Topic
Random effects model
About: Random effects model is a research topic. Over the lifetime, 8388 publications have been published within this topic receiving 438823 citations. The topic is also known as: random effects & random effect.
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TL;DR: In this article, a Poisson model was proposed for nested random effects Cox proportional hazards models, where the principal results depend only on the first and second moments of the unobserved random effects.
Abstract: SUMMARY We propose a Poisson modelling approach to nested random effects Cox proportional hazards models. An important feature of this approach is that the principal results depend only on the first and second moments of the unobserved random effects. The orthodox best linear unbiased predictor approach to random effects Poisson modelling techniques enables us to justify appropriate consistency and optimality. The explicit expressions for the random effects given by our approach facilitate incorporation of a relatively large number of random effects. The use of the proposed methods is illustrated through the reanalysis of data from a large-scale cohort study of particulate air pollution and mortality previously reported by Pope et al. (1995).
111 citations
TL;DR: In this paper, the authors present the results of a simulation study that examines the estimation quality of univariate 2-level autoregressive models of order 1, AR(1), using Bayesian analysis in Mplus Version 8.
Abstract: Dynamic structural equation modeling (DSEM) is a novel, intensive longitudinal data (ILD) analysis framework. DSEM models intraindividual changes over time on Level 1 and allows the parameters of these processes to vary across individuals on Level 2 using random effects. DSEM merges time series, structural equation, multilevel, and time-varying effects models. Despite the well-known properties of these analysis areas by themselves, it is unclear how their sample size requirements and recommendations transfer to the DSEM framework. This article presents the results of a simulation study that examines the estimation quality of univariate 2-level autoregressive models of order 1, AR(1), using Bayesian analysis in Mplus Version 8. Three features are varied in the simulations: complexity of the model, number of subjects, and number of time points per subject. Samples with many subjects and few time points are shown to perform substantially better than samples with few subjects and many time points.
110 citations
TL;DR: In this article, a linear model with one additional random effect was used to analyze multiple predictors on the same subjects and each predictor was analyzed separately. But the model was not applied to a large-scale association study of multiple sclerosis including over 20,000 individuals and 500,000 genetic variants.
Abstract: Motivated by genome-wide association studies, we consider a standard linear model with one additional random effect in situations where many predictors have been collected on the same subjects and each predictor is analyzed separately. Three novel contributions are (1) a transformation between the linear and log-odds scales which is accurate for the important genetic case of small effect sizes; (2) a likelihood-maximization algorithm that is an order of magnitude faster than the previously published approaches; and (3) efficient methods for computing marginal likelihoods which allow Bayesian model comparison. The methodology has been successfully applied to a large-scale association study of multiple sclerosis including over 20,000 individuals and 500,000 genetic variants.
110 citations
TL;DR: In this paper, the authors present a survey of the literature on experimental design for linear and non-linear data sets and compare the results of four experimental designs: the basic factorial design, the complete block design (CB), the split plot/repeated measures design (SP/RM), the Latin square design (LS), and the two-way BF design (BF).
Abstract: To the Instructor. Sample Exam Questions. To the Student. Acknowledgments. 1. Introduction to Experimental Design. 1. The Challenge of planning a good experiment. 2. Three basic principles and four experimental designs. 3. The factor structure of the four experimental designs. 2. Informal Analysis and Checking Assumptions. 1. What analysis of variance does. 2. The six fisher assumptions. 3. Informal analysis, part 1: parallel dot graphs and choosing a scale. 4. Informal analysis, part 2: interaction graph for the log concentrations. 3. Formal Anova: Decomposing the Data and Measuring Variability, Testing Hypothesis and Estimating True Differences. 1. Decomposing the data. 2. Computing mean squares to measure average variability. 3. Standard deviation = root mean square for residuals. 4. Formal hypothesis testing: are the effects detectable? 5. Confidence intervals: the likely size of true differences. 4. Decisions About the Content of an Experiment. 1. The response. 2. Conditions. 3. Material. 5. Randomization and the Basic Factorial Design. 1. The basic factorial design ("What you do"). 2. Informal analysis. 3. Factor structure ("What you get"). 4. Decomposition and analysis of variance for one-way BF designs. 5. Using a computer [Optional]. 6. Algebraic notation for factor structure [Optional]. 6. Interaction and the Principle of Factorial Crossing. 1. Factorial crossing and the two-way basic factorial design, or BF[2]. 2. Interaction and the interaction graph. 3. Decomposition and ANOVA for the two-way design. 4. Using a computer [Optional]. 5. Algebraic notation for the two-way BF design [Optional]. 7. The Principle of Blocking. 1. Blocking and the complete block design (CB). 2. Two nuisance factors: the Latin square design(LS). 3. The split plot/repeated measures design (SP/RM). 4. Decomposition and analysis of variance. 5. Scatterplots for data sets with blocks. 6. Using a computer. [Optional]. 7. Algebraic notation for the CB, LS And SP/RM Designs. 8. Working with the Four Basic Designs. 1. Comparing and recognizing design structures. 2. Choosing a design structure: deciding about blocking. 3. Informal analysis: examples. 4. Recognizing alternative to ANOVA. 9. Extending the Basic Designs by Factorial Crossing. 1. Extending the BF design: general principles. 2. Three or more crossed factors of interest. 3. Compound within-blocks factors. 4.Graphical methods for 3-factor interactions. 5. Analysis of variance. 10. Decomposing a Data Set. 1. The basic decomposition step and the BF[1] design. 2. Decomposing data from balanced designs. 11. Comparisons, Contrasts, and Confidence Intervals. 1. Comparisons: confidence intervals and tests. 2. Adjustments for multiple comparisons. 3. Between-blocks factors and compound within-blocks factors. 4. Linear estimators and orthogonal contrasts [Optional]. 12. The Fisher Assumptions and How to Check Them. 1. Same SDs (s). 2. Independent chance errors (I). 3. The normality assumption (N). 4. Effects are additive (A) and constant (C). 5. Estimating replacement values for outliers. 13. Other Experimental Designs and Models. 1. New factor structures built by crossing and nesting. 2. New uses for old factor structures: fixed versus random effects. 3. Models with mixed interaction effects. 4. Expected mean square and f-ratios. 14. Continuous Carriers: A Visual Approach to Regression, Correlation and Analysis of Covariance. 1. Regression. 2. Balloon summaries and correlation. 3. Analysis of covariance. 15. Sampling Distributions and the Role of the Assumptions. 1. The logic of hypothesis testing. 2. Ways to think about sampling distributions. 3. Four fundamental families of distributions. 4. Sampling distributions for linear estimators. 5. Approximate sampling distributions for f-ratios. 6. Why (and when) are the models reasonable? Tables. Data Sources. Subject Index. Examples.
110 citations
TL;DR: Half a century of research efforts indicate that approximately every sixth child shows signs of emotional or behavioural disorders, and conclusions regarding period effects are not robust.
Abstract: Background This meta-analysis aimed to determine the overall prevalence of emotional and behavioural disorders among children and adolescents in Germany, the dependence of prevalence estimates upon the methods employed and potential secular trends. Methods Primary studies were subjected to meta-analytical analyses using a random effects model. Mean estimates of primary study effects were averaged using the precision-weighted method and were subsequently subjected to sensitivity analyses using hierarchical regression and (co-)variance analyses. Results The precision-weighted average primary study prevalence for the 33 studies included was M=17.6%. The effect size primarily depended on the case definition employed, with studies applying questionnaire criteria showing, on average, lower primary study effects. Moreover, a negative relationship was found between study validity and primary study effect. Conclusion Half a century of research efforts indicate that approximately every sixth child shows signs of emotional or behavioural disorders, and conclusions regarding period effects are not robust.
110 citations