Variance Components For 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.

Diallel crosses in Picea abies III. Variation and inheritance patterns in nursery trials

Abstract The complete diallel cross is the only mating design that provides estimates of variance components of general combining (GCA), specific combining ability (SCA), maternal and reciprocal effects, in addition to heritabilities and genetic correlations. To obtain such estimates, complete diallels were made among 10 trees in each of three natural Norway spruce populations from altitude 300 and 500 m in Norway. Nursery trials were performed with the families from these crosses and families from seeds collected from open pollination. Traits measured and analysed are seed weight, germination rate, germination percentage, terminal bud set, and seedling heights the first and second years. The seedlings from the population at origin 500 m had lower seed weight, lower heights and earlier bud set than those from the two populations from lower altitude. A considerable variation was present among families within each diallel, and the GCA variance components had the highest values and were significant for most traits. Variance components for SCA and maternal effects were also significant for some traits, but with inconsistent values in the three diallels. A strong relationship was present between the weight of the seed lots from the maternal parent and mean family height after one and two growing seasons. The highest estimate of heritability was observed for bud set, with similar values in all three diallels.

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.

An IBD-based mixed model approach for QTL mapping in multiparental populations

Key messageThe identity-by-descent (IBD)-based mixed model approach introduced in this study can detect quantitative trait loci (QTLs) referring to the parental origin and simultaneously account for multilevel relatedness of individuals within and across families. This unified approach is proved to be a powerful approach for all kinds of multiparental population (MPP) designs.Multiparental populations (MPPs) have become popular for quantitative trait loci (QTL) detection. Tools for QTL mapping in MPPs are mostly developed for specific MPPs and do not generalize well to other MPPs. We present an IBD-based mixed model approach for QTL mapping in all kinds of MPP designs, e.g., diallel, Nested Association Mapping (NAM), and Multiparental Advanced Generation Intercross (MAGIC) designs. The first step is to compute identity-by-descent (IBD) probabilities using a general Hidden Markov model framework, called reconstructing ancestry blocks bit by bit (RABBIT). Next, functions of IBD information are used as design matrices, or genetic predictors, in a mixed model approach to estimate variance components for multiallelic genetic effects associated with parents. Family-specific residual genetic effects are added, and a polygenic effect is structured by kinship relations between individuals. Case studies of simulated diallel, NAM, and MAGIC designs proved that the advanced IBD-based multi-QTL mixed model approach incorporating both kinship relations and family-specific residual variances (IBD.MQMkin_F) is robust across a variety of MPP designs and allele segregation patterns in comparison to a widely used benchmark association mapping method, and in most cases, outperformed or behaved at least as well as other tools developed for specific MPP designs in terms of mapping power and resolution. Successful analyses of real data cases confirmed the wide applicability of our IBD-based mixed model methodology.

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.

General Gaussian estimation

This article proposes a general Gaussian estimation approach for situations where the implementation of maximum likelihood estimation is difficult. The primary task is to construct a Gaussian estimation function by putting exact expressions of the mean vector and the variance–covariance matrix of the response vector into the log-likelihood function of the multivariate normal distribution. A Gaussian estimator is derived by maximizing the Gaussian estimation function. This construction can induce an optimality condition that the true parameter vector is the unique maximizer of the expected value of the Gaussian estimation function. The optimality condition is equally important to that given by the Kullback–Leibler information number in the maximum likelihood approach. It is a major condition in the derivation of nice theoretical properties such as consistency and asymptotic normality. The general Gaussian estimation approach can significantly reduce the computational burden when the log-likelihood function of a statistical model contains intractable high-dimensional integrals. By applying it to the Poisson-lognormal model, a special case of generalized linear mixed effect models, a closed-form (i.e., without intractable integrals) estimation approach for fixed effect parameters and variance components is derived. The simulation study shows that the resulting estimator is precise, reliable, and computationally efficient.

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.

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

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

Multilevel Modeling of Binary Outcomes with Three-Level Complex Health Survey Data

Complex survey designs often involve unequal selection probabilities of clus-ters or units within clusters. When estimating models for complex survey data, scaled weights are incorporated into the likelihood, producing a pseudo likeli-hood. In a 3-level weighted analysis for a binary outcome, we implemented two methods for scaling the sampling weights in the National Health Survey of Pa-kistan (NHSP). For NHSP with health care utilization as a binary outcome we found age, gender, household (HH) goods, urban/rural status, community de-velopment index, province and marital status as significant predictors of health care utilization (p-value < 0.05). The variance of the random intercepts using scaling method 1 is estimated as 0.0961 (standard error 0.0339) for PSU level, and 0.2726 (standard error 0.0995) for household level respectively. Both esti-mates are significantly different from zero (p-value < 0.05) and indicate consid-erable heterogeneity in health care utilization with respect to households and PSUs. The results of the NHSP data analysis showed that all three analyses, weighted (two scaling methods) and un-weighted, converged to almost identical results with few exceptions. This may have occurred because of the large num-ber of 3rd and 2nd level clusters and relatively small ICC. We performed a sim-ulation study to assess the effect of varying prevalence and intra-class correla-tion coefficients (ICCs) on bias of fixed effect parameters and variance components of a multilevel pseudo maximum likelihood (weighted) analysis. The simulation results showed that the performance of the scaled weighted estimators is satisfactory for both scaling methods. Incorporating simulation into the analysis of complex multilevel surveys allows the integrity of the results to be tested and is recommended as good practice.

Genotypic and environmental variability of yield from seven different crops in Croatian official variety trials and comparison with on-farm trends

SUMMARYAssessment of the value for cultivation and use (VCU) of a new cultivar, essential for its official registration, is done through a series of trials carried out over a 2–3-year period and across many locations. In a set of multi-environment VCU trials, evaluation of new genotypes can be a laborious task due to the presence of genotype by environment interactions, which can hide their true genetic value. In an attempt to reveal the true genetic value of new cultivars, a good starting point is investigation of the importance of various genetic and environmental sources of variation, which can be done by estimating relative magnitude of corresponding variance components within the mixed model framework.Genotype × location × year (G × L × Y) data set for seven crops taken from the 10-year period 2001–10 was used in the present study to estimate the variance components for main effects and their interactions in Croatian VCU trials. Depending on the crop, the most important and least important components were Y or LY, and L or GL, respectively. Genotypic effect was relatively small, ranging from 2·1 to 13·4% of the total variation. The current results are comparable with the relative sizes of the variance components obtained in studies from four- to sixfold larger countries, indicating that the environments within Croatia, if sufficiently widely sampled, can provide as extreme cultivar responses as a geographically more dispersed set of VCU trials. The gap range in different crops is much wider (30–60%) than in Western Europe (up to 30%), but it remained constant over the 10-year period.

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.

Approximate uniform shrinkage prior for a multivariate generalized linear mixed model

Multivariate generalized linear mixed models (MGLMM) are used for jointly modeling the clustered mixed outcomes obtained when there are two or more responses repeatedly measured on each individual in scientific studies. Bayesian methods are widely used techniques for analyzing MGLMM. The need for noninformative priors arises when there is insufficient prior information on the model parameters. The main aim of the present study is to propose an approximate uniform shrinkage prior for the random effect variance components in the Bayesian analysis for the MGLMM. This prior is an extension of the approximate uniform shrinkage prior proposed by Natarajan and Kass (2000). This prior is easy to apply and is shown to possess several nice properties. The use of the approximate uniform shrinkage prior is illustrated in terms of both a simulation study and osteoarthritis data.

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.

Joint prior distributions for variance parameters in Bayesian analysis of normal hierarchical models

In random effect models, error variance (stage 1 variance) and scalar random effect variance components (stage 2 variances) are a priori modeled independently. Considering the intrinsic link between the stages 1 and 2 variance components and their interactive effect on the parameter draws in Gibbs sampling, we propose modeling the variances of the two stages a priori jointly in a multivariate fashion. We use random effects linear growth model for illustration and consider multivariate distributions to model the variance components jointly including the recently developed generalized multivariate log gamma (G-MVLG) distribution. We discuss these variance priors as well as the independent variance priors exercised in the literature in different aspects including noninformativeness and propriety of the associated posterior density. We show through an extensive simulation experiment that modeling the variance components of different stages multivariately results in better estimation properties for the response and random effect model parameters compared to independent modeling. We scrutinize the sensitivity of response model coefficient estimates to the parameters of considered noninformative variance priors and find that their full conditional expectations are insensitive to noninformative G-MVLG prior parameters. We apply independent and joint models for analysis of a real dataset and find that multivariate priors for variance components lead to better fitted hierarchical model than the univariate variance priors.

Outlier robust nonlinear mixed model estimation.

In standard analyses of data well-modeled by a nonlinear mixed model, an aberrant observation, either within a cluster, or an entire cluster itself, can greatly distort parameter estimates and subsequent standard errors. Consequently, inferences about the parameters are misleading. This paper proposes an outlier robust method based on linearization to estimate fixed effects parameters and variance components in the nonlinear mixed model. An example is given using the four-parameter logistic model and bioassay data, comparing the robust parameter estimates with the nonrobust estimates given by SAS(®).

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.

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.

Testing for random effect in the Fuller–Battese model

We consider the Fuller–Battese model where random effects are allowed to be from non-normal universes. The asymptotic distribution of the F-statistic in this model is derived as the number of groups tends to infinity (is large) and sample size from any group is either fixed or large. The result is used to establish an approximate test for the significance of the random effect variance component. Robustness of the established approximate test is given.

Permutation tests for centre effect on survival endpoints with application in an acute myeloid leukaemia multicentre study

When analysing multicentre data, it may be of interest to test whether the distribution of the endpoint varies among centres. In a mixed-effect model, testing for such a centre effect consists in testing to zero a random centre effect variance component. It has been shown that the usual asymptotic χ(2) distribution of the likelihood ratio and score statistics under the null does not necessarily hold. In the case of censored data, mixed-effects Cox models have been used to account for random effects, but few works have concentrated on testing to zero the variance component of the random effects. We propose a permutation test, using random permutation of the cluster indices, to test for a centre effect in multilevel censored data. Results from a simulation study indicate that the permutation tests have correct type I error rates, contrary to standard likelihood ratio tests, and are more powerful. The proposed tests are illustrated using data of a multicentre clinical trial of induction therapy in acute myeloid leukaemia patients.