Linear Mixed Model Framework Research Articles

An Alternate Approach to Pseudo-Likelihood Model Selection in the Generalized Linear Mixed Modeling Framework

In this paper, we propose and investigate an alternate approach to pseudo-likelihood model selection in the generalized linear mixed modeling framework. The problem with the natural approach to the computation of pseudo-likelihood model selection criteria is that the pseudo-data vary for each candidate model, leading to criteria based on fundamentally different goodness-of-fit statistics, rendering them incomparable. We propose a technique that circumvents this problem. This new approach can be implemented using a SAS macro that obtains and applies the pseudo-data from the full model to fitting candidate models based on all possible subsets of predictor variables. We justify the propriety of the resulting pseudo-likelihood selection criteria through an extensive study designed as a factorial experiment. We then illustrate this new method in a modeling application pertaining to bullying in public schools. The data set for the application is taken from three waves of the Iowa Youth Survey.

A structural equation modeling approach for examining position effects in large-scale assessments

Position effects may occur in both paper–pencil tests and computerized assessments when examinees respond to the same test items located in different positions on the test. To examine position effects in large-scale assessments, previous studies often used multilevel item response models within the generalized linear mixed modeling framework. Using the equivalence of the item response theory and binary factor analysis frameworks when modeling dichotomous item responses, this study introduces a structural equation modeling (SEM) approach that is capable of estimating various types of position effects. Using real data from a large-scale reading assessment, the SEM approach is demonstrated for investigating form, passage position, and item position effects for reading items. The results from a simulation study are also presented to evaluate the accuracy of the SEM approach in detecting item position effects. The implications of using the SEM approach are discussed in the context of large-scale assessments.

General Methods for Evolutionary Quantitative Genetic Inference from Generalized Mixed Models.

Methods for inference and interpretation of evolutionary quantitative genetic parameters, and for prediction of the response to selection, are best developed for traits with normal distributions. Many traits of evolutionary interest, including many life history and behavioral traits, have inherently nonnormal distributions. The generalized linear mixed model (GLMM) framework has become a widely used tool for estimating quantitative genetic parameters for nonnormal traits. However, whereas GLMMs provide inference on a statistically convenient latent scale, it is often desirable to express quantitative genetic parameters on the scale upon which traits are measured. The parameters of fitted GLMMs, despite being on a latent scale, fully determine all quantities of potential interest on the scale on which traits are expressed. We provide expressions for deriving each of such quantities, including population means, phenotypic (co)variances, variance components including additive genetic (co)variances, and parameters such as heritability. We demonstrate that fixed effects have a strong impact on those parameters and show how to deal with this by averaging or integrating over fixed effects. The expressions require integration of quantities determined by the link function, over distributions of latent values. In general cases, the required integrals must be solved numerically, but efficient methods are available and we provide an implementation in an R package, QGglmm. We show that known formulas for quantities such as heritability of traits with binomial and Poisson distributions are special cases of our expressions. Additionally, we show how fitted GLMM can be incorporated into existing methods for predicting evolutionary trajectories. We demonstrate the accuracy of the resulting method for evolutionary prediction by simulation and apply our approach to data from a wild pedigreed vertebrate population.

Testing for additivity in non‐parametric regression

AbstractThis article discusses a novel approach for testing for additivity in non‐parametric regression. We represent the model using a linear mixed model framework and equivalently rewrite the original testing problem as testing for a subset of zero variance components. We propose two testing procedures: the restricted likelihood ratio test and the generalized F test. We develop the finite sample null distribution of the restricted likelihood ratio test and generalized F test using the spectral decomposition of the restricted likelihood ratio and the residual sum of squares, respectively. The null distribution is non‐standard and we provide a fast algorithm to simulate from the null distribution of the tests. We show, through numerical investigation, that the proposed testing procedures outperform the available alternatives and apply the methods to a diabetes data set. The Canadian Journal of Statistics 44: 445–462; 2016 © 2016 Statistical Society of Canada

Flexible analysis of digital PCR experiments using generalized linear mixed models

The use of digital PCR for quantification of nucleic acids is rapidly growing. A major drawback remains the lack of flexible data analysis tools. Published analysis approaches are either tailored to specific problem settings or fail to take into account sources of variability. We propose the generalized linear mixed models framework as a flexible tool for analyzing a wide range of experiments. We also introduce a method for estimating reference gene stability to improve accuracy and precision of copy number and relative expression estimates. We demonstrate the usefulness of the methodology on a complex experimental setup.

Unaccounted uncertainty from qPCR efficiency estimates entails uncontrolled false positive rates.

BackgroundAccurate adjustment for the amplification efficiency (AE) is an important part of real-time quantitative polymerase chain reaction (qPCR) experiments. The most commonly used correction strategy is to estimate the AE by dilution experiments and use this as a plug-in when efficiency correcting the ΔΔCq. Currently, it is recommended to determine the AE with high precision as this plug-in approach does not account for the AE uncertainty, implicitly assuming an infinitely precise AE estimate. Determining the AE with such precision, however, requires tedious laboratory work and vast amounts of biological material. Violation of the assumption leads to overly optimistic standard errors of the ΔΔCq, confidence intervals, and p-values which ultimately increase the type I error rate beyond the expected significance level. As qPCR is often used for validation it should be a high priority to account for the uncertainty of the AE estimate and thereby properly bounding the type I error rate and achieve the desired significance level.ResultsWe suggest and benchmark different methods to obtain the standard error of the efficiency adjusted ΔΔCq using the statistical delta method, Monte Carlo integration, or bootstrapping. Our suggested methods are founded in a linear mixed effects model (LMM) framework, but the problem and ideas apply in all qPCR experiments. The methods and impact of the AE uncertainty are illustrated in three qPCR applications and a simulation study. In addition, we validate findings suggesting that MGST1 is differentially expressed between high and low abundance culture initiating cells in multiple myeloma and that microRNA-127 is differentially expressed between testicular and nodal lymphomas.ConclusionsWe conclude, that the commonly used efficiency corrected quantities disregard the uncertainty of the AE, which can drastically impact the standard error and lead to increased false positive rates. Our suggestions show that it is possible to easily perform statistical inference of ΔΔCq, whilst properly accounting for the AE uncertainty and better controlling the false positive rate.

MTG2: an efficient algorithm for multivariate linear mixed model analysis based on genomic information.

Summary: We have developed an algorithm for genetic analysis of complex traits using genome-wide SNPs in a linear mixed model framework. Compared to current standard REML software based on the mixed model equation, our method is substantially faster. The advantage is largest when there is only a single genetic covariance structure. The method is particularly useful for multivariate analysis, including multi-trait models and random regression models for studying reaction norms. We applied our proposed method to publicly available mice and human data and discuss the advantages and limitations.Availability and implementation: MTG2 is available in https://sites.google.com/site/honglee0707/mtg2.Contact: hong.lee@une.edu.auSupplementary information: Supplementary data are available at Bioinformatics online.

Associating Multivariate Quantitative Phenotypes with Genetic Variants in Family Samples with a Novel Kernel Machine Regression Method.

The recent development of sequencing technology allows identification of association between the whole spectrum of genetic variants and complex diseases. Over the past few years, a number of association tests for rare variants have been developed. Jointly testing for association between genetic variants and multiple correlated phenotypes may increase the power to detect causal genes in family-based studies, but familial correlation needs to be appropriately handled to avoid an inflated type I error rate. Here we propose a novel approach for multivariate family data using kernel machine regression (denoted as MF-KM) that is based on a linear mixed-model framework and can be applied to a large range of studies with different types of traits. In our simulation studies, the usual kernel machine test has inflated type I error rates when applied directly to familial data, while our proposed MF-KM method preserves the expected type I error rates. Moreover, the MF-KM method has increased power compared to methods that either analyze each phenotype separately while considering family structure or use only unrelated founders from the families. Finally, we illustrate our proposed methodology by analyzing whole-genome genotyping data from a lung function study.

Four-way data analysis within the linear mixed modelling framework

Cultivars have to be evaluated under different crop management systems across agro-ecosystems and years using multi-environment trials (MET) before releasing them to the market. Frequently, data collected in METs are arranged according to cultivar (G), management (M), location, (L) and year (Y) combinations in a four-way G x M x L x Y data table that is highly unbalanced for cultivars across locations and time. Therefore, we present the restricted maximum likelihood method (REML) for linear mixed models (LMM) with a factor analytic variance-covariance matrix for assessing cultivar adaptation to crop management systems and environments based on unbalanced datasets. Such a multi-environmental trial system has been in operation in Poland for winter wheat (Triticum aestivum L.) in the form of the Post-registration Variety Testing System (PVTS). This study aimed to illustrate the use of LMM in the analysis of unbalanced four-way G x M x L x Y data. LMM analysis provided adjusted means of grain yield for 51 winter wheat cultivars bred in different regions in Europe, tested across 18 trial locations and seven consecutive cropping seasons in two crop management intensities. The application of the four-way LMM with a factor analytic variance-covariance matrix is a complementary and effective tool for evaluating the unbalanced G x M x L x Y table. Cultivars tested had different adaptive responses to the Polish agro-ecosystems separately for each of the crop management intensities. Wide adaptation in both crop management systems was exhibited by cultivars Mulan and Jenga bred in Germany.

Probing soil physical and biological resilience data from a broad sampling of arable farms in Scotland

AbstractPhysical and biological soil stabilities (i.e. resistance and resilience) were measured on a range of arable farms across eastern Scotland under a range of management practices, with the objective of using a geographically restricted set of soils under similar land use to detect any underlying associations between soil stability, management factors and soil properties. Data were analysed using a combination of a stepwise fixed effects model selection within a linear mixed‐model framework (LMM) and neural network analysis using a Kohonen self‐organising map (KSOM). In general, physical and biological measures of stability were associated with both physical and biological soil properties, particularly bulk density, water retention characteristics, soil carbon and bacterial community structure. A strength of KSOM is its ability to fit more flexible models than the linear relationships of LMM. However, a weakness is that it does not have the ability of LMM to model the sampling design, which is likely to lead to overstating statistical significance. Consequently, KSOM identified more significant associations between soil properties and stability than LMM, while the latter identified significant associations at the between‐farm level. The high‐level land management decisions of farm type (conventional, organic, integrated), crop type or underlying soil type were not associated with stability at this regional scale, thus indicating that the effects of different management practices between farms were overridden by the soil properties on each farm. Management decisions on improving soil stability therefore need to be taken at the individual field scale.

Effects of environmental variables on the movement and space use of coastal sea snakes over multiple temporal scales

Natural and anthropogenic changes in the marine environment can strongly influence the biology and behaviour of coastal organisms. Understanding how animals that rely on these habitats respond to environmental change is crucial to inform when management actions should be implemented to mitigate or reduce impacts. Here passive acoustic telemetry was used to monitor the movements of spine-bellied sea snakes (Hydrophis curtus) within a coastal ecosystem to define activity patterns in relation to environmental conditions. Presence, movement and three-dimensional home range metrics calculated from monitoring data were tested against environmental (water temperature, atmospheric pressure, wind speed, accumulated rainfall and tidal range) and biological (snout-vent length) factors on daily and monthly temporal scales to identify key environmental drivers of movement and the use of space. A generalised linear mixed model (GLMM) framework using Akaike information criterion (AIC) indicated that tidal reach and atmospheric pressure strongly influenced the daily presence and movements of tagged individuals, respectively. Accumulated rainfall significantly influenced the volume of space used on a monthly timescale. This study presents first estimates of three-dimensional home ranges of sea snakes as well as novel information on how environmental variables influence daily and monthly presence, movements and use of space of coastal sea snakes. These data are important in further understanding the ecology of sea snakes and can inform future management actions for this poorly studied taxon in the light of increased environmental and anthropogenic disturbances.

A Linear Mixed Model Spline Framework for Analysing Time Course 'Omics' Data.

Time course ‘omics’ experiments are becoming increasingly important to study system-wide dynamic regulation. Despite their high information content, analysis remains challenging. ‘Omics’ technologies capture quantitative measurements on tens of thousands of molecules. Therefore, in a time course ‘omics’ experiment molecules are measured for multiple subjects over multiple time points. This results in a large, high-dimensional dataset, which requires computationally efficient approaches for statistical analysis. Moreover, methods need to be able to handle missing values and various levels of noise. We present a novel, robust and powerful framework to analyze time course ‘omics’ data that consists of three stages: quality assessment and filtering, profile modelling, and analysis. The first step consists of removing molecules for which expression or abundance is highly variable over time. The second step models each molecular expression profile in a linear mixed model framework which takes into account subject-specific variability. The best model is selected through a serial model selection approach and results in dimension reduction of the time course data. The final step includes two types of analysis of the modelled trajectories, namely, clustering analysis to identify groups of correlated profiles over time, and differential expression analysis to identify profiles which differ over time and/or between treatment groups. Through simulation studies we demonstrate the high sensitivity and specificity of our approach for differential expression analysis. We then illustrate how our framework can bring novel insights on two time course ‘omics’ studies in breast cancer and kidney rejection. The methods are publicly available, implemented in the R CRAN package lmms.

Restricted Maximum Likelihood Estimation for Parameters of the Social Relations Model.

In many areas of research, the round-robin design is used to study interpersonal judgments and behaviors. The resulting data are analyzed with the social relations model (SRM), whereby almost all previously published studies have used ANOVA-based methods or multilevel-based methods to obtain SRM parameter estimates. In this article, the SRM is embedded into the linear mixed model framework, and it is shown how restricted maximum likelihood can be employed to estimate the SRM parameters. It is also described how the effect of covariates on the SRM-specific effects can be estimated. An example is presented to illustrate the approach. We also present the results of a simulation study in which the performance of the proposed approach is compared to the ANOVA method.

Effects of Land Use on Lake Nutrients: The Importance of Scale, Hydrologic Connectivity, and Region.

Catchment land uses, particularly agriculture and urban uses, have long been recognized as major drivers of nutrient concentrations in surface waters. However, few simple models have been developed that relate the amount of catchment land use to downstream freshwater nutrients. Nor are existing models applicable to large numbers of freshwaters across broad spatial extents such as regions or continents. This research aims to increase model performance by exploring three factors that affect the relationship between land use and downstream nutrients in freshwater: the spatial extent for measuring land use, hydrologic connectivity, and the regional differences in both the amount of nutrients and effects of land use on them. We quantified the effects of these three factors that relate land use to lake total phosphorus (TP) and total nitrogen (TN) in 346 north temperate lakes in 7 regions in Michigan, USA. We used a linear mixed modeling framework to examine the importance of spatial extent, lake hydrologic class, and region on models with individual lake nutrients as the response variable, and individual land use types as the predictor variables. Our modeling approach was chosen to avoid problems of multi-collinearity among predictor variables and a lack of independence of lakes within regions, both of which are common problems in broad-scale analyses of freshwaters. We found that all three factors influence land use-lake nutrient relationships. The strongest evidence was for the effect of lake hydrologic connectivity, followed by region, and finally, the spatial extent of land use measurements. Incorporating these three factors into relatively simple models of land use effects on lake nutrients should help to improve predictions and understanding of land use-lake nutrient interactions at broad scales.

Transformed Gaussian Markov random fields and spatial modeling of species abundance

Gaussian random field and Gaussian Markov random field have been widely used to accommodate spatial dependence under the generalized linear mixed models framework. To model spatial count and spatial binary data, we present a class of transformed Gaussian Markov random fields, constructed by transforming the margins of a Gaussian Markov random field to desired marginal distributions that accommodate asymmetry and heavy tail, as needed in many empirical circumstances. The Gaussian copula that characterizes the dependence structure facilitates inferences and applications in modeling spatial dependence. This construction leads to new models such as gamma or beta Markov fields with Gaussian copulas, that are used to model Poisson intensities or Bernoulli rates in hierarchical spatial analyses. The method is naturally implemented in a Bayesian framework. To illustrate our methodology, abundances of variety of gastropod species were collected as counts or presence versus absence from a network of spatial locations in the Luquillo Mountains of Puerto Rico. Gastropods are of considerable ecological importance in terrestrial ecosystems because of their species richness, abundances, and critical roles in ecosystem processes such as decomposition and nutrient cycling. The new models outperform the traditional models based on Bayesian model comparison with conditional predictive ordinate. The validity of Bayesian inferences and model selection were assessed through simulation studies for both spatial Poisson regression and spatial Bernoulli regression.

A modular approach for item response theory modeling with the R package flirt

The new R package flirt is introduced for flexible item response theory (IRT) modeling of psychological, educational, and behavior assessment data. flirt integrates a generalized linear and nonlinear mixed modeling framework with graphical model theory. The graphical model framework allows for efficient maximum likelihood estimation. The key feature of flirt is its modular approach to facilitate convenient and flexible model specifications. Researchers can construct customized IRT models by simply selecting various modeling modules, such as parametric forms, number of dimensions, item and person covariates, person groups, link functions, etc. In this paper, we describe major features of flirt and provide examples to illustrate how flirt works in practice.

Covariance pattern mixture models for the analysis of multivariate heterogeneous longitudinal data

We propose a novel approach for modeling multivariate longitudinal data in the presence of unobserved heterogeneity for the analysis of the Health and Retirement Study (HRS) data. Our proposal can be cast within the framework of linear mixed models with discrete individual random intercepts; however, differently from the standard formulation, the proposed Covariance Pattern Mixture Model (CPMM) does not require the usual local independence assumption. The model is thus able to simultaneously model the heterogeneity, the association among the responses and the temporal dependence structure. We focus on the investigation of temporal patterns related to the cognitive functioning in retired American respondents. In particular, we aim to understand whether it can be affected by some individual socio-economical characteristics and whether it is possible to identify some homogenous groups of respondents that share a similar cognitive profile. An accurate description of the detected groups allows government policy interventions to be opportunely addressed. Results identify three homogenous clusters of individuals with specific cognitive functioning, consistent with the class conditional distribution of the covariates. The flexibility of CPMM allows for a different contribution of each regressor on the responses according to group membership. In so doing, the identified groups receive a global and accurate phenomenological characterization.

A non linear mixed effects model of plant growth and estimation via stochastic variants of the EM algorithm

ABSTRACTThere is a strong genetic variability among plants, even of the same variety, which, combined with the locally varying environmental conditions in a given field, can lead to the development of highly different neighboring plants. This is one of the reasons why population-based methods for modeling plant growth are of great interest. GreenLab is a functional–structural plant growth model which has already been shown to be successful in describing plant growth dynamics primarily at individual level. In this study, we extend its formulation to the population level. In order to model the deviations from some fixed but unknown important biophysical and genetic parameters we introduce random effects. The resulting model can be cast into the framework of non linear mixed models, which can be seen as particular types of incomplete data models. A stochastic variant of an EM-type algorithm (expectation–maximization) is generally needed to perform maximum likelihood estimation for this type of models. Under some assumptions, the complete data distribution belongs to a subclass of the exponential family of distributions for which the M-step can be solved explicitly. In such cases, the interest is focused on the best approximation of the E-step by competing simulation methods. In this direction, we propose to compare two commonly used stochastic algorithms: the Monte-Carlo EM (MCEM) and the SAEM algorithm. The performances of both algorithms are compared on simulated data, and an application to real data from sugar beet plants is also given.

Bootstrap Restricted Likelihood Ratio Test for the Detection of Rare Variants

In this paper the detection of rare variants association with continuous phenotypes of interest is investigated via the likelihood-ratio based variance component test under the framework of linear mixed models. The hypothesis testing is challenging and nonstandard, since under the null the variance component is located on the boundary of its parameter space. In this situation the usual asymptotic chisquare distribution of the likelihood ratio statistic does not necessarily hold. To circumvent the derivation of the null distribution we resort to the bootstrap method due to its generic applicability and being easy to implement. Both parametric and nonparametric bootstrap likelihood ratio tests are studied. Numerical studies are implemented to evaluate the performance of the proposed bootstrap likelihood ratio test and compare to some existing methods for the identification of rare variants. To reduce the computational time of the bootstrap likelihood ratio test we propose an effective approximation mixture for the bootstrap null distribution. The GAW17 data is used to illustrate the proposed test.

Detecting the Genomic Signature of Divergent Selection in Presence of Gene Flow.

The study of local adaptation is a main focus of evolutionary biology since it may contribute to explain the current species diversity. The genomic scan procedures permit for the first time to study the connection between specific DNA patterns and processes as natural selection, genetic drift, recombination, mutation and gene flow. Accordingly, the information on genomes from non-model organisms increases and the interest on detecting the signal of natural selection in the DNA sequences of different populations also raises. The main goal of the present work is to explore a sequence-based method for detecting natural selection in divergent populations connected by migration. In doing so, we rely on a recently published statistic based upon th e definition of haplotype allelic classes (HAC). The original measure was modified to be more sensitive to intermediate frequencies in non-model species. A linkage-disequilibrium-based method was also assayed and individual-based simulations were performed to test the methods. The results suggest that the HAC-based methods and, specifically, the new proposed method are quite powerful for detecting the footprint of moderate divergent selection. They are also robust to reasonable model misspecification. One obvious advantage of the new algorithm is that it does not require knowledge of the allelic state.