Showing papers on "Random effects model published in 2014"

Using observation-level random effects to model overdispersion in count data in ecology and evolution

Abstract: Overdispersion is common in models of count data in ecology and evolutionary biology, and can occur due to missing covariates, non-independent (aggregated) data, or an excess frequency of zeroes (zero-inflation). Accounting for overdispersion in such models is vital, as failing to do so can lead to biased parameter estimates, and false conclusions regarding hypotheses of interest. Observation-level random effects (OLRE), where each data point receives a unique level of a random effect that models the extra-Poisson variation present in the data, are commonly employed to cope with overdispersion in count data. However studies investigating the efficacy of observation-level random effects as a means to deal with overdispersion are scarce. Here I use simulations to show that in cases where overdispersion is caused by random extra-Poisson noise, or aggregation in the count data, observation-level random effects yield more accurate parameter estimates compared to when overdispersion is simply ignored. Conversely, OLRE fail to reduce bias in zero-inflated data, and in some cases increase bias at high levels of overdispersion. There was a positive relationship between the magnitude of overdispersion and the degree of bias in parameter estimates. Critically, the simulations reveal that failing to account for overdispersion in mixed models can erroneously inflate measures of explained variance (r2), which may lead to researchers overestimating the predictive power of variables of interest. This work suggests use of observation-level random effects provides a simple and robust means to account for overdispersion in count data, but also that their ability to minimise bias is not uniform across all types of overdispersion and must be applied judiciously.

Extension of Nakagawa & Schielzeth's R2GLMM to random slopes models.

Abstract: Nakagawa & Schielzeth extended the widely used goodness-of-fit statistic R2 to apply to generalized linear mixed models (GLMMs). However, their R2GLMM method is restricted to models with the simplest random effects structure, known as random intercepts models. It is not applicable to another common random effects structure, random slopes models. I show that R2GLMM can be extended to random slopes models using a simple formula that is straightforward to implement in statistical software. This extension substantially widens the potential application of R2GLMM. Keywords: coefficient of determination, generalized linear mixed model, random slopes model, random regression Introduction The coefficient of determination, R2, is a widely used statistic for assessing the goodness-of-fit, on a scale from 0 to 1, of a linear regression model (LM). It is defined as the proportion of variance in the response variable that is explained by the explanatory variables or, equivalently, the proportional reduction in unexplained variance. Unexplained variance can be viewed as variance in model prediction error, so R2 can also be defined in terms of reduction in prediction error variance. Insofar as it is justifiable to make the leap from ‘prediction’ to ‘understanding’, R2 can be intuitively interpreted as a measure of how much better we understand a system once we have measured and modelled some of its components. R2 has been extended to apply to generalized linear models (GLMs) (Maddala 1983) and linear mixed effects models (LMMs) (Snijders & Bosker 1994) [reviewed by (Nakagawa & Schielzeth 2013)]. Nakagawa & Schielzeth (2013) proposed a further generalization of R2 to generalized linear mixed effects models (GLMMs), a useful advance given the ubiquity of GLMMs for data analysis in ecology and evolution (Bolker et al. 2009). A function to estimate this R2GLMM statistic, r.squaredGLMM, has been included in the MuMIn package (Barton 2014) for the R statistical software (R Core Team 2014). However, Nakagawa and Schielzeth's R2GLMM formula is applicable to only a subset of GLMMs known as random intercepts models. Random intercepts models are used to model clustered observations, for example, where multiple observations are taken on each of a sample of individuals. Correlations between clustered observations within individuals are accounted for by allowing each subject to have a different intercept representing the deviation of that subject from the global intercept. Random intercepts are typically modelled as being sampled from a normal distribution with mean zero and a variance parameter that is estimated from the data. Although random intercepts are probably the most popular random effects models in ecology and evolution, other random effect specifications are also common, in particular random slopes models, where not only the intercept but also the slope of the regression line is allowed to vary between individuals. Random intercepts and slopes are typically modelled as normally distributed deviations from the global intercept and slope, respectively. For example, random slopes models, under the name of ‘random regression’ models, are used to investigate individual variation in response to different environments (Nussey, Wilson & Brommer 2007). The aim of this article is to show how Nakagawa and Schielzeth's R2GLMM can be further extended to encompass random slopes models.

Longitudinal Analysis: Modeling Within-Person Fluctuation and Change

Abstract: Section 1: Building Blocks for Longitudinal Analysis 1. Introduction to the Analysis of Longitudinal Data 2. Between-Person Analysis and Interpretation of Interactions 3. Introduction to Within-Person Analysis and Model Comparisons Section 2: Modeling the Effects of Time 4. Describing Within-Person Fluctuation over Time 5. Introduction to Random Effects of Time and Model Estimation 6. Describing Within-Person Change over Time Section 3: Modeling the Effects of Predictors 7. Time-Invariant Predictors in Longitudinal Models 8. Time-Varying Predictors in Models of Within-Person Fluctuation 9. Time-Varying Predictors in Models of Within-Person Change Section 4: Advanced Applications 10. Analysis over Alternative Metrics and Multiple Dimensions of Time 11. Analysis of Individuals within Groups over Time 12. Analysis of Repeated Measures Designs Not Involving Time 13. Additional Considerations and Related Models

Random-effects meta-analysis of inconsistent effects: a time for change.

Abstract: A primary goal of meta-analysis is to improve the estimation of treatment effects by pooling results of similar studies. This article discusses the problems associated with using the DerSimonian–La...

Fixed effects analysis of repeated measures data

Abstract: The analysis of repeated measures or panel data allows control of some of the biases which plague other observational studies, particularly unmeasured confounding. When this bias is suspected, and the research question is: 'Does a change in an exposure cause a change in the outcome?', a fixed effects approach can reduce the impact of confounding by time-invariant factors, such as the unmeasured characteristics of individuals. Epidemiologists familiar with using mixed models may initially presume that specifying a random effect (intercept) for every individual in the study is an appropriate method. However, this method uses information from both the within-individual/unit exposure-outcome association and the between-individual/unit exposure-outcome association. Variation between individuals may introduce confounding bias into mixed model estimates, if unmeasured time-invariant factors are associated with both the exposure and the outcome. Fixed effects estimators rely only on variation within individuals and hence are not affected by confounding from unmeasured time-invariant factors. The reduction in bias using a fixed effects model may come at the expense of precision, particularly if there is little change in exposures over time. Neither fixed effects nor mixed models control for unmeasured time-varying confounding or reverse causation.

MultiBLUP: improved SNP-based prediction for complex traits

Abstract: BLUP (best linear unbiased prediction) is widely used to predict complex traits in plant and animal breeding, and increasingly in human genetics. The BLUP mathematical model, which consists of a single random effect term, was adequate when kinships were measured from pedigrees. However, when genome-wide SNPs are used to measure kinships, the BLUP model implicitly assumes that all SNPs have the same effect-size distribution, which is a severe and unnecessary limitation. We propose MultiBLUP, which extends the BLUP model to include multiple random effects, allowing greatly improved prediction when the random effects correspond to classes of SNPs with distinct effect-size variances. The SNP classes can be specified in advance, for example, based on SNP functional annotations, and we also provide an adaptive procedure for determining a suitable partition of SNPs. We apply MultiBLUP to genome-wide association data from the Wellcome Trust Case Control Consortium (seven diseases), and from much larger studies of celiac disease and inflammatory bowel disease, finding that it consistently provides better prediction than alternative methods. Moreover, MultiBLUP is computationally very efficient; for the largest data set, which includes 12,678 individuals and 1.5 M SNPs, the total analysis can be run on a single desktop PC in less than a day and can be parallelized to run even faster. Tools to perform MultiBLUP are freely available in our software LDAK.

Linear quantile mixed models

Abstract: Dependent data arise in many studies. Frequently adopted sampling designs, such as cluster, multilevel, spatial, and repeated measures, may induce this dependence, which the analysis of the data needs to take into due account. In a previous publication (Geraci and Bottai in Biostatistics 8:140–154, 2007), we proposed a conditional quantile regression model for continuous responses where subject-specific random intercepts were included to account for within-subject dependence in the context of longitudinal data analysis. The approach hinged upon the link existing between the minimization of weighted absolute deviations, typically used in quantile regression, and the maximization of a Laplace likelihood. Here, we consider an extension of those models to more complex dependence structures in the data, which are modeled by including multiple random effects in the linear conditional quantile functions. We also discuss estimation strategies to reduce the computational burden and inefficiency associated with the Monte Carlo EM algorithm we have proposed previously. In particular, the estimation of the fixed regression coefficients and of the random effects’ covariance matrix is based on a combination of Gaussian quadrature approximations and non-smooth optimization algorithms. Finally, a simulation study and a number of applications of our models are presented.

Testing environmental and genetic effects in the presence of spatial autocorrelation

Abstract: Spatial autocorrelation is a well-recognized concern for observational data in general, and more specifically for spatial data in ecology. Generalized linear mixed models (GLMMs) with spatially autocorrelated random effects are a potential general framework for handling these spatial correlations. However, as the result of statistical and practical issues, such GLMMs have been fitted through the undocumented use of procedures based on penalized quasi-likelihood approximations (PQL), and under restrictive models of spatial correlation. Alternatively, they are often neglected in favor of simpler but more questionable approaches. In this work we aim to provide practical and validated means of inference under spatial GLMMs, that overcome these limitations. For this purpose, a new software is developed to fit spatial GLMMs. We use it to assess the performance of likelihood ratio tests for fixed effects under spatial autocorrelation, based on Laplace or PQL approximations of the likelihood. Expectedly, the Laplace approximation performs generally slightly better, although a variant of PQL was better in the binary case. We show that a previous implementation of PQL methods in the R language, glmmPQL, is not appropriate for such applications. Finally, we illustrate the efficiency of a bootstrap procedure for correcting the small sample bias of the tests, which applies also to non-spatial models.

A design‐by‐treatment interaction model for network meta‐analysis with random inconsistency effects

Abstract: Network meta-analysis is becoming more popular as a way to analyse multiple treatments simultaneously and, in the right circumstances, rank treatments. A difficulty in practice is the possibility of ‘inconsistency’ or ‘incoherence’, where direct evidence and indirect evidence are not in agreement. Here, we develop a random-effects implementation of the recently proposed design-by-treatment interaction model, using these random effects to model inconsistency and estimate the parameters of primary interest. Our proposal is a generalisation of the model proposed by Lumley and allows trials with three or more arms to be included in the analysis. Our methods also facilitate the ranking of treatments under inconsistency. We derive R and I2 statistics to quantify the impact of the between-study heterogeneity and the inconsistency. We apply our model to two examples. © 2014 The Authors. Statistics in Medicine published by John Wiley & Sons, Ltd.

Linear Quantile Mixed Models: The lqmm Package for Laplace Quantile Regression

Abstract: Inference in quantile analysis has received considerable attention in the recent years. Linear quantile mixed models (Geraci and Bottai 2014) represent a flexible statistical tool to analyze data from sampling designs such as multilevel, spatial, panel or longitudinal, which induce some form of clustering. In this paper, I will show how to estimate conditional quantile functions with random effects using the R package lqmm. Modeling, estimation and inference are discussed in detail using a real data example. A thorough description of the optimization algorithms is also provided.

Closed-skew normality in stochastic frontiers with individual effects and long/short-run efficiency

Abstract: This paper considers the estimation of Kumbhakar et al. (J Prod Anal. doi: 10.1007/s11123-012-0303-1 , 2012) (KLH) four random components stochastic frontier (SF) model using MLE techniques. We derive the log-likelihood function of the model using results from the closed-skew normal distribution. Our Monte Carlo analysis shows that MLE is more efficient and less biased than the multi-step KLH estimator. Moreover, we obtain closed-form expressions for the posterior expected values of the random effects, used to estimate short-run and long-run (in)efficiency as well as random-firm effects. The model is general enough to nest most of the currently used panel SF models; hence, its appropriateness can be tested. This is exemplified by analyzing empirical results from three different applications.

FIRM HETEROGENEITY, PERSISTENT AND TRANSIENT TECHNICAL INEFFICIENCY: A GENERALIZED TRUE RANDOM-EFFECTS model

Abstract: This paper considers a panel data stochastic frontier model that disentangles unobserved firm effects (firm heterogeneity) from persistent (time-invariant/long-term) and transient (time-varying/short-term) technical inefficiency. The model gives us a four-way error component model, viz., persistent and time-varying inefficiency, random firm effects and noise. We use Bayesian methods of inference to provide robust and efficient methods of estimating inefficiency components in this four-way error component model. Monte Carlo results are provided to validate its performance. We also present results from an empirical application that uses a large panel of US commercial banks

Random-effects, fixed-effects and the within-between specification for clustered data in observational health studies: a simulation study.

Abstract: Background When unaccounted-for group-level characteristics affect an outcome variable, traditional linear regression is inefficient and can be biased. The random- and fixed-effects estimators (RE and FE, respectively) are two competing methods that address these problems. While each estimator controls for otherwise unaccounted-for effects, the two estimators require different assumptions. Health researchers tend to favor RE estimation, while researchers from some other disciplines tend to favor FE estimation. In addition to RE and FE, an alternative method called within-between (WB) was suggested by Mundlak in 1978, although is utilized infrequently. Methods We conduct a simulation study to compare RE, FE, and WB estimation across 16,200 scenarios. The scenarios vary in the number of groups, the size of the groups, within-group variation, goodness-of-fit of the model, and the degree to which the model is correctly specified. Estimator preference is determined by lowest mean squared error of the estimated marginal effect and root mean squared error of fitted values. Results Although there are scenarios when each estimator is most appropriate, the cases in which traditional RE estimation is preferred are less common. In finite samples, the WB approach outperforms both traditional estimators. The Hausman test guides the practitioner to the estimator with the smallest absolute error only 61% of the time, and in many sample sizes simply applying the WB approach produces smaller absolute errors than following the suggestion of the test. Conclusions Specification and estimation should be carefully considered and ultimately guided by the objective of the analysis and characteristics of the data. The WB approach has been underutilized, particularly for inference on marginal effects in small samples. Blindly applying any estimator can lead to bias, inefficiency, and flawed inference.

Identification and Estimation of Dynamic Binary Response Panel Data Models: Empirical Evidence Using Alternative Approaches

Abstract: We examine the roles of sample initial conditions and unobserved individual effects in consistent estimation of the dynamic binary response panel data model. Different specifications of the model are estimated using female welfare and labor force participation data from the Survey of Income and Program Participation. These include alternative random effects (RE) models, in which the conditional distributions of both the unobserved heterogeneity and the initial conditions are specified, and fixed effects (FE) conditional logit models that make no assumptions on either distribution. There are several findings. First, the hypothesis that the sample initial conditions are exogenous is rejected by both samples. Misspecification of the initial conditions results in drastically overstated estimates of the state dependence and understated estimates of the short- and long-run effects of children on labor force participation. The FE conditional logit estimates are similar to the estimates from the RE model that is flexible with respect to both the initial conditions and the correlation between the unobserved heterogeneity and the covariates. For female labor force participation, there is evidence that fertility choices are correlated with both unobserved heterogeneity and pre-sample participation histories.

Mixed-effects random forest for clustered data

Abstract: This paper presents an extension of the random forest (RF) method to the case of clustered data. The proposed ‘mixed-effects random forest’ (MERF) is implemented using a standard RF algorithm within the framework of the expectation–maximization algorithm. Simulation results show that the proposed MERF method provides substantial improvements over standard RF when the random effects are non-negligible. The use of the method is illustrated to predict the first-week box office revenues of movies.

Diabetes and Oral Implant Failure A Systematic Review

Abstract: The aim of this systematic review and meta-analysis was to investigate whether there are any effects of diabetes mellitus on implant failure rates, postoperative infections, and marginal bone loss. An electronic search without time or language restrictions was undertaken in March 2014. The present review followed the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines. Eligibility criteria included clinical human studies. The search strategy resulted in 14 publications. The I (2) statistic was used to express the percentage of total variation across studies due to heterogeneity. The inverse variance method was used for the random effects model when heterogeneity was detected or for the fixed effects model when heterogeneity was not detected. The estimates of an intervention for dichotomous outcomes were expressed in risk ratio and in mean difference in millimeters for continuous outcomes, both with a 95% confidence interval. There was a statistically significant difference (p = .001; mean difference = 0.20, 95% confidence interval = 0.08, 0.31) between diabetic and non-diabetic patients concerning marginal bone loss, favoring non-diabetic patients. A meta-analysis was not possible for postoperative infections. The difference between the patients (diabetic vs. non-diabetic) did not significantly affect implant failure rates (p = .65), with a risk ratio of 1.07 (95% confidence interval = 0.80, 1.44). Studies are lacking that include both patient types, with larger sample sizes, and that report the outcome data separately for each group. The results of the present meta-analysis should be interpreted with caution because of the presence of uncontrolled confounding factors in the included studies.

Fixed- and random-effects meta-analytic structural equation modeling: examples and analyses in R.

Abstract: Meta-analytic structural equation modeling (MASEM) combines the ideas of meta-analysis and structural equation modeling for the purpose of synthesizing correlation or covariance matrices and fitting structural equation models on the pooled correlation or covariance matrix. Cheung and Chan (Psychological Methods 10:40–64, 2005b, Structural Equation Modeling 16:28–53, 2009) proposed a two-stage structural equation modeling (TSSEM) approach to conducting MASEM that was based on a fixed-effects model by assuming that all studies have the same population correlation or covariance matrices. The main objective of this article is to extend the TSSEM approach to a random-effects model by the inclusion of study-specific random effects. Another objective is to demonstrate the procedures with two examples using the metaSEM package implemented in the R statistical environment. Issues related to and future directions for MASEM are discussed.

Analysis of Capture-Recapture Data

Abstract: Introduction History and motivation Marking Introduction to the Cormorant data set Modelling population dynamics Model fitting, averaging, and comparison Introduction Classical inference Bayesian inference Computing Estimating the size of closed populations Introduction The Schnabel census Analysis of Schnabel census data Model classes Accounting for unobserved heterogeneity Logistic-linear models Spuriously large estimates, penalized likelihood and elicited priors Bayesian modeling Medical and social applications Testing for closure-mixture estimators Spatial capture-recapture models Computing Survival modeling: single-site models Introduction Mark-recovery models Mark-recapture models Combining separate mark-recapture and recovery data sets Joint recapture-recovery models Computing Survival modeling: multi-site models Introduction Matrix representation Multi-site joint recapture-recovery models Multi-state models as a unified framework Extensions to multi-state models Model selection for multi-site models Multi-event models Computing Occupancy modelling Introduction The two-parameter occupancy model Extensions Moving from species to individual: abundance-induced heterogeneity Accounting for spatial information Computing Covariates and random effects Introduction External covariates Threshold models Individual covariates Random effects Measurement error Use of P-splines Senescence Variable selection Spatial covariates Computing Simultaneous estimation of survival and abundance Introduction Estimating abundance in open populations Batch marking Robust design Stopover models Computing Goodness-of-fit assessment Introduction Diagnostic goodness-of-fit tests Absolute goodness-of-fit tests Computing Parameter redundancy Introduction Using symbolic computation Parameter redundancy and identifiability Decomposing the derivative matrix of full rank models Extension The moderating effect of data Covariates Exhaustive summaries and model taxonomies Bayesian methods Computing State-space models Introduction Definitions Fitting linear Gaussian models Models which are not linear Gaussian Bayesian methods for state-space models Formulation of capture-re-encounter models Formulation of occupancy models Computing Integrated population modeling Introduction Normal approximations of component likelihoods Model selection Goodness of fit for integrated population modelling: calibrated simulation Previous applications Hierarchical modelling to allow for dependence of data sets Computing Appendix: Distributions reference Summary, Further reading, and Exercises appear at the end of each chapter.

Multilevel structured additive regression

Abstract: Models with structured additive predictor provide a very broad and rich framework for complex regression modeling. They can deal simultaneously with nonlinear covariate effects and time trends, unit- or cluster-specific heterogeneity, spatial heterogeneity and complex interactions between covariates of different type. In this paper, we propose a hierarchical or multilevel version of regression models with structured additive predictor where the regression coefficients of a particular nonlinear term may obey another regression model with structured additive predictor. In that sense, the model is composed of a hierarchy of complex structured additive regression models. The proposed model may be regarded as an extended version of a multilevel model with nonlinear covariate terms in every level of the hierarchy. The model framework is also the basis for generalized random slope modeling based on multiplicative random effects. Inference is fully Bayesian and based on Markov chain Monte Carlo simulation techniques. We provide an in depth description of several highly efficient sampling schemes that allow to estimate complex models with several hierarchy levels and a large number of observations within a couple of minutes (often even seconds). We demonstrate the practicability of the approach in a complex application on childhood undernutrition with large sample size and three hierarchy levels.

Crossed and Nested Mixed-Effects Approaches for Enhanced Model Development and Removal of the Ergodic Assumption in Empirical Ground-Motion Models

Abstract: Limitations in the size of strong‐motion databases that are used for the development of empirical ground‐motion models has necessitated the use of the ergodic assumption. Several recent efforts, using different databases from around the world, have been made to estimate the single‐station standard deviation of spectral accelerations. The computed estimates have been found to be very stable globally, despite the various researchers using quite different approaches. This paper demonstrates that the multistage procedures that have been adopted by previous researchers can be replaced by the use of more elaborate mixed‐effects regression analyses. Additionally, the traditional use of additive random effects to capture source, path, and site effects is shown to have conceptual shortcomings that are addressed through the use of a more complex treatment of mixed‐effects models. A model for the residual variance (within‐event single‐station variance) is presented using these advanced approaches.

Demystifying fixed and random effects meta-analysis

Abstract: Objective Systematic reviewers often need to choose between two statistical methods when synthesising evidence in a meta-analysis: the fixed effect and the random effects models. The two approaches entail different assumptions about the treatment effect in the included studies. The aim of this paper was to explain the assumptions underlying each model and their implications in the interpretation of summary results. Methods We discussed the key assumptions underlying the two methods and the subsequent implications on interpreting results. We used two illustrative examples from a published meta-analysis and highlighted differences in results. Results The two meta-analytic approaches may yield similar or contradicting results. Even if results between the two models are similar, summary estimates should be interpreted in a different way. Conclusions Selection between fixed or random effects should be based on the clinical relevance of the assumptions that characterise each approach. Researchers should consider the implications of the analysis model in the interpretation of the findings and use prediction intervals in the random effects meta-analysis.

Nonparametric Regression Analysis of Longitudinal Data

Abstract: Nonparametric approaches have recently emerged as a flexible way to model longitudinal data. This entry reviews some of the common nonparametric approaches to incorporate time and other covariate effects for longitudinally observed response data. Smoothing procedures are invoked to estimate the associated nonparametric functions, but the choice of smoothers can vary and is often subjective. Both fixed and random effects may be included for vector or longitudinal covariates. A closely related type of data is functional data, where the prevailing approaches to model random effects are through functional principal components analysis and B-splines. Related semiparametric regression models also play an increasingly important role. Keywords: functional data analysis; scatter-plot smoother; mean curve; fixed effects; random effects; principal components analysis; semiparametric regression

A note on BIC in mixed-effects models

Abstract: The Bayesian Information Criterion (BIC) is widely used for variable selection in mixed effects models. However, its expression is unclear in typical situations of mixed effects models, where simple definition of the sample size is not meaningful. We derive an appropriate BIC expression that is consistent with the random effect structure of the mixed effects model. We illustrate the behavior of the proposed criterion through a simulation experiment and a case study and we recommend its use as an alternative to various existing BIC versions that are implemented in available software.