Variance Components Of Random Effects Research Articles

Control chart for detecting the scale parameter of the zero‐inflated Poisson model

AbstractWhen monitoring risk in public health, count data commonly exhibit an excessive number of zero, and the zero‐inflated Poisson (ZIP) model is often used to fit this type of data. Most previous methods for monitoring of the ZIP model have focused on the changes in the location parameter and the existence of the scale parameter and usually assumed that the scale parameter is zero in the H0 stage. However, in an objective environment, data often have certain fluctuations, meaning that the scale parameter always exists. Therefore, it is more meaningful to monitor the changes in the scale parameter on top of the predefined baseline than to monitor its existence. In this study, we derive a score test statistic based on the generalized Henderson's joint likelihood function, construct a risk‐adjusted exponentially weighted moving average (EWMA) control chart to monitor the variability of the random effects variance component in the ZIP mixed‐effects model. And the convergence property of the score test statistic is proved through derivation, which shows that the new method has theoretical reliability. The simulation results Indicate that when the scale parameter has different predefined baselines and different variation amplitudes, the proposed method is more effective than the existing RA‐ZIP and PR‐ZIP control charts. In addition, the proposed method is applied to real data from a Hong Kong hospital for online influenza surveillance to demonstrate its practicability.

Designing multicenter individually randomized group treatment trials.

In an individually randomized group treatment (IRGT) trial, participant outcomes can be positively correlated due to, for example, shared therapists in treatment delivery. Oftentimes, because of limited treatment resources or participants at one location, an IRGT trial can be carried out across multiple centers. This design can be subject to potential correlations in the participant outcomes between arms within the same center. While the design of a single-center IRGT trial has been studied, little is known about the planning of a multicenter IRGT trial. To address this gap, this paper provides analytical sample size formulas for designing multicenter IRGT trials with a continuous endpoint under the linear mixed model framework. We found that accounting for the additional center-level correlation at the design stage can lead to sample size reduction, and the magnitude of reduction depends on the amount of between-therapist correlation. However, if the variance components of therapist-level random effects are considered as input parameters in the design stage, accounting for the additional center-level variance component has no impact on the sample size estimation. We presented our findings through numeric illustrations and performed simulation studies to validate our sample size procedures under different scenarios. Optimal design configurations under the multicenter IRGT trials have also been discussed, and two real-world trial examples are drawn to illustrate the use of ourmethod.

RESTRICTED SELECTION INDEX FOR GROWTH TRAITS OF SHAMI KIDS

A Restricted Selection Index was constructed to genetically evaluate animals using a dataset composed of body weights of Shami kids at the ages of birth, weaning, and 6-month. The variance-covariance matrix (VCV) was generated and used to estimate genetic parameters for the index construction after adjusting the fixed effects; year, birth month, kid sex, type (single, twin or triplet) of birth, doe age, weights at kidding (KW), birth (BWT) and weaning (WWT) as covariates. General Linear Model and Restricted Maximum Likelihood methods were used to estimate BLUE for fixed effects and variance components for random effects, respectively. BW was 3.6 ± 0.017, WW 16.8 ± 0.10, and weight at 6 months (MWT) was 26.7 ± 0.21 Kg. With the exception of buck origin and doe age, all tested factors significantly affected growth traits. Heritability for BWT, WWT, and MWT was 0.70 ± 0.10, 0.32 ± 0.075, and 0.41 ± 0.12, and repeatability was 0.78, 0.35, and 0.47, respectively. Genetic and phenotypic correlations were positive and significant between BWT and WWT, and between WWT and MWT. The restricted selection index constructed for increasing weights at MWT and WWT with restriction on BWT yielded a strong correlation coefficient (rIA) between the genetic merit and the index at 0.54 (p<0.01).

The effect of missing levels of nesting in multilevel analysis.

Multilevel analysis is an appropriate and powerful tool for analyzing hierarchical structure data widely applied from public health to genomic data. In practice, however, we may lose the information on multiple nesting levels in the multilevel analysis since data may fail to capture all levels of hierarchy, or the top or intermediate levels of hierarchy are ignored in the analysis. In this study, we consider a multilevel linear mixed effect model (LMM) with single imputation that can involve all data hierarchy levels in the presence of missing top or intermediate-level clusters. We evaluate and compare the performance of a multilevel LMM with single imputation with other models ignoring the data hierarchy or missing intermediate-level clusters. To this end, we applied a multilevel LMM with single imputation and other models to hierarchically structured cohort data with some intermediate levels missing and to simulated data with various cluster sizes and missing rates of intermediate-level clusters. A thorough simulation study demonstrated that an LMM with single imputation estimates fixed coefficients and variance components of a multilevel model more accurately than other models ignoring data hierarchy or missing clusters in terms of mean squared error and coverage probability. In particular, when models ignoring data hierarchy or missing clusters were applied, the variance components of random effects were overestimated. We observed similar results from the analysis of hierarchically structured cohort data.

A phase II EWMA chart for the balanced one‐way random effects model

AbstractStatistical process control (SPC) techniques are used in applications where more than one sources of variation are present, for example, in a one‐way random effects (variance components) model. The Shewhart control charts for this situation have been studied by several researchers. However, exponentially weighted moving average (EWMA) charts are generally recommended in Phase II, as they are more sensitive to detecting smaller process mean shifts. We consider EWMA charts for the one‐way random effects model in the balanced case, properly accounting for the effects of parameter estimation while designing and implementing the control charts. In the sequel we derive and calculate the corrected (adjusted) control limits for Phase II applications. Following the recent literature, the limits are formulated under two perspectives, the unconditional and the conditional. Tabulations of the charting constants are provided under both perspectives along with an illustration with some actual data. A simulation study examining in‐control (IC) robustness performance is conducted under both perspectives. Finally, some conclusions are given. An R package is provided to support deployment of the proposed control chart in practice.

Adjusted maximum likelihood method for multivariate Fay–Herriot model

For the Fay–Herriot model, the empirical best linear unbiased predictor (EBLUP) is the weighted sum of direct estimate and regression-synthetic estimate, where the weight depends on the estimate of variance component of random area effects. However, in some cases, the weight of direct survey estimator is zero and the EBLUP reduces to regression-synthetic estimator. This leads to unfavourable estimates. Therefore, Lahiri and Li (2009) introduced the concept of adjusted maximum likelihood method for linear mixed models. The method was then generalized in Li and Lahiri (2010) and Yoshimori and Lahiri (2014) to develop adjusted maximum likelihood consistent variance estimators with positive variance estimates. These adjustments prevent zero weight of direct estimate. In this paper, we extend their methods to propose adjusted maximum likelihood estimates for multivariate Fay–Herriot models. Moreover, we derive their asymptotic properties and perform numerical results to investigate performances of the proposed estimates.

Phase II process monitoring for the balanced one‐way random effects model

AbstractStatistical process control (SPC) and monitoring techniques are useful in a variety of applications. In this paper, we consider prospective (Phase II) process monitoring for the balanced random effects (variance components) model with Shewhart‐type charts when parameters are estimated from a Phase I study. Such a model is a nonstandard application of control charts and arises in a number of situations in practice. Effects of parameter estimation need to be accounted for or there maybe too many false alarms that will disrupt the monitoring regime. To this end, two types of corrected (adjusted) control limits are proposed, based on two perspectives, namely the unconditional and the conditional, as recommended in the recent literature. Results and derivations are provided along with tabulations and illustrations with real data. Robustness of the charts is examined and a summary and recommendations are given. An accompanying R package is provided for deploying the methodology. Other Phase II charts such as the EWMA and the CUSUM can be considered along similar lines and will be presented elsewhere.

GENETIC AND NON GENETIC PARAMETERS FOR BODY WEIGHTS OF TWO IRAQI LOCAL CHICKNS

This study aimed to investigate the genetic parameters for body weights of White and Black local chickens. The experiment conducted at College of Agric., Salahaddien Univ. during the period from Sept. 2016 until April 2018. 520 fertile eggs were taken from Agri. Res. Center, Ministry of Agric., Baghdad. Hatched chicks considered as parents (G0), and distributed randomly in to ten families. Resulted eggs from each family were collected during the peak of production for each generation to produce chicks of the next generation (G1 and G2). Body weights of resulted chicks were recorded at 1-day old and weekly till maturity. SAS program used to analyze the body weights (BW) and body weight gains (BWG) at different ages. The model includes genetic groups and generations for traits before sexing and the effect of sex added for the traits after sexing. Variance component of random effects estimated by REML and tested for positive definiteness to develop reliable estimates. Repeatability for body weights estimated. BW of chicks at 1 day, 4, 8, 9, 10, 16 and 17 week were 31.02, 292.47, 679.29, 794.58, 892.82, 1362.53 and 1252.17 g, and BWG at (1-4, 4-8, 9-10 and10-16) weeks were 261.45, 386.82, 98.24, and 469.51 g, respectively. The chicks of black group significantly excelled the white group in their weight at 1 day, 4, 8, 16 and 17, as well at ages 1-4 and 10-16 weeks. The effect of generation on BW of chicks at all ages and BWG at 1-4, 4-8 weeks was highly significant and (P<0.05) during 9-10 and 10-16 weeks. Males surpassed females significantly (p<0.01) in their BW at 9, 10 and 16 weeks and in their BWG during 9-10 and 10-16 weeks. Estimates of heritability were 0.42, 0.61, 0.76, 0.71, 0.43, 0.51, and 0.70 and of repeatability were 0.29, 0.26, 0.22, 0.38, 0.41, 0.74, and 0.78 for BW at 1 day, 4, 8, 9, 10, 16 and 17 weeks respectively. Higher (0.78) and lower (0.14) genetic correlations were recorded between BW at 8 weeks with each of BW at 10 and 17 weeks respectively. While the phenotypic correlations ranged between 0.04 (among BW at 1 day with weight at 9 weeks) and 0.58 (among BW 16 with 17 weeks).

EFFECT OF FIXED FACTORS AND ESTIMATION OF GENETIC PARAMETERS OF GROWTH TRAITS FOR MOUNTAIN KIDS

Body weights at birth (469), weaning (394) and at six month of age (358) for kids utilized in this study were raised at private project in Duhok governorate, Iraq during two kidding season (2016-2017) and (2017-2018). GLM within SAS programme was used to analyze the data which include the fixed effects (age of doe, year and season of kidding, sex of kid and type of birth, regression on doe weight at kidding, and the regression of later weights of kids on earlier weights) influencing the studied traits. Restricted Maximum Likelihood Method was used to estimate repeatability, heritability, genetic and phenotypic correlations after adjusting the records for fixed effects. Variance components of random effects were tested for positive definite. Overall mean of weights at birth (BWT), weaning (WWT) and 6 month of age (WT6M) were 2.92, 15.32 and 24.45 kg, respectively. Differences among groups of age of doe in all studied traits were not significant, while year of kidding and sex of kid affect all traits significantly (p<0.01). Season of kidding affect BWT and WWT significantly (P<0.01). Single born kids were heavier (P<0.01) than twins in BWT only. Regression of BWT on doe weight at kidding (0.033 kg/kg) was significant (P<0.01), while the regressions of WWT and WT6M were not significant. The regression coefficients of WWT on BWT (1.906 kg/kg) and of WT6M on WWT (0.835 kg/kg) were highly significant (P<0.01). Repeatability estimates for BWT, WWT and WT6M were 0.47, 0.45 and 0.35, respectively; on the same order the estimates of heritability were 0.41, 0.61 and 0.79. Genetic correlations between BWT with each of WWT (0.45) and WT6M (0.55), and between WWT and WT6M (0.68) were highly significant. All phenotypic correlations between each pair of body weights were higher than genetic correlations and ranged between 0.48 and 0.73.

The effect of number of clusters and cluster size on statistical power and Type I error rates when testing random effects variance components in multilevel linear and logistic regression models

When using multilevel regression models that incorporate cluster-specific random effects, the Wald and the likelihood ratio (LR) tests are used for testing the null hypothesis that the variance of the random effects distribution is equal to zero. We conducted a series of Monte Carlo simulations to examine the effect of the number of clusters and the number of subjects per cluster on the statistical power to detect a non-null random effects variance and to compare the empirical type I error rates of the Wald and LR tests. Statistical power increased with increasing number of clusters and number of subjects per cluster. Statistical power was greater for the LR test than for the Wald test. These results applied to both the linear and logistic regressions, but were more pronounced for the latter. The use of the LR test is preferable to the use of the Wald test.

Variance components for direct and maternal effects on body weights of Katahdin lambs.

The aim of this study was to estimate genetic parameters for BW in Katahdin lambs. Six animal models were used to study direct and maternal effects on birth weight (BWT), weaning weight (WWT), and postweaning weight (PWWT) using 41,066 BWT, 33,980 WWT, and 22,793 PWWT records collected over 17 yr in 100 flocks. Models included fixed effects of management group, dam age, type of birth (for BWT) or birth and rearing (for WWT and PWWT), and lamb age at weighing (fitted as a covariate for WWT and PWWT; all < 0.05). Variance components for random effects were estimated in sequentially more complex models and tested for significance with likelihood-ratio tests. A model that fitted only an additive animal effect overestimated additive variance for all BW, resulting in larger estimates of direct heritability than models that included maternal effects. Maternal effects explained variation ( < 0.05) in all BW. Heritability estimates for optimal models were 0.15 ± 0.01 for BWT, 0.18 ± 0.02 for WWT, and 0.20 ± 0.02 for PWWT. Estimates of maternal heritabilities were 0.14 for BWT, 0.10 for WWT, and 0.06 for PWWT, with SE = 0.01. Permanent environmental maternal effects explained 4 to 6% (±1%) of total phenotypic variances for these BW. Litter effects included temporary environmental effects common to littermates and a proportion of the dominance genetic variance and accounted for 16 to 19% (±1%) of phenotypic variance. Correlations between additive direct and maternal genetic effects were -0.14 for BWT, -0.23 for WWT, and -0.04 for PWWT but differed from 0 ( < 0.05) only for WWT. The total heritability predicted the total response in direct and maternal genetic effects from mass selection and was 0.23 for BWT, 0.20 for WWT, and 0.23 for PWWT. Direct and maternal additive, maternal permanent environmental, residual, and phenotypic correlations between BWT and WWT were 0.53 ± 0.05, 0.58 ± 0.06, 0.51 ± 0.06, 0.39 ± 0.01, and 0.44 ± 0.01, respectively; those between BWT and PWWT were 0.45 ± 0.06, 0.58 ± 0.08, 0.36 ± 0.08, 0.33 ± 0.01, and 0.37 ± 0.01 respectively; and those between WWT and PWWT were 0.85, 0.99, 0.92, 0.77, and 0.81, respectively, with SE ≤ 0.02. Therefore, both direct and maternal effects had an important impact on BW in Katahdin lambs. Models that included both additive and permanent environmental maternal effects as well as a temporary environmental litter effect should result in more accurate estimates of breeding values and better selection decisions.

Flexible results for quadratic forms with applications to variance components estimation

We derive convenient uniform concentration bounds and finite sample multivariate normal approximation results for quadratic forms, then describe some applications involving variance components estimation in linear random-effects models. Random-effects models and variance components estimation are classical topics in statistics, with a corresponding well-established asymptotic theory. However, our finite sample results for quadratic forms provide additional flexibility for easily analyzing random-effects models in nonstandard settings, which are becoming more important in modern applications (e.g., genomics). For instance, in addition to deriving novel non-asymptotic bounds for variance components estimators in classical linear random-effects models, we provide a concentration bound for variance components estimators in linear models with correlated random-effects and discuss an application involving sparse random-effects models. Our general concentration bound is a uniform version of the Hanson–Wright inequality. The main normal approximation result in the paper is derived using Reinert and Röllin [Ann. Probab. (2009) 37 2150–2173] embedding technique for Stein’s method of exchangeable pairs.

Local influence diagnostics for hierarchical count data models with overdispersion and excess zeros.

We consider models for hierarchical count data, subject to overdispersion and/or excess zeros. Molenberghs etal. () and Molenberghs etal. () extend the Poisson-normal generalized linear-mixed model by including gamma random effects to accommodate overdispersion. Excess zeros are handled using either a zero-inflation or a hurdle component. These models were studied by Kassahun etal. (). While flexible, they are quite elaborate in parametric specification and therefore model assessment is imperative. We derive local influence measures to detect and examine influential subjects, that is subjects who have undue influence on either the fit of the model as a whole, or on specific important sub-vectors of the parameter vector. The latter include the fixed effects for the Poisson and for the excess-zeros components, the variance components for the normal random effects, and the parameters describing gamma random effects, included to accommodate overdispersion. Interpretable influence components are derived. The method is applied to data from a longitudinal clinical trial involving patients with epileptic seizures. Even though the data were extensively analyzed in earlier work, the insight gained from the proposed diagnostics, statistically and clinically, is considerable. Possibly, a small but important subgroup of patients has been identified.

Inter- and intraobserver variability of (semi-)quantitative parameters commonly used in feline thyroid scintigraphy

The aim of this study was to assess inter- and intraobserver variability of commonly used semi-quantitative and quantitative parameters in feline thyroid scintigraphy: thyroid to salivary gland ratio (T/S), thyroid to background ratio (T/B) and the percentage technetium pertechnetate uptake for the thyroid glands (%TcUT). These parameters are being used to diagnose thyroid disease and to assess its severity, but may be influenced by operator related factors when processing the images. Additionally, inter- and intraobserver variability of the percentage technetium pertechnetate uptake for the salivary glands was determined (%TcUSG). The study included technetium pertechnetate scans of 100 hyperthyroid cats. Variability within and between three observers was determined using a random effects model and variance components were estimated by the restricted maximum likelihood procedure. The %TcU for the thyroid and salivary glands, as well as the T/S ratio, showed little to no difference in inter- and intraobserver variability, whereas this was clearly present for the T/B ratio. Overall, the T/S ratio and %TcUSG showed a good repeatability and reproducibility with low inter- and intraobserver variabilities. Inter- and intraobserver variability was higher for the %TcUT, however variations were still considered to be acceptable. On the contrary, inter- and intraobserver variability was clearly larger for the T/B ratio. These findings suggest the preferential use of the T/S ratio or %TcU, especially in facilities with a less experienced staff.

SCP-relevance and class-effect in performance – A comparative analysis of restaurants and petroleum firms

The importance of industry-specific factors for a firm's performance has often attracted the attention of researchers, managers, and investment analysts. This research uses random-effect variance component analysis to examine the relevance of structure-conduct-performance (SCP) paradigm in the context of restaurant and petroleum/natural gas firms. The study further investigates class-effect in firm performance by analyzing whether the relative importance of industry-and-firm-level effects varies across different performance groups. Results suggest a direct relevance of the SCP paradigm and industry-specific factors for firm performance, and a distinct dominance of industry-effect over firm-effect regardless of the choice of accounting or value based performance measures. Results further reveal varying roles of industry and firm-level factors (corporate or strategic) across middle-of-the road and non-average (exceptional) performance groups. As such the importance of SCP paradigm and the strategic role of both industry-and-firm effect factors for value creation in US based restaurant firms is better understood.

Permutation-based variance component test in generalized linear mixed model with application to multilocus genetic association study.

BackgroundIn many medical studies the likelihood ratio test (LRT) has been widely applied to examine whether the random effects variance component is zero within the mixed effects models framework; whereas little work about likelihood-ratio based variance component test has been done in the generalized linear mixed models (GLMM), where the response is discrete and the log-likelihood cannot be computed exactly. Before applying the LRT for variance component in GLMM, several difficulties need to be overcome, including the computation of the log-likelihood, the parameter estimation and the derivation of the null distribution for the LRT statistic.MethodsTo overcome these problems, in this paper we make use of the penalized quasi-likelihood algorithm and calculate the LRT statistic based on the resulting working response and the quasi-likelihood. The permutation procedure is used to obtain the null distribution of the LRT statistic. We evaluate the permutation-based LRT via simulations and compare it with the score-based variance component test and the tests based on the mixture of chi-square distributions. Finally we apply the permutation-based LRT to multilocus association analysis in the case–control study, where the problem can be investigated under the framework of logistic mixed effects model.ResultsThe simulations show that the permutation-based LRT can effectively control the type I error rate, while the score test is sometimes slightly conservative and the tests based on mixtures cannot maintain the type I error rate. Our studies also show that the permutation-based LRT has higher power than these existing tests and still maintains a reasonably high power even when the random effects do not follow a normal distribution. The application to GAW17 data also demonstrates that the proposed LRT has a higher probability to identify the association signals than the score test and the tests based on mixtures.ConclusionsIn the present paper the permutation-based LRT was developed for variance component in GLMM. The LRT outperforms existing tests and has a reasonably higher power under various scenarios; additionally, it is conceptually simple and easy to implement.

A Parametric Bootstrap Test for Two-Way ANOVA Model Without Interaction Under Heteroscedasticity

In this article we consider the two-way ANOVA model without interaction under heteroscedasticity. For the problem of testing equal effects of factors, we propose a parametric bootstrap (PB) approach and compare it with existing the generalized F (GF) test. The Type I error rates and powers of the tests are evaluated using Monte Carlo simulation. Our studies show that the PB test performs better than the GF test. The PB test performs very satisfactorily even for small samples while the GF test exhibits poor Type I error properties when the number of factorial combinations or treatments goes up. It is also noted that the same tests can be used to test the significance of random effect variance component in a two-way mixed-effects model under unequal error variances.

Functional-mixed effects models for candidate genetic mapping in imaging genetic studies.

The aim of this paper is to develop a functional-mixed effects modeling (FMEM) framework for the joint analysis of high-dimensional imaging data in a large number of locations (called voxels) of a three-dimensional volume with a set of genetic markers and clinical covariates. Our FMEM is extremely useful for efficiently carrying out the candidate gene approaches in imaging genetic studies. FMEM consists of two novel components including a mixed effects model for modeling nonlinear genetic effects on imaging phenotypes by introducing the genetic random effects at each voxel and a jumping surface model for modeling the variance components of the genetic random effects and fixed effects as piecewise smooth functions of the voxels. Moreover, FMEM naturally accommodates the correlation structure of the genetic markers at each voxel, while the jumping surface model explicitly incorporates the intrinsically spatial smoothness of the imaging data. We propose a novel two-stage adaptive smoothing procedure to spatially estimate the piecewise smooth functions, particularly the irregular functional genetic variance components, while preserving their edges among different piecewise-smooth regions. We develop weighted likelihood ratio tests and derive their exact approximations to test the effect of the genetic markers across voxels. Simulation studies show that FMEM significantly outperforms voxel-wise approaches in terms of higher sensitivity and specificity to identify regions of interest for carrying out candidate genetic mapping in imaging genetic studies. Finally, FMEM is used to identify brain regions affected by three candidate genes including CR1, CD2AP, and PICALM, thereby hoping to shed light on the pathological interactions between these candidate genes and brain structure and function.

Simultaneous variable selection for joint models of longitudinal and survival outcomes.

Joint models of longitudinal and survival outcomes have been used with increasing frequency in clinical investigations. Correct specification of fixed and random effects is essential for practical data analysis. Simultaneous selection of variables in both longitudinal and survival components functions as a necessary safeguard against model misspecification. However, variable selection in such models has not been studied. No existing computational tools, to the best of our knowledge, have been made available to practitioners. In this article, we describe a penalized likelihood method with adaptive least absolute shrinkage and selection operator (ALASSO) penalty functions for simultaneous selection of fixed and random effects in joint models. To perform selection in variance components of random effects, we reparameterize the variance components using a Cholesky decomposition; in doing so, a penalty function of group shrinkage is introduced. To reduce the estimation bias resulted from penalization, we propose a two-stage selection procedure in which the magnitude of the bias is ameliorated in the second stage. The penalized likelihood is approximated by Gaussian quadrature and optimized by an EM algorithm. Simulation study showed excellent selection results in the first stage and small estimation biases in the second stage. To illustrate, we analyzed a longitudinally observed clinical marker and patient survival in a cohort of patients with heart failure.

Parametric Bootstrap Tests for Unbalanced Three-factor Nested Designs under Heteroscedasticity

In this article, we consider the three-factor unbalanced nested design model without the assumption of equal error variance. For the problem of testing “main effects” of the three factors, we propose a parametric bootstrap (PB) approach and compare it with the existing generalized F (GF) test. The Type I error rates of the tests are evaluated using Monte Carlo simulation. Our studies show that the PB test performs better than the generalized F-test. The PB test performs very satisfactorily even for small samples while the GF test exhibits poor Type I error properties when the number of factorial combinations or treatments goes up. It is also noted that the same tests can be used to test the significance of the random effect variance component in a three-factor mixed effects nested model under unequal error variances.