Violations Of Model Assumptions Research Articles

LS³: A Method for Improving Phylogenomic Inferences When Evolutionary Rates Are Heterogeneous among Taxa.

Phylogenetic inference artifacts can occur when sequence evolution deviates from assumptions made by the models used to analyze them. The combination of strong model assumption violations and highly heterogeneous lineage evolutionary rates can become problematic in phylogenetic inference, and lead to the well-described long-branch attraction (LBA) artifact. Here, we define an objective criterion for assessing lineage evolutionary rate heterogeneity among predefined lineages: the result of a likelihood ratio test between a model in which the lineages evolve at the same rate (homogeneous model) and a model in which different lineage rates are allowed (heterogeneous model). We implement this criterion in the algorithm Locus Specific Sequence Subsampling (LS³), aimed at reducing the effects of LBA in multi-gene datasets. For each gene, LS³ sequentially removes the fastest-evolving taxon of the ingroup and tests for lineage rate homogeneity until all lineages have uniform evolutionary rates. The sequences excluded from the homogeneously evolving taxon subset are flagged as potentially problematic. The software implementation provides the user with the possibility to remove the flagged sequences for generating a new concatenated alignment. We tested LS³ with simulations and two real datasets containing LBA artifacts: a nucleotide dataset regarding the position of Glires within mammals and an amino-acid dataset concerning the position of nematodes within bilaterians. The initially incorrect phylogenies were corrected in all cases upon removing data flagged by LS³.

Geography and end use drive the diversification of worldwide winter rye populations.

To meet the current challenges in human food production, improved understanding of the genetic diversity of crop species that maximizes the selection efficacy in breeding programs is needed. The present study offers new insights into the diversity, genetic structure and demographic history of cultivated rye (Secale cereale L.). We genotyped 620 individuals from 14 global rye populations with a different end use (grain or forage) at 32 genome-wide simple sequence repeat markers. We reveal the relationships among these populations, their sizes and the timing of domestication events using population genetics and model-based inference with approximate Bayesian computation. Our main results demonstrate (i) a high within-population variation and genetic diversity, (ii) an unexpected absence of reduction in diversity with an increasing improvement level and (iii) patterns suggestive of multiple domestication events. We suggest that the main drivers of diversification of winter rye are the end use of rye in two early regions of cultivation: rye forage in the Mediterranean area and grain in northeast Europe. The lower diversity and stronger differentiation of eastern European populations were most likely due to more intensive cultivation and breeding of rye in this region, in contrast to the Mediterranean region where it was considered a secondary crop or even a weed. We discuss the relevance of our results for the management of gene bank resources and the pitfalls of inference methods applied to crop domestication due to violation of model assumptions and model complexity.

A broader definition of occupancy: Comment on Hayes and Monfils

Occupancy models are widely used to analyze presence-absence data for a variety of taxa while accounting for observation error (MacKenzie et al. 2002, 2006; Tyre et al. 2003; Royle and Dorazio 2008). Hayes and Monfils (2015) question their use for analyzing avian point count data based on purported violations of model assumptions incurred by avian mobility. Animal mobility is an important consideration, not just for occupancy models, but for a variety of population and habitat models (Boyce 2006, Royle et al. 2009, Manning and Goldberg 2010, Dormann et al. 2013, Renner et al. 2015). Nevertheless, we believe the ultimate conclusions of Hayes and Monfils are shortsighted mainly due to a narrow interpretation of occupancy. Rather than turn away from the use of occupancy models, we believe they remain an appropriate method for analyzing many data sets collected from avian point count surveys. Further, we suggest that there is value in having a broader and more nuanced interpretation of occupancy that incorporates the potential for animal movement.

Assessing the robustness of quantitative fatty acid signature analysis to assumption violations

Summary Knowledge of animal diets can provide important insights into life history and ecology, relationships among species in a community and potential response to ecosystem change or perturbation. Quantitative fatty acid signature analysis (QFASA) is a method of estimating diets from data on the composition, or signature, of fatty acids stored in adipose tissue. Given data on signatures of potential prey, a predator diet is estimated by minimizing the distance between its signature and a mixture of prey signatures. Calibration coefficients, constants derived from feeding trials, are used to account for differential metabolism of individual fatty acids. QFASA has been widely applied since its introduction and several variants of the original estimator have appeared in the literature. However, work to compare the statistical properties of QFASA estimators has been limited. One important characteristic of an estimator is its robustness to violations of model assumptions. The primary assumptions of QFASA are that prey signature data contain representatives of all prey types consumed and the calibration coefficients are known without error. We investigated the robustness of two QFASA estimators to a range of violations of these assumptions using computer simulation and recorded the resulting bias in diet estimates. We found that the Aitchison distance measure was most robust to errors in the calibration coefficients. Conversely, the Kullback–Leibler distance measure was most robust to the consumption of prey without representation in the prey signature data. In most QFASA applications, investigators will generally have some knowledge of the prey available to predators and be able to assess the completeness of prey signature data and sample additional prey as necessary. Conversely, because calibration coefficients are derived from feeding trials with captive animals and their values may be sensitive to consumer physiology and nutritional status, their applicability to free‐ranging animals is difficult to establish. We therefore recommend that investigators first make any improvements to the prey signature data that seem warranted and then base estimation on the Aitchison distance measure, as it appears to minimize risk from violations of the assumption that is most difficult to verify.

Integrated likelihoods in parametric survival models for highly clustered censored data.

In studies that involve censored time-to-event data, stratification is frequently encountered due to different reasons, such as stratified sampling or model adjustment due to violation of model assumptions. Often, the main interest is not in the clustering variables, and the cluster-related parameters are treated as nuisance. When inference is about a parameter of interest in presence of many nuisance parameters, standard likelihood methods often perform very poorly and may lead to severe bias. This problem is particularly evident in models for clustered data with cluster-specific nuisance parameters, when the number of clusters is relatively high with respect to the within-cluster size. However, it is still unclear how the presence of censoring would affect this issue. We consider clustered failure time data with independent censoring, and propose frequentist inference based on an integrated likelihood. We then apply the proposed approach to a stratified Weibull model. Simulation studies show that appropriately defined integrated likelihoods provide very accurate inferential results in all circumstances, such as for highly clustered data or heavy censoring, even in extreme settings where standard likelihood procedures lead to strongly misleading results. We show that the proposed method performs generally as well as the frailty model, but it is superior when the frailty distribution is seriously misspecified. An application, which concerns treatments for a frequent disease in late-stage HIV-infected people, illustrates the proposed inferential method in Weibull regression models, and compares different inferential conclusions from alternative methods.

REVIEW: Wildlife camera trapping: a review and recommendations for linking surveys to ecological processes

Summary Reliable assessment of animal populations is a long‐standing challenge in wildlife ecology. Technological advances have led to widespread adoption of camera traps (CTs) to survey wildlife distribution, abundance and behaviour. As for any wildlife survey method, camera trapping must contend with sources of sampling error such as imperfect detection. Early applications focused on density estimation of naturally marked species, but there is growing interest in broad‐scale CT surveys of unmarked populations and communities. Nevertheless, inferences based on detection indices are controversial, and the suitability of alternatives such as occupancy estimation is debatable. We reviewed 266 CT studies published between 2008 and 2013. We recorded study objectives and methodologies, evaluating the consistency of CT protocols and sampling designs, the extent to which CT surveys considered sampling error, and the linkages between analytical assumptions and species ecology. Nearly two‐thirds of studies surveyed more than one species, and a majority used response variables that ignored imperfect detection (e.g. presence–absence, relative abundance). Many studies used opportunistic sampling and did not explicitly report details of sampling design and camera deployment that could affect conclusions. Most studies estimating density used capture–recapture methods on marked species, with spatially explicit methods becoming more prominent. Few studies estimated density for unmarked species, focusing instead on occupancy modelling or measures of relative abundance. While occupancy studies estimated detectability, most did not explicitly define key components of the modelling framework (e.g. a site) or discuss potential violations of model assumptions (e.g. site closure). Studies using relative abundance relied on assumptions of equal detectability, and most did not explicitly define expected relationships between measured responses and underlying ecological processes (e.g. animal abundance and movement). Synthesis and applications. The rapid adoption of camera traps represents an exciting transition in wildlife survey methodology. We remain optimistic about the technology's promise, but call for more explicit consideration of underlying processes of animal abundance, movement and detection by cameras, including more thorough reporting of methodological details and assumptions. Such transparency will facilitate efforts to evaluate and improve the reliability of camera trap surveys, ultimately leading to stronger inferences and helping to meet modern needs for effective ecological inquiry and biodiversity monitoring.

Methodology Turns 10

Since its inception in February 2005, Methodology, the official journal of the European Association of Methodology, has been an online journal with a strong European vocation and dedication ‘‘to promote research and the development of empirical research methods in the fields of behavioral, social, educational, health and economic sciences, as well as in the field of evaluation research’’ (Ato & Eid, 2005; Ato & Hox, 2009). In 2009, the then editors of Methodology, Manuel Ato and Joop Hox, wrote an editorial in which they looked back at the first 4 years of Methodology (Ato & Hox, 2009). Now, 6 years later, two different editors, Peter Lugtig of Utrecht University and Nekane Balluerka of the University of the Basque Country, have taken over the editorship of Methodology. As Methodology celebrates its 10th birthday, it is time to look back and forward. Just like the editors before us, we firmly believe that the methodology underpinning the social sciences has many similarities across disciplines. Any differences between the sciences mostly reflect differences in the type of research questions asked, in research designs and data analysis practices, and in historical developments. Many of the articles published in Methodology have taken a cross-disciplinary perspective and many of the developments in social science methodology are similar across disciplines. A large number of articles in Methodology have explored the methodology of the Generalized Linear Model (Schweizer, 2010; Voelkle & McKnight, 2012). Simulation studies have, for example, focused on the properties of multilevel models (Bell, Morgan, Schoeneberger, Kromrey, & Ferron, 2014; Pacagnella, 2011). Latent variables in general, and how to model the measurements, is probably the topic that has been written about most, whether in the context of psychometrics (Balluerka, Plewis, Gorostiaga, & Padilla, 2014; Botella & Suero, 2012; Gonzalez-Betanzos & Abad, 2012), or of factor analysis to estimate equivalence across groups (Kankaras & Moors, 2011; Lugtig, Boeije, & Lensvelt-Mulders, 2012; Steinmetz, 2013). Other articles dealing with data collection methods have often focused on comparing different approaches to deal with violations of model assumptions (Blanca, Arnau, Lopez-Montiel, Bono, & Bendayan, 2013; Haupt, Losel, & Stemmler, 2014; Schmider, Ziegler, Danay, Beyer, & Buhner, 2010; Wolff Smith, & Beretvas, 2014). Apart from methodological advances in the field of data analysis, another development in social science research methodology is the availability of software tools. Here, a number of articles have discussed methods to implement new statistical modeling methodologies in software packages (e.g., Flora, 2011; Grilli & Variale, 2014). We envisage that in the coming years developments in this field of research will continue. The growing possibilities in terms of statistical modeling will increase demand for articles explaining which model should be used when, and how. For this reason, future issues of Methodology will feature a section with tutorial articles which show how to implement statistical modeling techniques in widely used software packages. To ensure such articles can be used by applied social science researchers, we will publish the data and code accompanying these articles. It is our continuing goal to feature special thematic issues edited by prominent researchers in their field. Since 2009, four special issues have been published. In 2009, Michael Eid and Fridtjof Nussbeck edited an issue to celebrate the 50th anniversary of the multitrait-multimethod matrix (Eid & Nussbeck, 2009). In 2010, Elmar Schlueter and Peter Schmidt provided an issue on ‘‘survey experiments’’ (Schlueter & Schmidt, 2010), while in the same year Andries Van der Ark and Jeroen Vermunt edited an issue on ‘‘new developments in missing data analysis’’ (Van der Ark & Vermunt, 2010). In 2013, Gordon Willis and Hennie Boeije contributed a special issue on the ‘‘systematic reporting of questionnaire development and pretesting’’ (Willis & Boeije, 2013). Readers of Methodology

The simplified reference tissue model: model assumption violations and their impact on binding potential.

Reference tissue models have gained significant traction over the last two decades as the methods of choice for the quantification of brain positron emission tomography data because they balance quantitative accuracy with less invasive procedures. The principal advantage is the elimination of the need to perform arterial cannulation of the subject to measure blood and metabolite concentrations for input function generation. In particular, the simplified reference tissue model (SRTM) has been widely adopted as it uses a simplified model configuration with only three parameters that typically produces good fits to the kinetic data and a stable parameter estimation process. However, the model's simplicity and its ability to generate good fits to the data, even when the model assumptions are not met, can lead to misplaced confidence in binding potential (BPND) estimates. Computer simulation were used to study the bias introduced in BPND estimates as a consequence of violating each of the four core SRTM model assumptions. Violation of each model assumption led to bias in BPND (both over and underestimation). Careful assessment of the bias in SRTM BPND should be performed for new tracers and applications so that an appropriate decision about its applicability can be made.

A re-evaluation of the size of the white shark (Carcharodon carcharias) population off California, USA.

White sharks are highly migratory and segregate by sex, age and size. Unlike marine mammals, they neither surface to breathe nor frequent haul-out sites, hindering generation of abundance data required to estimate population size. A recent tag-recapture study used photographic identifications of white sharks at two aggregation sites to estimate abundance in “central California” at 219 mature and sub-adult individuals. They concluded this represented approximately one-half of the total abundance of mature and sub-adult sharks in the entire eastern North Pacific Ocean (ENP). This low estimate generated great concern within the conservation community, prompting petitions for governmental endangered species designations. We critically examine that study and find violations of model assumptions that, when considered in total, lead to population underestimates. We also use a Bayesian mixture model to demonstrate that the inclusion of transient sharks, characteristic of white shark aggregation sites, would substantially increase abundance estimates for the adults and sub-adults in the surveyed sub-population. Using a dataset obtained from the same sampling locations and widely accepted demographic methodology, our analysis indicates a minimum all-life stages population size of >2000 individuals in the California subpopulation is required to account for the number and size range of individual sharks observed at the two sampled sites. Even accounting for methodological and conceptual biases, an extrapolation of these data to estimate the white shark population size throughout the ENP is inappropriate. The true ENP white shark population size is likely several-fold greater as both our study and the original published estimate exclude non-aggregating sharks and those that independently aggregate at other important ENP sites. Accurately estimating the central California and ENP white shark population size requires methodologies that account for biases introduced by sampling a limited number of sites and that account for all life history stages across the species' range of habitats.

An adaptive permutation approach for genome-wide association study: evaluation and recommendations for use.

BackgroundPermutation testing is a robust and popular approach for significance testing in genomic research, which has the broad advantage of estimating significance non-parametrically, thereby safe guarding against inflated type I error rates. However, the computational efficiency remains a challenging issue that limits its wide application, particularly in genome-wide association studies (GWAS). Because of this, adaptive permutation strategies can be employed to make permutation approaches feasible. While these approaches have been used in practice, there is little research into the statistical properties of these approaches, and little guidance into the proper application of such a strategy for accurate p-value estimation at the GWAS level.MethodsIn this work, we advocate an adaptive permutation procedure that is statistically valid as well as computationally feasible in GWAS. We perform extensive simulation experiments to evaluate the robustness of the approach to violations of modeling assumptions and compare the power of the adaptive approach versus standard approaches. We also evaluate the parameter choices in implementing the adaptive permutation approach to provide guidance on proper implementation in real studies. Additionally, we provide an example of the application of adaptive permutation testing on real data.ResultsThe results provide sufficient evidence that the adaptive test is robust to violations of modeling assumptions. In addition, even when modeling assumptions are correct, the power achieved by adaptive permutation is identical to the parametric approach over a range of significance thresholds and effect sizes under the alternative. A framework for proper implementation of the adaptive procedure is also generated.ConclusionsWhile the adaptive permutation approach presented here is not novel, the current study provides evidence of the validity of the approach, and importantly provides guidance on the proper implementation of such a strategy. Additionally, tools are made available to aid investigators in implementing these approaches.

Food and space revisited: The role of drift-feeding theory in predicting the distribution, growth, and abundance of stream salmonids

In this paper we review drift-feeding models for stream salmonids. We assess their historical development and current state, and we propose areas for future research. Drift-feeding models serve as the critical input for energetics-based habitat selection and habitat quality models, which have recently begun to see widespread use for predicting salmonid distribution, growth and abundance. We use a bibliometric approach to find drift-feeding model publications, especially those citing three landmark papers that began the quantification of drift feeding by stream fish (Fausch 1984; Hughes and Dill 1990; Hill and Grossman 1993). Subsequent drift-feeding models have largely been built upon these models. Research effort has focused on model development and applications but model testing has been neglected. To date, the only rigorous test of a drift-feeding model (Hughes et al. 2003) identified several limitations and violations of model assumptions. The most important limitation was that prey capture- and gross energy intake rates were overestimated by a factor of two, due largely to poor predictions of prey detection probabilities. Consequences of error in drift-feeding models, and consequently in the habitat selection/quality models that employ them, are greater for applications aimed at predicting growth and abundance than they are for predicting distribution. Research effort on a broad front is needed to advance both drift-feeding models and habitat selection/quality models, including: further development of drift-foraging theory, revision and testing of drift-feeding models (specifically new, functional prey detection and interception sub-models), and revision of habitat selection/quality models to incorporate spatial, temporal, and flow-dependent variation in drift concentration.

Estimating age‐specific survival when age is unknown: open population capture–recapture models with age structure and heterogeneity

Summary When studying senescence in wildlife populations, we are often limited by the sparseness of the available information on the ages of the individuals under study. Additionally, heterogeneity between individuals can be substantial. Ignoring this heterogeneity can lead to biased estimates of the population parameters of interest and can mask senescence. This article demonstrates the use of a recently developed capture–recapture model for extracting age‐dependent estimates of survival probabilities for individuals of unknown age and extends the model by allowing for heterogeneity in survival and capture probabilities using finite mixtures. Using simulation, we show that the estimates of age‐dependent survival probabilities when age is unknown can be biased when heterogeneity in capture probabilities is not modelled, in contrast to the case of time‐dependent survival probabilities when the estimates are robust to similar violations of model assumptions. The methods are demonstrated using a long‐term data set of female brushtail possums (Trichosurus vulpecula Kerr) for which age‐specific models for survival probabilities indicating senescence are strongly favoured. We found no evidence of heterogeneity in survival but strong evidence of heterogeneity in capture probabilities. These models have a wide range of applications for estimating age dependence in survival when the age is unknown as they can be applied to any capture–recapture data set, as long as it is collected over a period which is longer, and preferably considerably so, than the life span of the species studied.

A robustness study of parametric and non-parametric tests in model-based multifactor dimensionality reduction for epistasis detection

BackgroundApplying a statistical method implies identifying underlying (model) assumptions and checking their validity in the particular context. One of these contexts is association modeling for epistasis detection. Here, depending on the technique used, violation of model assumptions may result in increased type I error, power loss, or biased parameter estimates. Remedial measures for violated underlying conditions or assumptions include data transformation or selecting a more relaxed modeling or testing strategy. Model-Based Multifactor Dimensionality Reduction (MB-MDR) for epistasis detection relies on association testing between a trait and a factor consisting of multilocus genotype information. For quantitative traits, the framework is essentially Analysis of Variance (ANOVA) that decomposes the variability in the trait amongst the different factors. In this study, we assess through simulations, the cumulative effect of deviations from normality and homoscedasticity on the overall performance of quantitative Model-Based Multifactor Dimensionality Reduction (MB-MDR) to detect 2-locus epistasis signals in the absence of main effects.MethodologyOur simulation study focuses on pure epistasis models with varying degrees of genetic influence on a quantitative trait. Conditional on a multilocus genotype, we consider quantitative trait distributions that are normal, chi-square or Student’s t with constant or non-constant phenotypic variances. All data are analyzed with MB-MDR using the built-in Student’s t-test for association, as well as a novel MB-MDR implementation based on Welch’s t-test. Traits are either left untransformed or are transformed into new traits via logarithmic, standardization or rank-based transformations, prior to MB-MDR modeling.ResultsOur simulation results show that MB-MDR controls type I error and false positive rates irrespective of the association test considered. Empirically-based MB-MDR power estimates for MB-MDR with Welch’s t-tests are generally lower than those for MB-MDR with Student’s t-tests. Trait transformations involving ranks tend to lead to increased power compared to the other considered data transformations.ConclusionsWhen performing MB-MDR screening for gene-gene interactions with quantitative traits, we recommend to first rank-transform traits to normality and then to apply MB-MDR modeling with Student’s t-tests as internal tests for association.

A New Electromagnetic Induction Calibration Model for Estimating Low Range Salinity in Calcareous Soils

In arid and semiarid regions, calibrating bulk soil salinity sensing technologies such as electromagnetic induction (EMI) relies on the assumption of uniformity of all soil factors influencing the reading, except soil salinity, to create a calibration model. When potentially perturbing factors are non‐homogeneous or interact in a non‐systematic way, conditional mean calibration models based on the least squares method fail to completely describe the entire salinity distribution due to the violation of model assumptions (i.e., homogeneity of perturbing factors). Therefore a new approach is needed. The main objective of this study is to produce a salinity calibration model capable of reasonably predicting salinity directly from the EMI signal readings irrespective of the heterogeneity of perturbing factors. Toward this end we collected ground‐truth samples and corresponding EMI measurements in 35 agricultural fields covering 495 ha of the Irrigated Middle Bear (IMB) subbasin of Cache County in Utah. Using quantile regression (QR), which makes no assumption about the distribution of error, we estimated a subset of conditional quantiles of salinity as a function of EMI reading. We found that the mean effects estimated by previous models are misleading because they model behavior around the 0.9th quantile of the distribution, and thus grossly underestimate salinities in the lower quantiles. We developed a new EMI weighting procedure to account for the high heterogeneity that may have caused the upper‐tailed distributional behavior. Variability was effectively captured and well modeled at specified quantiles of the salinity distribution using the QR technique. Independent validation of selected multiple QR models indicates that at low salinity ranges corresponding to conditional quantile (τ) ≤ 0.25, the QR models may be applied to any soil with low range salinity.

Are Chlorophyll a–Total Phosphorus Correlations Useful for Inference and Prediction?

Correlations between chlorophyll a and total phosphorus in freshwater ecosystems were first documented in the 1960s and have been used since then to infer phosphorus limitation, build simple models, and develop management targets. Often these correlations are considered indicative of a cause-effect relationship. However, many scientists regard the use of these associations for modeling and inference to be misleading due to their potentially spurious nature. Using data from Saginaw Bay, Lake Huron, we examine the relationship among chlorophyll a, total phosphorus, and algal biomass measurements. We apply graphical models and recently developed "structure learning" principles that use conditional dependencies to help identify causal relationships among observational data. The spurious relationship suspected by some is not supported by our data, whereas a direct relationship between chlorophyll a and total phosphorus is always supported, and an additional indirect relationship with an algal biomass intermediary is plausible under some circumstances. Thus, we conclude that these correlations are useful for simple model building but encourage the use of modern statistical methods to avoid common model-assumption violations.

How should we assess the fit of Rasch-type models? Approximating the power of goodness-of-fit statistics in categorical data analysis.

We investigate the performance of three statistics, R1, R2 (Glas in Psychometrika 53:525-546, 1988), and M2 (Maydeu-Olivares & Joe in J. Am. Stat. Assoc. 100:1009-1020, 2005, Psychometrika 71:713-732, 2006) to assess the overall fit of a one-parameter logistic model (1PL) estimated by (marginal) maximum likelihood (ML). R1 and R2 were specifically designed to target specific assumptions of Rasch models, whereas M2 is a general purpose test statistic. We report asymptotic power rates under some interesting violations of model assumptions (different item discrimination, presence of guessing, and multidimensionality) as well as empirical rejection rates for correctly specified models and some misspecified models. All three statistics were found to be more powerful than Pearson's X(2) against two- and three-parameter logistic alternatives (2PL and 3PL), and against multidimensional 1PL models. The results suggest that there is no clear advantage in using goodness-of-fit statistics specifically designed for Rasch-type models to test these models when marginal ML estimation is used.

A Maximum-Likelihood Method to Correct for Allelic Dropout in Microsatellite Data with No Replicate Genotypes

Allelic dropout is a commonly observed source of missing data in microsatellite genotypes, in which one or both allelic copies at a locus fail to be amplified by the polymerase chain reaction. Especially for samples with poor DNA quality, this problem causes a downward bias in estimates of observed heterozygosity and an upward bias in estimates of inbreeding, owing to mistaken classifications of heterozygotes as homozygotes when one of the two copies drops out. One general approach for avoiding allelic dropout involves repeated genotyping of homozygous loci to minimize the effects of experimental error. Existing computational alternatives often require replicate genotyping as well. These approaches, however, are costly and are suitable only when enough DNA is available for repeated genotyping. In this study, we propose a maximum-likelihood approach together with an expectation-maximization algorithm to jointly estimate allelic dropout rates and allele frequencies when only one set of nonreplicated genotypes is available. Our method considers estimates of allelic dropout caused by both sample-specific factors and locus-specific factors, and it allows for deviation from Hardy–Weinberg equilibrium owing to inbreeding. Using the estimated parameters, we correct the bias in the estimation of observed heterozygosity through the use of multiple imputations of alleles in cases where dropout might have occurred. With simulated data, we show that our method can (1) effectively reproduce patterns of missing data and heterozygosity observed in real data; (2) correctly estimate model parameters, including sample-specific dropout rates, locus-specific dropout rates, and the inbreeding coefficient; and (3) successfully correct the downward bias in estimating the observed heterozygosity. We find that our method is fairly robust to violations of model assumptions caused by population structure and by genotyping errors from sources other than allelic dropout. Because the data sets imputed under our model can be investigated in additional subsequent analyses, our method will be useful for preparing data for applications in diverse contexts in population genetics and molecular ecology.

An empirical examination of distributional assumptions underlying the relationship between personality disorder symptoms and personality traits.

This article examines the relationship between personality disorder (PD) symptoms and personality traits using a variety of distributional assumptions. Prior work in this area relies almost exclusively on linear models that treat PD symptoms as normally distributed and continuous. However, these assumptions rarely hold, and thus the results of prior studies are potentially biased. Here we explore the effect of varying the distributions underlying regression models relating PD symptomatology to personality traits using the initial wave of the Longitudinal Study of Personality Disorders (N=250; Lenzenweger, 1999), a university-based sample selected to include PD rates resembling epidemiological samples. PD symptoms were regressed on personality traits. The distributions underlying the dependent variable (i.e., PD symptoms) were variously modeled as normally distributed, as counts (Poisson, Negative-Binomial), and with two-part mixture distributions (zero-inflated, hurdle). We found that treating symptoms as normally distributed resulted in violations of model assumptions, that the negative-binomial and hurdle models were empirically equivalent, but that the coefficients achieving significance often differ depending on which part of the mixture distributions are being predicted (i.e., presence vs. severity of PD). Results have implications for how the relationship between normal and abnormal personality is understood.

Bootstrapping U-statistics: applications in least squares and robust regression

Suppose that inference about parameters of interest is to be based on an unbiased estimating function that is U-statistic of degree 1 or 2. We define pivotal or approximate pivotal statistics based on such estimating functions and propose asymptotic approximations as well as estimating function bootstrap (EFB) methods based on resampling the estimated terms in the estimating functions. These methods are justified asymptotically and lead to confidence intervals produced directly from the estimating function based quantities that are pivotal or asymptotically pivotal. Particular examples in this class of estimating functions arise in least-squares regression, robust L a estimation (1 ≤ a < 2), Wilcoxon rank regression and other related estimation problems. The proposed methods are evaluated in simulations and applied to a real data set. When compared with existing asymptotic and resampling methods, the EFB method is found to be more accurate in small sample situations and robust to violation of model assumptions.

Using Classroom Data to Teach Students about Data Cleaning and Testing Assumptions

This paper discusses the influence that decisions about data cleaning and violations of statistical assumptions can have on drawing valid conclusions to research studies. The datasets provided in this paper were collected as part of a National Science Foundation grant to design online games and associated labs for use in undergraduate and graduate statistics courses that can effectively illustrate issues not always addressed in traditional instruction. Students play the role of a researcher by selecting from a wide variety of independent variables to explain why some students complete games faster than others. Typical project data sets are “messy,” with many outliers (usually from some students taking much longer than others) and distributions that do not appear normal. Classroom testing of the games over several semesters has produced evidence of their efficacy in statistics education. The projects tend to be engaging for students and they make the impact of data cleaning and violations of model assumptions more relevant. We discuss the use of one of the games and associated guided lab in introducing students to issues prevalent in real data and the challenges involved in data cleaning and dangers when model assumptions are violated.