Latent transition regression for mixed outcomes

Health status is a complex outcome, often characterized by multiple measures. When assessing changes in health status over time, multiple measures are typically collected longitudinally. Analytic challenges posed by these multivariate longitudinal data are further complicated when the outcomes are combinations of continuous, categorical, and count data. To address these challenges, we propose a fully Bayesian latent transition regression approach for jointly analyzing a mixture of longitudinal outcomes from any distribution. Health status is assumed to be a categorical latent variable, and the multiple outcomes are treated as surrogate measures of the latent health state, observed with error. Using this approach, both baseline latent health state prevalences and the probabilities of transitioning between the health states over time are modeled as functions of covariates. The observed outcomes are related to the latent health states through regression models that include subject-specific effects to account for residual correlation among repeated measures over time, and covariate effects to account for differential measurement of the latent health states. We illustrate our approach with data from a longitudinal study of back pain.     

Estimating equations for a latent transition model with multiple discrete indicators

This paper proposes a two-part model for studying transitions between health states over time when multiple, discrete health indicators are available. The includes a measurement model positing underlying latent health states and a transition model between latent health states over time. Full maximum likelihood estimation procedures are computationally complex in this latent variable framework, making only a limited class of models feasible and estimation of standard errors problematic. For this reason, an estimating equations analogue of the pseudo-likelihood method for the parameters of interest, namely the transition model parameters, is considered. The finite sample properties of the proposed procedure are investigated through a simulation study and the importance of choosing strong indicators of the latent variable is demonstrated. The applicability of the methodology is illustrated with health survey data measuring disability in the elderly from the Longitudinal Study of Aging.     

结构方程混合模型在SNP分析中的应用

采用结构方程混合模型(SEMM)对实际SNP数据进行分析,为遗传统计学提供一种新的有效的分析方法。本研究的数据是由GAW17提供的,包含697个个体的22条常染色体的上万个SNP和根据这些SNP所模拟的697个个体的性状特点。随机挑选了1号染色体上的4个SNP和3个定量性状作为研究变量,分别进行潜在类别分析和结构方程混合模型分析。根据4个SNP数据,人群被分为3个潜在类别,概率分别为0.53,0.34,0.13。潜在类别1、2和3中的因子均值Q分别为-4.029、-2.052和0,潜在类别1、2的因子均值均低于3(<0.001)。研究表明:结构方程混合模型(SEMM)综合了结构方程模型和潜在类别模型的思想,形成了自己的优势,可用于处理同时包含分类潜变量和连续潜变量的数据。     

Bayesian modeling of embryonic growth using latent variables

In a growth model, individuals move progressively through a series of states in which each state is indicative of developmental status. Interest lies in estimating the rate of progression through each state while incorporating covariates that might affect the transition rates. We develop a Bayesian discrete-time multistate growth model for inference from cross-sectional data with unknown initiation times. For each subject, data are collected at only one time point at which we observe the state as well as covariates that measure developmental progress. We link the developmental progress variables to an underlying latent growth variable that can also affect the state transition rates. A subject with slow latent growth will then have relatively small developmental progress covariates and move through state transitions slowly. We then examine the association between latent growth and the probability of future events in a novel study of embryonic development and pregnancy loss. Using a Markov chain Monte Carlo (MCMC) algorithm for posterior computation, we found evidence in favor of a previously hypothesized but unproven association between slow growth early in pregnancy and increased risk of future spontaneous abortion.     

Graphs, random sums, and sojourn time distributions, with application to ion-channel modeling.

This paper considers the distribution of a sojourn time in a class of states of a stochastic process having finite discrete state space where sojourn times in any individual state are independent and identically distributed, and transitions between states follow a Markov chain. The state space and possible transitions of the process are represented by a graph. Class sojourn time distributions are derived by modifying this graph using 'composition' of states, defining a new Markov chain on the modified graph, and expressing the sojourn time in a composition state as a random sum. Appropriate compositions are chosen according to the possible "cores" of sojourns in the particular class, where a core describes the structure of a sojourn in terms of a single state or a chain in the original graph. Graph methods provide an algorithmic basis for the derivation, which can be simplified by using symmetry results. Models of ion-channel kinetics are used throughout for illustration; class sojourn time distributions are important in such models because individual states are often indistinguishable experimentally. Markov processes are the special case where sojourn times in individual states are exponentially distributed. In this case kinetic parameter estimation based on the observed class sojourn time distribution is briefly discussed; explicit estimating equations applicable to sequential models of nicotinic receptor kinetics are given.     

Quantifying individual heterogeneity and its influence on life‐history trajectories: different methods for different questions and contexts

Heterogeneity among individuals influences the life‐history trajectories we observe at the population level because viability selection, selective immigration and emigration processes, and ontogeny change the proportion of individuals with specific trait values with increasing age. Here, we review the two main approaches that have been proposed to account for these processes in life‐history trajectories, contrasting how they quantify ontogeny and selection, and proposing ways to overcome some of their limitations. Nearly all existing approaches to model individual heterogeneity assume either a single normal distribution or a priori known groups of individuals. Ontogenetic processes, however, can vary across individuals through variation in life‐history tactics. We show the usefulness of describing ontogenetic processes by modelling trajectories with a mixture model that focuses on heterogeneity in life‐history tactics. Additionally, most methods examine individual heterogeneity in a single trait, ignoring potential correlations among multiple traits caused by latent common sources of individual heterogeneity. We illustrate the value of using a joint modelling approach to assess the presence of a shared latent correlation and its influence on life‐history trajectories. We contrast the strengths and limitations of different methods for different research questions, and we exemplify the differences among methods using empirical data from long‐term studies of ungulates.     

GROUP SIZE FACTORS AND GEOGRAPHIC VARIATION OF MORPHOMETRIC CORRELATION

Within-locality correlations among eight morphological traits of the fundatrix and among 15 morphological traits of the alate fundatrigeniae of the aphid Pemphigus populicaulis Fitch were examined for among-locality variation. A jackknife procedure revealed highly significant differences among correlation matrices representing 34 local samples from eastern North America. Most bivariate correlations also differed significantly among samples. Although very low correlations cannot differ, for moderate or strong correlations the average magnitude of correlation is not a good predictor of the degree of interlocality difference. Nearly half of the variation among localities is in the level of “overall correlation,” which is positively correlated with intralocality size variation. Despite significant differences among localities, spatial autocorrelation tests failed to reveal any significant geographic pattern in correlations. Monte Carlo experiments suggest that if geographic patterns in the correlations were of the same magnitude as those for the means of these traits, some of these patterns would have been detected. Factor analyses of the pooled within-locality correlation matrices, after oblique rotation to simple structure, reveal appendage and body-size factors for both alates and stem mothers. In general, correlations between traits with high loadings on the same factor differ among localities, whereas substantial correlations that do not vary geographically are between traits that are not well resolved by the factor analyses. It is hypothesized that the apparently random geographic differences in correlation are caused by chance differences in the mode of response to short-term selection. Geographic patterns in trait means are established by selection, but, because local population sizes are finite, similar response to selection occurs by diverse physiological or developmental mechanisms in different populations, just as replicate lines in artificial selection experiments may achieve the same response by diverse mechanisms. These diverse mechanisms of response will have diverse effects on genetic variance and covariance, causing correlation patterns to vary geographically. Several forces will oppose continued divergence of these patterns.     

Introgression and repeated co‐option facilitated the recurrent emergence of C4 photosynthesis among close relatives

The origins of novel traits are often studied using species trees and modeling phenotypes as different states of the same character, an approach that cannot always distinguish multiple origins from fewer origins followed by reversals. We address this issue by studying the origins of C₄ photosynthesis, an adaptation to warm and dry conditions, in the grass Alloteropsis. We dissect the C₄ trait into its components, and show two independent origins of the C₄ phenotype via different anatomical modifications, and the use of distinct sets of genes. Further, inference of enzyme adaptation suggests that one of the two groups encompasses two transitions to a full C₄ state from a common ancestor with an intermediate phenotype that had some C₄ anatomical and biochemical components. Molecular dating of C₄ genes confirms the introgression of two key C₄ components between species, while the inheritance of all others matches the species tree. The number of origins consequently varies among C₄ components, a scenario that could not have been inferred from analyses of the species tree alone. Our results highlight the power of studying individual components of complex traits to reconstruct trajectories toward novel adaptations.     

Robustness of ancestral state estimates: evolution of life history strategy in ichneumonoid parasitoids

We test hypotheses for the evolution of a life history trait among a group of parasitoid wasps (Hymenoptera: Ichneumonoidea), namely, the transition among koinobiont parasitoids (parasitoids whose hosts continue development after oviposition) between attacking exposed hosts and attacking hosts that are concealed within plant tissue. Using a range of phylogeny estimates based on 28S rDNA sequences, we use maximum parsimony (MP) and maximum likelihood (ML) methods to estimate the ancestral life history traits for the main clades in which both traits occur (using the programs MacClade and Discrete, respectively). We also assess the robustness of these estimates; for MP, we use step matrices in PAUP* to find the minimum weight necessary to reverse estimates or make them ambiguous, and for ML, we measure the differences in likelihood after fixing the ancestral nodes at the alternative states. We also measure the robustness of the MP ancestral state estimate against uncertainties in the phylogeny estimate, manipulating the most-parsimonious tree in MacClade to find the shortest suboptimal tree in which the ancestral state estimate is reversed or made ambiguous. Using these methods, we find strong evidence supporting two transitions among koinobiont Ichneumonoidea: (1) to attacking exposed hosts in a clade consisting of the Helconinae and related subfamilies, and (2) the reverse transition in a clade consisting of the Euphorinae and related subfamilies. In exploring different methods of analyzing variable-length DNA sequences, we found that direct optimization with POY gave some clearly erroneous results that had a profound effect on the overall phylogeny estimate. We also discuss relationships within the superfamily and expand the Mesostoinae to include all the gall-associated braconids that form the sister group of the Aphidiinae.     

A Multi-Trait,Meta-analysis for Detecting Pleiotropic Polymorphisms for Stature,Fatness and Reproduction in Beef Cattle

Polymorphisms that affect complex traits or quantitative trait loci (QTL) often affect multiple traits. We describe two novel methods (1) for finding single nucleotide polymorphisms (SNPs) significantly associated with one or more traits using a multi-trait, meta-analysis, and (2) for distinguishing between a single pleiotropic QTL and multiple linked QTL. The meta-analysis uses the effect of each SNP on each of n traits, estimated in single trait genome wide association studies (GWAS). These effects are expressed as a vector of signed t-values (t) and the error covariance matrix of these t values is approximated by the correlation matrix of t-values among the traits calculated across the SNP (V). Consequently, t''V⁻¹t is approximately distributed as a chi-squared with n degrees of freedom. An attractive feature of the meta-analysis is that it uses estimated effects of SNPs from single trait GWAS, so it can be applied to published data where individual records are not available. We demonstrate that the multi-trait method can be used to increase the power (numbers of SNPs validated in an independent population) of GWAS in a beef cattle data set including 10,191 animals genotyped for 729,068 SNPs with 32 traits recorded, including growth and reproduction traits. We can distinguish between a single pleiotropic QTL and multiple linked QTL because multiple SNPs tagging the same QTL show the same pattern of effects across traits. We confirm this finding by demonstrating that when one SNP is included in the statistical model the other SNPs have a non-significant effect. In the beef cattle data set, cluster analysis yielded four groups of QTL with similar patterns of effects across traits within a group. A linear index was used to validate SNPs having effects on multiple traits and to identify additional SNPs belonging to these four groups.     

The importance of individual developmental variation in stage‐structured population models

Population stage structure is fundamental to ecology, and models of this structure have proven useful in many different systems. Many ecological variables other than stage, such as habitat type, site occupancy and metapopulation status are also modelled using transitions among discrete states. Transitions among life stages can be characterised by the distribution of time spent in each stage, including the mean and variance of each stage duration and within‐individual correlations among multiple stage durations. Three modelling traditions represent stage durations differently. Matrix models can be derived as a long‐run approximation from any distribution of stage durations, but they are often interpreted directly as a Markov model for stage transitions. Statistical stage‐duration distribution models accommodate the variation typical of cohort development data, but such realism has rarely been incorporated in population theory or statistical population models. Delay‐differential equation models include lags but no variation, except in limited cases. We synthesise these models in one framework and illustrate how individual variation and correlations in development can impact population growth. Furthermore, different development models can yield the same long‐term matrix transition rates but different sensitivities and elasticities. Finally, we discuss future directions for estimating realistic stage duration models from data.     

Open-state disulfide crosslinking between Mycobacterium tuberculosis mechanosensitive channel subunits

The mechanosensitive channel of large conductance from Mycobacterium tuberculosis (Tb-MscL) was subjected to cysteine-scanning mutagenesis at several residues in the M1 region. The V15C channel displayed disulfide crosslinking in air, but not in the presence of 100 mM beta-mercaptoethanol. In single-channel experiments, the V15C channel was more sensitive to tension than was wild-type Tb-MscL. In air, Tb-MscL V15C occasionally displayed signature-events: at constant tension, there was first a sojourn in the highest conductance open state, then a series of transitions to substates. During a signature-event, these transitions do not appear to be reversible. Some sojourns in the lower conductance states lasted for > or =100 s. These signature-events were abolished by 100 mM beta-mercaptoethanol and did not occur in a cysteineless gain-of-function mutant, suggesting that the signature-events represent disulfide crosslinking between channel subunits. We conclude that the crosslinking occurs during an open state during asymmetric sojourns that bring the alpha-carbons of adjacent 15C side chains within 3.6-6.8 A. Such asymmetric structures must be considered in models of TB-MscL gating.     

Looking for a needle in a haystack: inference about individual fitness components in a heterogeneous population

Studies of wild vertebrates have provided evidence of substantial differences in lifetime reproduction among individuals and the sequences of life history ‘states’ during life (breeding, nonbreeding, etc.). Such differences may reflect ‘fixed’ differences in fitness components among individuals determined before, or at the onset of reproductive life. Many retrospective life history studies have translated this idea by assuming a ‘latent’ unobserved heterogeneity resulting in a fixed hierarchy among individuals in fitness components. Alternatively, fixed differences among individuals are not necessarily needed to account for observed levels of individual heterogeneity in life histories. Individuals with identical fitness traits may stochastically experience different outcomes for breeding and survival through life that lead to a diversity of ‘state’ sequences with some individuals living longer and being more productive than others, by chance alone. The question is whether individuals differ in their underlying fitness components in ways that cannot be explained by observable ‘states’ such as age, previous breeding success, etc. Here, we compare statistical models that represent these opposing hypotheses, and mixtures of them, using data from kittiwakes. We constructed models that accounted for observed covariates, individual random effects (unobserved heterogeneity), first‐order Markovian transitions between observed states, or combinations of these features. We show that individual sequences of states are better accounted for by models incorporating unobserved heterogeneity than by models including first‐order Markov processes alone, or a combination of both. If we had not considered individual heterogeneity, models including Markovian transitions would have been the best performing ones. We also show that inference about age‐related changes in fitness components is sensitive to incorporation of underlying individual heterogeneity in models. Our approach provides insight into the sources of individual heterogeneity in life histories, and can be applied to other data sets to examine the ubiquity of our results across the tree of life.     

Personality traits in captive lion-tailed macaques (Macaca silenus)

Personality influences an individual's perception of a situation and orchestrates behavioral responses. It is an important factor in elucidating variation in behavior both within and between species. The major focus of this research was to test a method that differs from those used in most previous personality studies, while investigating the personality traits of 52 captive lion-tailed macaques from four zoos. In this study, data from behavioral observations, a P-type principal components analysis (PCA), and bootstrapped confidence intervals as criteria for judging the significance of factor loadings were used rather than subjective ratings, R-type factor analyses, and arbitrary rules of thumb to determine significance. We investigated the relationships among individual component scores and sex, hormonal status, and dominance rank (controlling for age and social group) using a multiple regression analysis with bootstrapped confidence intervals. Three personality dimensions emerged from this analysis: Component 1 contained Extraversion-like behaviors related to sociability and affiliativeness. The higher mean Component score for females suggests that they are more "extraverted" than males. Only agonistic behaviors were significantly related to component 2. High-ranking individuals exhibited higher mean Component 2 scores than mid- or low-ranked individuals. Bold and cautious behaviors both loaded positively on Component 3, suggesting a dimension related to curiosity. The mean Component 3 score for females was higher than the mean score for males. The method used in this study should facilitate intraspecific and general interspecific comparisons. Developing a standardized trait term list that is applicable to many species, and collecting trait term data in the same manner and concurrent with behavioral observations (and physiologic measures when feasible) could prove useful in primate research and should be explored.     

Bayesian dynamic modeling of latent trait distributions

Studies of latent traits often collect data for multiple items measuring different aspects of the trait. For such data, it is common to consider models in which the different items are manifestations of a normal latent variable, which depends on covariates through a linear regression model. This article proposes a flexible Bayesian alternative in which the unknown latent variable density can change dynamically in location and shape across levels of a predictor. Scale mixtures of underlying normals are used in order to model flexibly the measurement errors and allow mixed categorical and continuous scales. A dynamic mixture of Dirichlet processes is used to characterize the latent response distributions. Posterior computation proceeds via a Markov chain Monte Carlo algorithm, with predictive densities used as a basis for inferences and evaluation of model fit. The methods are illustrated using data from a study of DNA damage in response to oxidative stress.     

THE FITNESS OF MANIPULATING PHENOTYPES: IMPLICATIONS FOR STUDIES OF FLUCTUATING ASYMMETRY AND MULTIVARIATE SELECTION

Phenotypic manipulation (or phenotypic engineering) that alters trait distributions provides a way to increase the statistical power of detecting relationships between traits and fitness. Manipulations relying on plastic responses, however, assume a specific relationship between the perturbation and the alteration of the traits when multiple traits are involved. We measured several traits, including condition measured as fluctuating asymmetry, in the ladybird beetle Harmonia axyridis under six different diets to examine how altered environments affected multiple traits and their distributions. Although diet affected fluctuating asymmetry, we found no consistent relationship between degree of asymmetry and other phenotypic measures. As expected, individual traits were altered by our treatments. Contrary to expectation, relationships among traits were not constant among diets. Our results suggest that assumptions about the relationship between condition and trait values, especially fluctuating asymmetry, cannot be made. Further, studies that use manipulated phenotypes to statistically determine the form of selection must first demonstrate that the pattern of the phenotypic correlation matrix is not itself altered by the manipulation. If the phenotypic correlation matrix is not constant, then experimental estimates of selection coefficients may not reflect selection that occurs in the wild.     

The importance of spatial scale for trait–abundance relations

The concept of community assembly through trait‐based environmental filtering has played a key role in our understanding of how communities change over space and time, however, the importance of spatial scale in the filtering process remains unclear. We propose that different environmental filters may operate at different spatial scales, and that filters at finer scales would be nested within those acting at coarser scales. We tested for the existence of spatially nested sets of trait‐based filters in a temperate native grassland by applying the recently proposed maximum entropy (MaxEnt) approach to trait‐based community assembly, which we extend through a trait selection procedure. We found that different traits were important in influencing the abundances of species at the three different spatial scales examined (micro‐habitat, habitat, landscape), supporting the idea that trait based filtering processes operating at coarse spatial scales can be quite distinct from those operating at fine scales. Despite this result, we identified several traits which were frequently related to abundance at all spatial scales. Taken together, our results support the proposition that trait‐based environmental filters at finer spatial scales are nested within those operating at coarser scales. We compared our results to those obtained using a simpler trait‐by‐trait analytical approach (correlation analysis and MaxEnt on individual traits). The capacity for MaxEnt to incorporate multiple traits simultaneously provided unique insights into the important traits at each spatial scale and presents significant advantages over existing univariate and multivariate approaches.     

Fluctuating asymmetry and morphometric variation of hand bones

The major aim of this study was to test three hypotheses: 1) more complex traits of the hand are less prone to developmental insults and therefore show lower fluctuating asymmetry (FA) as compared with simple traits; 2) the manifestation of FA correlates with the variability of the trait (i.e., CV); and 3) FA is an organ-wide property, and therefore a concordance exists between the FA measures of different traits in hand bones. Seventy-two bilateral measurements of hand bones, were made from plain-film radiographs of 365 cadavers. A complex trait was considered as the total length of the three phalanges of a finger and their contiguous metacarpals. Simple traits were considered to be the lengths of individual bone that made up the complex trait. The following results were obtained: 1) on the average simple traits, composing the complex trait, show much higher FA than the corresponding complex trait, but this result is expected if there is no correlation (or low correlation) between FA of simple traits within the complex trait, due to random direction of right-left differences; 2) strong and highly significant correlation was observed between FA and CV of studied traits, regardless of sex and age of individuals; and 3) the majority of FA measurements of hand bones showed no correlation. However, correlations between some sets of FA traits were highly significant. They were interpreted, although not specifically tested, as the result of a tight relationship between traits related not only developmentally but also by active performance of the same function. Am J Phys Anthropol 107:125–136, 1998. © 1998 Wiley-Liss, Inc.     

A latent variable model of developmental instability in relation to men's sexual behaviour

A single trait's fluctuating asymmetry (FA) is expected to be a poor measure of developmental instability. Hence, studies that examine associations between FA and outcomes expected to covary with developmental instability often have little power in detecting meaningful relationships. One way of increasing the power of detecting relationships between developmental instability and outcomes is through the use of multiple traits' FA. The way multiple traits have typically been used is in trait aggregates. Here, we illustrate another way of examining relationships with developmental instability using multiple traits' FA: through structural equation modelling. Covariances between measures of FA and an outcome variable are interpreted within the context of an explicit model of associations between variables, which is tested for fit and the parameters specified within the model are estimated. We used nine traits' FA as markers of a latent variable of men's developmental instability, which was associated with the number of sexual partners. The results indicate a sizeable correlation between developmental instability and men's sexual history, despite small correlations between individual traits' FA and sexual history.