Use Of Mixed Models Research Articles

Statistical power for identifying nucleotide markers associated with quantitative traits in genome-wide association analysis using a mixed model

Use of mixed models is in the spotlight as an emerging method for genome-wide association studies (GWASs). This study investigated the statistical power for identifying nucleotide variants associated with quantitative traits using the mixed model methodology. Quantitative traits were simulated through design of heritability, the number of causal variants (NCV), the number of polygenic variants, and genetic variance ratio of causal to polygenic variants (VRCTP). Statistical power estimates were influenced not only by individual factors of heritability, NCV, and VRCTP, but also by their interactions (P<0.05). As the genetic variance ratio decreased, the difference in power between heritabilities of 0.3 and 0.5 increased with the use of 20 causal variants, but decreased when there were 100 causal variants (P<0.05). The power empirically estimated from the simulation study would be applicable to the design of GWAS for quantitative traits with known genetic parameters by predicting the degree of false negative associations.

Quantifying the uncertainty in heritability

The use of mixed models to determine narrow-sense heritability and related quantities such as SNP heritability has received much recent attention. Less attention has been paid to the inherent variability in these estimates. One approach for quantifying variability in estimates of heritability is a frequentist approach, in which heritability is estimated using maximum likelihood and its variance is quantified through an asymptotic normal approximation. An alternative approach is to quantify the uncertainty in heritability through its Bayesian posterior distribution. In this paper, we develop the latter approach, make it computationally efficient and compare it to the frequentist approach. We show theoretically that, for a sufficiently large sample size and intermediate values of heritability, the two approaches provide similar results. Using the Atherosclerosis Risk in Communities cohort, we show empirically that the two approaches can give different results and that the variance/uncertainty can remain large.

Use of mixing models for Humboldt squid diet analysis: Reply to Field et al. (2014)

Use of mixing models for Humboldt squid diet analysis: Reply to Field et al. (2014)

Pacific herring Clupea pallasii and wrack macrophytes subsidize semi-terrestrial detritivores

MEPS Marine Ecology Progress Series Contact the journal Facebook Twitter RSS Mailing List Subscribe to our mailing list via Mailchimp HomeLatest VolumeAbout the JournalEditorsTheme Sections MEPS 495:49-64 (2014) - DOI: https://doi.org/10.3354/meps10588 Pacific herring Clupea pallasii and wrack macrophytes subsidize semi-terrestrial detritivores Caroline H. Fox1,2*, Rana El-Sabaawi1, Paul C. Paquet2,3, Thomas E. Reimchen1 1Department of Biology, and 3Department of Geography, University of Victoria, PO Box 3020, Station CSC, Victoria, British Columbia V8W 3N5, Canada 2Raincoast Conservation Foundation, PO Box 2429, Sidney, British Columbia V8L 3Y3, Canada *Corresponding author: caroline@raincoast.org ABSTRACT: The bi-directional movements of materials, nutrients and energy across the land-sea interface result in a number of ecological consequences. Migratory animals that move across ecosystems drive a number of these spatial subsidies (e.g. anadromous salmon), but many of the world’s animal migrations are in decline. The cross-ecosystem reach of Pacific herring Clupea pallasii, a migratory, iteroparous forage fish that spawns along the coastlines of the North Pacific Ocean, has never been studied. Spawn events represent large aggregations of biomass and energy, a portion of which is transferred to intertidal and supratidal zones. Using fatty acids and stable isotopic signatures of carbon and nitrogen, we (1) traced the sources of production and (2) tested the hypothesis that herring subsidizes detritivorous, semi-terrestrial amphipods (Talitridae: Traskorchestia spp.), which are often abundant in intertidal and supratidal zones. Amphipods and likely dietary items (macrophytes and herring eggs) were collected from 5 beaches before and after herring spawned in Quatsino Sound, British Columbia. Combined with the use of mixing models, stable isotopes suggest that herring, in addition to brown algae and seagrass, were major sources of production during the study period. Fatty acid results suggest that brown algae is generally a major dietary resource for amphipods, but herring eggs provide important omega-3 fatty acids that are low in abundance prior to herring spawn events. Taken together, we provide corroborative evidence of a previously unknown cross-ecosystem spatial subsidy by Pacific herring. Further, because amphipods are prey for several terrestrial consumers, we also identify previously unknown marine-terrestrial linkages. KEY WORDS: Pacific herring · Spatial subsidy · Wrack · Amphipoda · Detritivores · Fatty acids · Stable isotope Full text in pdf format PreviousNextCite this article as: Fox CH, El-Sabaawi R, Paquet PC, Reimchen TE (2014) Pacific herring Clupea pallasii and wrack macrophytes subsidize semi-terrestrial detritivores. Mar Ecol Prog Ser 495:49-64. https://doi.org/10.3354/meps10588 Export citation RSS - Facebook - Tweet - linkedIn Cited by Published in MEPS Vol. 495. Online publication date: January 09, 2014 Print ISSN: 0171-8630; Online ISSN: 1616-1599 Copyright © 2014 Inter-Research.

Analysis of series of variety trials with perennial crops

AbstractField trials with perennial crops give rise to repeated measurements taken on the same plot on several occasions. It is important to account for serial correlation among repeated measurements in such trials. This study illustrates the use of mixed models for this purpose. We consider the analysis of trials conducted at several locations and the combination of trials with different starting years. A key issue in the analysis is the distinction between effects of calendar years, which are associated with external environmental variation, and harvest years, which represent internal yield formation processes of the perennial crop. Two methods of two‐stage analysis are compared with single‐stage analysis. It is shown that results of two‐stage analysis are very similar to those of single‐stage analysis, if serial correlation is properly taken into account. Program code for the MIXED procedure of the SAS system is given in an Appendix S1 for all considered cases.

Robust and Sensitive Analysis of Mouse Knockout Phenotypes

A significant challenge of in-vivo studies is the identification of phenotypes with a method that is robust and reliable. The challenge arises from practical issues that lead to experimental designs which are not ideal. Breeding issues, particularly in the presence of fertility or fecundity problems, frequently lead to data being collected in multiple batches. This problem is acute in high throughput phenotyping programs. In addition, in a high throughput environment operational issues lead to controls not being measured on the same day as knockouts. We highlight how application of traditional methods, such as a Student’s t-Test or a 2-way ANOVA, in these situations give flawed results and should not be used. We explore the use of mixed models using worked examples from Sanger Mouse Genome Project focusing on Dual-Energy X-Ray Absorptiometry data for the analysis of mouse knockout data and compare to a reference range approach. We show that mixed model analysis is more sensitive and less prone to artefacts allowing the discovery of subtle quantitative phenotypes essential for correlating a gene’s function to human disease. We demonstrate how a mixed model approach has the additional advantage of being able to include covariates, such as body weight, to separate effect of genotype from these covariates. This is a particular issue in knockout studies, where body weight is a common phenotype and will enhance the precision of assigning phenotypes and the subsequent selection of lines for secondary phenotyping. The use of mixed models with in-vivo studies has value not only in improving the quality and sensitivity of the data analysis but also ethically as a method suitable for small batches which reduces the breeding burden of a colony. This will reduce the use of animals, increase throughput, and decrease cost whilst improving the quality and depth of knowledge gained.

Converting isotope values to diet composition: the use of mixing models

A common use of stable isotope analysis in mammalogy is to make inferences about diet from isotope values (typically δ13C and δ15N) measured in tissues and food sources of a consumer. Mathematical mixing models are used to estimate the proportional contributions of food sources to the isotopic composition of the tissues of a consumer, which reflect the assimilated diet. This paper reviews basic mixing models and how they work; additional refinements also are described that include addressing uncertainty, larger numbers of sources, combining sources, concentration effects, and Bayesian statistical frameworks. Information is provided on where to access software for the various models. Numerous examples are cited to show application of these models in the mammal research literature.

Genetic diversity in Australian Cedar genotypes selected by mixed models

The increasing demand for raw material for multiple uses of forest products and by-products has attracted the interest for fast growing species, such as the Australian Cedar (Toona ciliata), which presents high productive and economic potential. The present work aimed at estimating genetic diversity by DNA markers and morphological traits supported for the mixed models. The following traits were measured and genotypes were sampled randomly in different areas: diameter at breast height, height, cylindrical volume, diameter, distance between nodes and crown diameter. Twelve RAPD primers were used and generated a total of 91 marks, 82 of which were polymorphic. The high percentage of polymorphic markers, 90.10%, demonstrated that discrimination in this species is efficient, but it yet little studied, for this case we can find the extent of the genetic basis for the application of technical improvement. The assessment of genetic diversity by the UPGMA method using the binary and morphological data provided the expression of genetic dissimilarities among the accessions evaluated, optimizing the perception of this divergence. The use of mixed models was efficient to assess combined genetic diversity to optimize the selection of genotypes with divergent genetic values for diameter at breast height.

Stand structure and plant species diversity in managed and abandoned silver fir mature woodlands

Although few undisturbed forests remain in Europe, forest reserves and deforested areas that are no longer profitable have the potential to develop stand structures similar to those which preceded human disturbances. The direct effects of management cessation on forest diversity are confounded by many factors that should be controlled when comparing managed and abandoned stands. In the European Alps, however, the high variability of habitats makes it nearly impossible to find comparable stands located within forests large enough to be independent from the surrounding land. The aim of this study was to investigate the use of mixed models to compare deadwood and plant diversity between matched managed and unmanaged pairs of forests, with the hypothesis that their differences were due to direct effect of abandonment. Two neighbouring watersheds that were large enough to be independent from the surrounding forests were chosen. These watersheds had a common history of use, but one was non-intensively managed, while the other was untouched since 1957. Ten plots were randomly selected from each forest. Mixed models confirmed their matched topography and stand structure, while a similarity index confirmed their assignment to the same plant community. The unmanaged stand had higher soil nitrogen, higher Fagus sylvatica dendrological composition, higher tree species richness, higher dead logs and a different composition of the tree and understory layers. These results suggest that silver fir woodlands abandoned for more than 50years change spontaneously and that this approach may be an effective means for studying other forest communities.

Variable-top merchantable volume equations for Scots pine (Pinus sylvestris) and Sitka spruce (Picea sitchensis (Bong.) Carr.) in Northern Britain

Summary In this study, data collected from stands in Scotland and Northern England were used to develop variable-top merchantable volume equations for plantation-grown Scots pine (Pinus sylvestris) and Sitka spruce (Picea sitchensis). After fitting and evaluating a number of total volume and volume ratio equations, the Schumacher and Hall (1933) equation (Schumacher, F.X. and Hall, F.S. 1933 Logarithmic expression of timber tree volume. J. Agric. Res. 47, 719–734) gave the best results for total volume, while the Van Deusen et al. (1981) and Cao and Burkhart (1980) models (Van Deusen, P.C., Sullivan, A.D. and Matney, T.G. 1981 A pre diction system for cubic foot volume of loblolly pine applicable through much of its range. South. J. Appl. For. 5, 186–189; Cao, Q.V. and Burkhart, H.E. 1980 Cubic-foot volume of loblolly pine to any height limit. South. J. Appl. For. 4, 166–168) gave the best fits for volume ratio equations to variable-top diameter and height limits, respectively. Variable-top merchantable volume equations were jointly estimated as a product of total volume and volume ratio equations. The final models, obtained using a non-linear mixed-effects modelling approach, showed considerable improvements compared with their fixed-effects counterparts. Even though further modelling of serial correlation using a banded toeplitz error structure improved model fits, it also led to an increase in the residual variance of the models and could degenerate the predictive ability of the models. We therefore recommend the use of mixed models with simple ‘iid’ error structure. However, in situations where additional data are not available to predict the random effects, we recommend the use of the models based on non-linear least squares.

On Average: Data Exploration Based on Means Can Be Misleading

INTRODUCTIONOn the basis that “a picture is worth a thousand words,”data are often presented graphically in order to convey someof the information that they contain. Modelers use graphicalrepresentations of data for numerous purposes, two of themost important being, to inform and drive the modelingprocess and to communicate with their clients who are theend users of their models. However, it is not always clearwhich graphic should be used for a particular set of data andfor a particular purpose. As such, it is very well possible thatchoosing the wrong graph may mislead rather than enlighten,which is obviously a situation to be avoided if at all possible.Part of the difficulty lies in the fact that exploratory dataanalysis (EDA), which incorporates graphical exploration ofthe data, is perceived to be as much an art as it is a science.The artistic aspect of EDA is based on human creativity andintuition, and it is our intuition that can sometimes fail on us.One of the most intuitive graphs is one in which the dataare averaged in some way and the averages plotted. This useof averages is so intuitive that it is frequently used withoutvery much thought or consideration. It must be acknowledgedthat in many cases, this proves to be a good strategy thoughthere are occasions when it can be misleading. This paperexamines some commonly encountered situations in whichsuch graphics may be misleading. The reasons why they aremisleading are explored and explained. In addition, analternative strategy is suggested.In order to maintain the confidence of the end users in amodel, it is important that any apparent contradictionbetween the model and the graphical presentation of thedata is carefully explained. It is hoped that the followingsections will go some way in helping with that explanation.For the purposes of the following discussion, it will beassumed that the response variable (Y) is recorded on acontinuous scale. The independent variable (x)maybecontinuous or discrete.The next section describes a general approach tobuilding a mixed effects model. The following two sectionsdiscuss the use of data averages and their limitations. Analternative to data averaging is introduced in the followingsection. The data averaging and alternative methods arecompared by means of a simulated trial and a real caseexample. The paper finishes with a discussion.MIXED EFFECTS MODELWhen the data are grouped in such a way thatobservations within a group are correlated, the model needsto take account of such correlation. Longitudinal data are, ofcourse, grouped and correlated in this way because repeatedobservations on the same subject (experimental unit) arecorrelated. This correlation is due to the fact that suchobservations reflect the individual characteristics of thesubject. There are several options available for modelingcorrelated data (1), one of which is the use of a mixed effectsmodel incorporating both random and fixed effects. The useof mixed effects models is limited to situations where thecorrelation between observations within a group is positive,which is the case for many datasets. These mixed effectsmodels are widely used in pharmacometrics and will form thebasis of our discussion.Consider a situation where data were collected from nsubjects with m

Twice random, once mixed: Applying mixed models to simultaneously analyze random effects of language and participants

Psychologists, psycholinguists, and other researchers using language stimuli have been struggling for more than 30 years with the problem of how to analyze experimental data that contain two crossed random effects (items and participants). The classical analysis of variance does not apply; alternatives have been proposed but have failed to catch on, and a statistically unsatisfactory procedure of using two approximations (known as F(1) and F(2)) has become the standard. A simple and elegant solution using mixed model analysis has been available for 15 years, and recent improvements in statistical software have made mixed models analysis widely available. The aim of this article is to increase the use of mixed models by giving a concise practical introduction and by giving clear directions for undertaking the analysis in the most popular statistical packages. The article also introduces the DJMIXED: add-on package for SPSS, which makes entering the models and reporting their results as straightforward as possible.

Breeding self-pollinated plants

This presentation aims to discuss strategies to increase the efficiency of selection in self-pollinated plants. One of the strategies is the use of mixed models in order to appropriate genealogy information on the method of pedigree and through the sequential analysis in evaluation tests of progeny in several environments/generation. It is also discussed the use of multiline as an alternative to extend the life of a cultivar.

Recent Bayesian stable-isotope mixing models are highly sensitive to variation in discrimination factors

Stable isotopes are now used widely in ecological studies, including diet reconstruction, where quantitative inferences about diet composition are derived from the use of mixing models. Recent Bayesian models (MixSIR, SIAR) allow users to incorporate variability in discrimination factors (delta13C or delta15N), or the amount of change in either delta13C or delta15N between prey and consumer, but to date there has been no systematic assessment of the effect of variation in delta13C or delta15N on model outputs. We used whole blood from Common Terns (Sterna hirundo) and muscle from their common prey items (fish and euphausiids) to build a series of mixing models in SIAR (stable isotope analysis in R) using various discrimination factors from the published literature for marine birds. The estimated proportion of each diet component was affected significantly by delta13C or delta15N. We also use recently published stable-isotope data on the reliance of critically endangered Balearic Shearwaters (Puffinus mauretanicus) on fisheries discards to show that discrimination factor choice can have profound implications for conservation and management actions. It is therefore crucial for researchers wishing to use mixing models to have an accurate estimate of delta13C and delta15N, because quantitative diet estimates can help to direct future research or prioritize conservation and management actions.

The incretin effect in cats: comparison between oral glucose, lipids, and amino acids

Incretin hormones are secreted from the intestines in response to specific nutrients. They potentiate insulin secretion and have other beneficial effects in glucose homeostasis. We aimed to study the incretin effect in cats and to compare the effect of oral glucose, lipids, or amino acids on serum concentrations of insulin, total glucose-dependent insulinotropic peptide (GIP) and total glucagon-like peptide 1 (GLP-1). Ten healthy cats were used in a repeated measures design. Glucose, lipid, or amino acids were administered through nasoesophageal tubes on separate days. Blood glucose (BG) concentrations were matched between experiments by measuring BG every 5 min and infusing glucose intravenously at a changing rate. Intravenous glucose infusion with no prior treatment served as control. The incretin effect was estimated as the difference in insulin area under the curve (AUC) after oral compared with intravenous glucose. Temporal changes and total amount of hormone secretions were compared between treatment groups with the use of mixed models. Total glucose infused (TGI) at a mean dose of 0.49 g/kg resulted in slightly higher BG compared with 1 g/kg oral glucose ( P = 0.038), but insulin concentrations were not significantly different ( P = 0.367). BG and the TGI were not significantly different after the 3 oral challenges. Total GIP AUC was larger after lipids compared with amino acids ( P = 0.0012) but GIP concentrations did not increase after oral glucose. Insulin and GIP concentrations were positively correlated after lipid ( P < 0.001) and amino acids ( P < 0.001) stimulations, respectively, but not after oral glucose stimulation. Total GLP-1 AUC was similar after all three oral stimulations. Insulin and GLP-1 concentrations were positively correlated after glucose ( P = 0.001), amino acids ( P < 0.001), or lipids ( P = 0.001) stimulations. Our data indirectly support an insulinotropic effect of GIP and GLP-1. Potentiation of insulin secretion after oral glucose is minimal in cats and is mediated by GLP-1 but not GIP.

Source Partitioning Using Stable Isotopes: Coping with Too Much Variation

BackgroundStable isotope analysis is increasingly being utilised across broad areas of ecology and biology. Key to much of this work is the use of mixing models to estimate the proportion of sources contributing to a mixture such as in diet estimation.MethodologyBy accurately reflecting natural variation and uncertainty to generate robust probability estimates of source proportions, the application of Bayesian methods to stable isotope mixing models promises to enable researchers to address an array of new questions, and approach current questions with greater insight and honesty.ConclusionsWe outline a framework that builds on recently published Bayesian isotopic mixing models and present a new open source R package, SIAR. The formulation in R will allow for continued and rapid development of this core model into an all-encompassing single analysis suite for stable isotope research.

Software engineering the mixed model for genome-wide association studies on large samples

Mixed models improve the ability to detect phenotype-genotype associations in the presence of population stratification and multiple levels of relatedness in genome-wide association studies (GWAS), but for large data sets the resource consumption becomes impractical. At the same time, the sample size and number of markers used for GWAS is increasing dramatically, resulting in greater statistical power to detect those associations. The use of mixed models with increasingly large data sets depends on the availability of software for analyzing those models. While multiple software packages implement the mixed model method, no single package provides the best combination of fast computation, ability to handle large samples, flexible modeling and ease of use. Key elements of association analysis with mixed models are reviewed, including modeling phenotype-genotype associations using mixed models, population stratification, kinship and its estimation, variance component estimation, use of best linear unbiased predictors or residuals in place of raw phenotype, improving efficiency and software-user interaction. The available software packages are evaluated, and suggestions made for future software development.

Missing data: Discussion points from the PSI missing data expert group

The Points to Consider Document on Missing Data was adopted by the Committee of Health and Medicinal Products (CHMP) in December 2001. In September 2007 the CHMP issued a recommendation to review the document, with particular emphasis on summarizing and critically appraising the pattern of drop-outs, explaining the role and limitations of the 'last observation carried forward' method and describing the CHMP's cautionary stance on the use of mixed models. In preparation for the release of the updated guidance document, statisticians in the Pharmaceutical Industry held a one-day expert group meeting in September 2008. Topics that were debated included minimizing the extent of missing data and understanding the missing data mechanism, defining the principles for handling missing data and understanding the assumptions underlying different analysis methods. A clear message from the meeting was that at present, biostatisticians tend only to react to missing data. Limited pro-active planning is undertaken when designing clinical trials. Missing data mechanisms for a trial need to be considered during the planning phase and the impact on the objectives assessed. Another area for improvement is in the understanding of the pattern of missing data observed during a trial and thus the missing data mechanism via the plotting of data; for example, use of Kaplan-Meier curves looking at time to withdrawal.

Approaches for Modeling Vertical Distribution of Maximum Knot Size in Black Spruce: A Comparison of Fixed- and Mixed-Effects Nonlinear Models

Abstract Both linear and nonlinear hierarchical mixed-effects models have been used in recent years to analyze nested data sets. These types of models are effective for partitioning variance between hierarchical levels and increasing model flexibility. Models of knot size and distribution have been developed for several commercially important conifer species. Modeling knots is particularly amendable to the mixed-models approach as they are inherently nested at multiple levels including the individual whorl, tree, and stand levels. Although mixed models are effective for addressing hierarchical nesting of data, in this study we contend that improvements achieved by inclusion of mixed effects can be effectively negated with the use of an appropriate model form. This contention is presented as a case study on the development of a maximum knot size model for plantation-grown black spruce in Ontario (Picea mariana [Mill.] BSP). With a naive and simple model form, the nonlinear mixed-effects approach was significantly superior to comparable generalized nonlinear models as the root mean square error was 16% lower. In contrast, when a model form that accounted for primary covariates with a robust model form was used, difference in root mean square error between nonlinear mixed-effects and generalized nonlinear models was approximately 6%. In addition, graphic techniques for exploring distributions of random effects are presented and discussed. Mixed models are effective tools, but, as illustrated by this case study, their limitations need to be recognized and use of mixed models should not precede development of sound model forms.

Last Observation Carried Forward Versus Mixed Models in the Analysis of Psychiatric Clinical Trials

Last Observation Carried Forward Versus Mixed Models in the Analysis of Psychiatric Clinical Trials