir petit. Par contre, les effets aleatoires etaient mal estimes au regard du biais relatif. Pour une bonne estimation des effets aleatoires, une attention particuliere doit etre accordee a la recherche de la matrice de covariance entre mesures repetees optimale dans l'analyse des donnees longitudinales.

Predictive Modeling of Microbiome Data Using a Phylogeny-Regularized Generalized Linear Mixed Model.

Recent human microbiome studies have revealed an essential role of the human microbiome in health and disease, opening up the possibility of building microbiome-based predictive models for individualized medicine. One unique characteristic of microbiome data is the existence of a phylogenetic tree that relates all the microbial species. It has frequently been observed that a cluster or clusters of bacteria at varying phylogenetic depths are associated with some clinical or biological outcome due to shared biological function (clustered signal). Moreover, in many cases, we observe a community-level change, where a large number of functionally interdependent species are associated with the outcome (dense signal). We thus develop “glmmTree,” a prediction method based on a generalized linear mixed model framework, for capturing clustered and dense microbiome signals. glmmTree uses the similarity between microbiomes, which is defined based on the microbiome composition and the phylogenetic tree, to predict the outcome. The effects of other predictive variables (e.g., age, sex) can be incorporated readily in the regression framework. Additional tuning parameters enable a data-adaptive approach to capture signals at different phylogenetic depth and abundance level. Simulation studies and real data applications demonstrated that “glmmTree” outperformed existing methods in the dense and clustered signal scenarios.

An integrated -omics analysis of the epigenetic landscape of gene expression in human blood cells

BackgroundGene expression can be influenced by DNA methylation 1) distally, at regulatory elements such as enhancers, as well as 2) proximally, at promoters. Our current understanding of the influence of distal DNA methylation changes on gene expression patterns is incomplete. Here, we characterize genome-wide methylation and expression patterns for ~ 13 k genes to explore how DNA methylation interacts with gene expression, throughout the genome.ResultsWe used a linear mixed model framework to assess the correlation of DNA methylation at ~ 400 k CpGs with gene expression changes at ~ 13 k transcripts in two independent datasets from human blood cells. Among CpGs at which methylation significantly associates with transcription (eCpGs), > 50% are distal (> 50 kb) or trans (different chromosome) to the correlated gene. Many eCpG-transcript pairs are consistent between studies and ~ 90% of neighboring eCpGs associate with the same gene, within studies. We find that enhancers (P < 5e-18) and microRNA genes (P = 9e-3) are overrepresented among trans eCpGs, and insulators and long intergenic non-coding RNAs are enriched among cis and distal eCpGs. Intragenic-eCpG-transcript correlations are negative in 60–70% of occurrences and are enriched for annotated gene promoters and enhancers (P < 0.002), highlighting the importance of intragenic regulation. Gene Ontology analysis indicates that trans eCpGs are enriched for transcription factor genes and chromatin modifiers, suggesting that some trans eCpGs represent the influence of gene networks and higher-order transcriptional control.ConclusionsThis work sheds new light on the interplay between epigenetic changes and gene expression, and provides useful data for mining biologically-relevant results from epigenome-wide association studies.

Bootstrapping longitudinal data with multiple levels of variation

A set of estimators for model parameters in the framework of linear mixed models is considered for longitudinal data with multiple levels of random variation. Various bootstrap methods are assessed for making inference about the parameters including the variance components for which, typically, bootstrap confidence intervals show undercoverage. A new weighted estimating equation bootstrap, which uses different weight schemes for different parameter estimators, is proposed. It shows improved variance estimation for the variance component estimators and produces confidence intervals with better coverage for the variance components in cases with normal and non-normal errors.

Modelling the responses of Australian subtropical rainforest birds to changes in environmental conditions along elevational gradients

AbstractMontane birds face significant threats from a warming climate, so determining the environmental factors that most strongly influence the composition of such assemblages is of critical conservation importance. Changes in temperature and other environmental conditions along elevational gradients are known to influence the species richness and abundance of bird assemblages occupying mountains. However, the role of species‐specific traits in mediating the responses of bird species to changing conditions remains poorly understood. We aimed to determine whether different bird species responded differently to changing environmental conditions in a relatively understudied biodiversity hotspot in subtropical rainforest on the east coast of Australia. We examined patterns in avian species richness and abundance along two rainforest elevational gradients using monthly point counts between September 2015 and October 2016. Environmental data on temperature, wetness, canopy cover and canopy height were collected simultaneously, and trait information on body size and feeding guild membership for each bird species was obtained from the Handbook of Australian, New Zealand and Antarctic Birds. We used a generalized linear mixed modelling (GLMM) framework to determine the drivers of species richness and abundance and to quantify species’ trait–environment interactions. GLMMs indicated that temperature alone was significantly positively correlated with species richness and abundance. Species richness declined with increasing elevation. When modelling abundance, we found that feeding guild membership did not significantly affect species’ responses to environmental conditions. In contrast, the predicted abundance of a species was found to depend on its body size, due to significant positive interactions between this trait, temperature and canopy cover. Our findings indicate that large‐bodied birds are likely to increase in abundance more rapidly than small‐bodied birds with continued climatic warming. These results underline the importance of temperature as a driving factor of avian community assembly along environmental gradients.

Testing the response of macroinvertebrate communities and biomonitoring indices under multiple stressors in a lowland regulated river

River systems and their communities are exposed to diverse and multiple threats. Understanding how these threats affect the behaviour of biomonitoring indices is essential in order to provide reliable tools for the management and conservation of watercourses. To this purpose we tested the relationship of the STAR_ICMi index and its metrics, LIFE index and macroinvertebrate community with hydrology, water chemistry and land use in 8 sites located along the Oglio River course (Northern Italy), a watercourse originating from a large and deep lake. Macroinvertebrates and water samples were collected seasonally from summer 2013 to summer 2015 and daily discharge data were used to calculate several indices of hydrological alteration. A subset of these variables was selected by principal component analysis for using in the data analysis. The influence of hydrology, water chemistry and land use on macroinvertebrate community structure was explored with the variance partitioning method, while their influence on biomonitoring indices was analysed in a linear mixed effect model framework. Temporal and spatial constraints were explicitly considered in both analyses. Macroinvertebrate community structure was mainly related to these last two factors and to their joint effects with water chemistry and hydrology. STAR_ICMi, its metrics (with the exception of the Shannon index) and LIFE were related to the distance from the lake outlet, a proxy of mean annual discharge, groundwater input and artificial land use. STAR_ICMi, ASPT and EPT richness were also inversely related to the flow variability in the 3 months preceding sample collection. Surprisingly LIFE index was not related to any of the hydrological variables. The results of this study highlight weakness in the current biomonitoring tools and support the need for further investigations on macroinvertebrate interrelations with environmental drivers and their spatial and temporal structure. This is essential to overcome the limitations that may affect the reliability of macroinvertebrate-based indices in aquatic biomonitoring.

Diagnostic Assessment of Schools Using the Generalized Linear Mixed Model Framework

교육평가는 집단 수준에서도 진단적 정보를 제공할 수 있다. 본 연구의 목적은 학교에서 사용할 수 있는 집단 수준 진단평가 모형을 일반화선형혼합모형의 틀에서 제시하고 그 모형을 이용한 진단 결과의 정확성을 확인하는 것이다. 그러한 목적을 달성하기 위해 먼저 연구 모형을 제시하고 분석 결과의 정확성을 확인하는 모의실험을 실시하였다. 모의실험의 조건은 문항 수, 인지요소의 수, 문항 당 인지요소의 비율 등이었다. 모의실험 분석 결과 인지요소의 효과 추정치에 대한 편파(bias)나 RMSE의 측면에서 볼 때, 어떤 조건에서도 편파는 발견되지 않았으며, RMSE는 문항 수가 증가할수록, 인지요소 수가 증가 할수록 낮아졌다. 다만 문항 당 인지요소의 비율은 중간 수준일 때 가장 낮은 RMSE를 보 였다. 이는 학교별 문항 난이도의 차이를 설명함에 있어 인지요소의 사용과 미사용이 균 형 잡힌 정보를 제공하기 때문인 것으로 추정된다. 학교에 대한 진단이 어떤 방식으로 이루어질 수 있는지가 예시와 함께 설명되었으며, 연구의 장단점과 후속 과제 또한 논의 되었다.Educational assessment can provide diagnostic information at group levels. The purpose of this study was to provide a group-level diagnostic assessment model for schools as a generalized linear mixed model and to examine the factors that influence the accuracy of the diagnosis. For that purpose, the research model was presented in a generalized linear mixed model framework, and simulation analyses were conducted. Simulation factors were the number of items, the number of attributes, and the proportion of attributes to item. As a result of the simulation analyses, no biases were observed under all conditions, and root mean squared errors (RMSEs) decreased as the number of items and attributes increased. For the proportion of attributes to item, the RMSEs were lowest when the proportion was moderate. The reason is estimated to be that the presence and absence of the attributes are balanced when explaining the differences of item difficulties by schools. It was also exemplified how the schools could be diagnosed using the model. The strengths and weaknesses of the model were discussed with directions for further studies.

Simultaneous and temporal autoregressive network models

AbstractWhile logistic regression models are easily accessible to researchers, when applied to network data there are unrealistic assumptions made about the dependence structure of the data. For temporal networks measured in discrete time, recent work has made good advances (Almquist &amp; Butts, 2014), but there is still the assumption that the dyads are conditionally independent given the edge histories. This assumption can be quite strong and is sometimes difficult to justify. If time steps are rather large, one would typically expect not only the existence of temporal dependencies among the dyads across observed time points but also the existence of simultaneous dependencies affecting how the dyads of the network co-evolve. We propose a general observation-driven model for dynamic networks that overcomes this problem by modeling both the mean and the covariance structures as functions of the edge histories using a flexible autoregressive approach. This approach can be shown to fit into a generalized linear mixed model framework. We propose a visualization method that provides evidence concerning the existence of simultaneous dependence. We describe a simulation study to determine the method's performance in the presence and absence of simultaneous dependence, and we analyze both a proximity network from conference attendees and a world trade network. We also use this last data set to illustrate how simultaneous dependencies become more prominent as the time intervals become coarser.

KMgene: a unified R package for gene-based association analysis for complex traits.

SummaryIn this report, we introduce an R package KMgene for performing gene-based association tests for familial, multivariate or longitudinal traits using kernel machine (KM) regression under a generalized linear mixed model framework. Extensive simulations were performed to evaluate the validity of the approaches implemented in KMgene.Availability and implementation http://cran.r-project.org/web/packages/KMgene.Supplementary information Supplementary data are available at Bioinformatics online.

Assessing Grain Yield and Quality Traits Stability of Spring Wheat Cultivars at Different Crop Management Levels

Eleven spring wheat cultivars were compared in terms of the stability of their grain yield and grain quality. The cultivars’ stability was evaluated separately at two different crop management levels — moderate-input management and high-input management. Three stability models were used for the two crop management levels based on a linear mixed model framework with restricted maximum likelihood. The Shukla model was the most appropriate for the evaluation of stability of tested spring wheat cultivars. The thousand-grain weight, starch content, Zeleny sedimentation value and test weight were characterized, and the stability ranking cultivars at moderate-input management level was mostly consistent with the rank of cultivars 24 for high-input management level. For grain yield, grain protein content and wet gluten content, the stability rankings were not consistent. Cultivars ‘Monsun’ and ‘Parabola’ are the most stable cultivars for grain yield in moderate-input management and high-input management, respectively. Cultivar ‘Hewilla’ was the stable cultivar for all quality traits at moderate-input management. Cultivar ‘Arabella’ was the most stable cultivar at high-input management level.

Circadian rhythms of trematode parasites: applying mixed models to test underlying patterns.

Circadian rhythms of parasites and their hosts can influence processes such as transmission, pathology and life cycle evolution. For trematode parasites that depend on free-living infectious stages (i.e. cercariae) to move among host species, the timing of parasite release is hypothesized to increase the likelihood of contacting a host. Yet, a persistent challenge in studying such biorhythms involves selection of appropriate analytical techniques. Here, we extend a generalized linear mixed modelling (GLMM) framework to cosinor analyses, thereby allowing flexibility in the statistical distribution of the response variable, incorporation of multiple covariates and inclusion of hierarchical grouping effects. By applying this approach to 93 snails infected with trematode parasites from freshwater pond ecosystems, we detected non-random rhythms in six of eight species, with variation in both the timing of peak cercariae release (between 5:10 and 21:46 h) and its magnitude (between 13 and 386). The use of GLMM yielded more accurate and precise estimates of the cosinor parameters compared with classical least-squares (LS) based on a simulation-based sensitivity analysis. The sensitivity analysis revealed that the amplitude and rhythm-adjusted mean values from the LS models diverged from the true values at some limits. We highlight the importance of novel analytical approaches for evaluating parasite circadian rhythms and investigating their underlying mechanisms.

A Retrospective Multicenter Cohort Analysis of Complications Following Outpatient Therapeutic Endoscopic Procedures in Children: 2017 Presidential Poster Award

Introduction: The risk of complications following therapeutic endoscopic procedures in children is poorly understood, herein we analyzed a 44-center diagnostic-code based database for admissions, direct inpatient or ED-inpatient followig the commonest pediatric endoscopic therapeutic interventions. Methods: The study is a retrospective multi-institutional database analysis. PHIS was interrogated through ICD 9-CM principal procedure codes to identify patients undergoing therapeutic endoscopy in the ambulatory setting between 9/1/2005 and 8/30/2015 at 44 free-standing children's hospitals. Demographics, co-morbidities, and type of procedure were analyzed using the generalized linear mixed model framework. The R statistical package was used for analysis. Results: A total of 6,302 patients underwent therapeutic endoscopic procedures during the study period: 45.07% underwnt polypectomy, 21.61% underwent variceal sclerotherapy or banding and 33.32% underwent endoscopic control of bleeding. Of the 6,302 patients, 0.65% were readmitted (40 to ED, 13 to directly to inpatient) within 5 days with a gastrointestinal or pulmonary diagnosis. The mean age (SD) overall was 9.32 (5.36) years and 9.56 (5.29) years for readmissions. The majority of readmissions (33/53, 62.26%) were on the day of or the day after the procedure; 30.2% received abdomen imaging, 11.3% received chest imaging and none were reendoscoped. Readmissions were significantly associated with race (P = 0.010), being higher in minority children (OR 2.11, 95% CI: (1.19, 3.75)) but not age or gender (Age P=0.890; Gender P=0.947). Complex chronic conditions (CCC) conferred risk of readmission; each additional CCC increasing the odds by 44% (OR 1.44, 95% CI: (1.02,2.03), P=0.038). Type of procedure was significantly associated readmission (P=0.003). Endoscopic control of a bleed had higher odds than polypectomy / injection/banding (OR 2.26, 95% CI: (1.18, 2.26); OR 6.33, 95% CI: (1.85, 21.69)). Conclusion: This is the largest study, to date, reporting on adverse outcomes complicating elective therapeutic endoscopic procedures in children defined by ED or inpatient readmission postprocedure. It is limited by the inherent diagnostic constraints of a coding based database. We report a 0.65% readmission rate, with most readmissions on the day of procedure or the next day. Readmission is more likely in minority populations and in children with complex chronic comorbidities. Endoscopic hemostatic intervention entailed the highest risk of readmission.

A joint modeling and estimation method for multivariate longitudinal data with mixed types of responses to analyze physical activity data generated by accelerometers.

A mixed effect model is proposed to jointly analyze multivariate longitudinal data with continuous, proportion, count, and binary responses. The association of the variables is modeled through the correlation of random effects. We use a quasi-likelihood type approximation for nonlinear variables and transform the proposed model into a multivariate linear mixed model framework for estimation and inference. Via an extension to the EM approach, an efficient algorithm is developed to fit the model. The method is applied to physical activity data, which uses a wearable accelerometer device to measure daily movement and energy expenditure information. Our approach is also evaluated by a simulation study.

Overview of Admixture Mapping

Admixture mapping is a powerful method of gene mapping for diseases or traits that show differential risk by ancestry. Admixture mapping has been applied most often to Americans who trace ancestry to various combinations of Native Americans, Europeans, and West Africans. Recent developments in admixture mapping include improvements in methods and the reference data needed to make inferences about ancestry, as well as extensions of the mapping approach in the framework of linear mixed models. In this unit, the key concepts of admixture mapping are outlined. Several approaches for inferring local ancestry are described, and strategies for performing admixture mapping depending on the study design are provided. Finally, comparisons and contrasts between linkage analysis, association analysis, and admixture mapping are provided, with an emphasis on integrating admixture mapping and association testing. © 2017 by John Wiley & Sons, Inc.