Variance Random Effects Research Articles

The human sex ratio at birth and late fetal mortality: the Italian case

ABSTRACT This study explores the short-term relationships between sex ratio at birth and late fetal mortality in Italy from 1910 to 2016. As the leading scholars’ attention traditionally focused on long-term trends and variations in the sex ratios at birth among different populations, less interest regarded short-term fluctuations as they were mainly seen as an effect of random variability. We detrended the national series of males proportion among live births and stillbirths by their medium-term component to consider the annual deviations from a normal trend. After controlling for fertility tendencies and wars effects, regression models seem to show the effects of stillbirth on the proportion of male newborns. A sensitivity analysis was also carried out to assess the effects of the perinatal deaths on the proportion of males at birth, combining stillbirths and early neonatal losses to control the possible misspecification between stillborn infants and early neonatal deaths. The significance of late fetal mortality reflects the mortality excess among male fetuses during the intrauterine life, showing evidence for the in utero hypothesis selection.

Antithyroid drug use during pregnancy and the risk of birth defects in offspring: systematic review and meta-analysis of observational studies with methodological considerations.

Maternal antithyroid drug (ATD) use during pregnancy has been associated with an increased risk of birth defects in offspring. Uncertainty remains on the size of this risk and how it compares to untreated hyperthyroidism due to methodological limitations of previous studies. Systematic review of MEDLINE and EMBASE identifying observational studies examining ATD use during pregnancy and risk of birth defects by 28 August 2020. Data were extracted on study characteristics, effect estimates and comparator groups. Adjusted effect estimates were pooled using a random-effects generic inverse variance method and absolute risk calculated. Seven cohort studies and 1 case-control study involving 6 212 322 pregnancies and 388 976 birth defects were identified reporting regression effect estimates. Compared to an unexposed population comparison, the association between ATD use during pregnancy and birth defects in offspring was: adjusted risk ratio (aRR) 1.16 95% confidence interval (CI) 1.08-1.25 for propylthiouracil (PTU); aRR 1.28 95%CI 1.06-1.54 for methimazole/carbimazole (MMI/CMZ); aRR 1.51, 95%CI 1.16-1.97 for both MMI/CMZ and PTU; and aRR 1.15 95%CI 1.02-1.29 for untreated hyperthyroidism. The excess risk of any and major birth defects per 1000, respectively, was: 10.2 and 1.3 for PTU; 17.8 and 2.3 for MMI/CMZ; 32.5 and 4.1 for both MMI/CMZ and PTU; and 9.6 and 1.2 for untreated hyperthyroidism. When appropriately analysed the risk of birth defects associated with ATD use in pregnancy is attenuated. Although still elevated, the risk of birth defects is smallest with PTU compared to MMI/CMZ and may be similar to that of untreated hyperthyroidism.

Basin effects and limitations of 1D site response analysis from 2D numerical models of the Thorndon basin

Plane strain (2D) finite element models are used to examine factors contributing to basin effects observed for multiple seismic events at sites in the Thorndon basin of Wellington, New Zealand. The models consider linear elastic soil and rock response when subjected to vertically-propagating shear waves. Depth-dependent shear wave velocities are considered in the soil layers, and the effects of random variations of soil velocity within layers are modelled. Various rock shear wave velocity configurations are considered to evaluate their effect on the modelled surficial response. It is shown that these simple 2D models are able to capture basin reverberations and compare more favourably to observations from strong motion recordings than conventional 1D site response models. It is also shown that consideration of a horizontal impedance contrast across the Wellington Fault affects spectral response and amplification at longer periods, suggesting the importance of this feature in future ground motion modelling studies in the Wellington region.

Effects of electromyographic biofeedback interventions for shoulder pain and function: Systematic review and meta-analysis

Objective: To systematically review the effectiveness of electromyographic biofeedback interventions to improve pain and function of patients with shoulder pain. Design: Systematic review of controlled clinical trials. Literature search: Databases (Medline, EMBASE, CINAHL, PEDro, CENTRAL, Web of Science, and SCOPUS) were searched in December 2020. Study selection criteria: Randomized clinical trials that investigated the effects of electromyographic biofeedback for individuals with shoulder pain. Patient-reported pain and functional outcomes were collected and synthesized. Data synthesis: The level of evidence was synthesized using GRADE and Standardized Mean Differences and 95% confidence interval were calculated using a random-effects inverse variance model for meta-analysis. Results: Five studies were included with a total sample of 272 individuals with shoulder pain. Very-low quality of evidence indicated that electromyographic biofeedback was not superior to control for reducing shoulder pain (standardized mean differences = −0.21, 95% confidence interval: −0.67 to 0.24, P = 0.36). Very-low quality of evidence indicated that electromyographic biofeedback interventions were not superior to control for improving shoulder function (standardized mean differences = −0.11, 95% confidence interval: −0.41 to 0.19, P = 0.48). Conclusion: Electromyographic biofeedback may be not effective for improving shoulder pain and function. However, the limited number of included studies and very low quality of evidence does not support a definitive recommendation about the effectiveness of electromyographic biofeedback to treat individuals with shoulder pain.

Gradient boosting for linear mixed models.

Gradient boosting from the field of statistical learning is widely known as a powerful framework for estimation and selection of predictor effects in various regression models by adapting concepts from classification theory. Current boosting approaches also offer methods accounting for random effects and thus enable prediction of mixed models for longitudinal and clustered data. However, these approaches include several flaws resulting in unbalanced effect selection with falsely induced shrinkage and a low convergence rate on the one hand and biased estimates of the random effects on the other hand. We therefore propose a new boosting algorithm which explicitly accounts for the random structure by excluding it from the selection procedure, properly correcting the random effects estimates and in addition providing likelihood-based estimation of the random effects variance structure. The new algorithm offers an organic and unbiased fitting approach, which is shown via simulations and data examples.

Bayesian Multilevel Analysis of Postnatal Care Utilization in Ethiopia

The postnatal period is defined as the first six weeks after birth; it is critical to the health and survival. The study was conducted to determine the key factors of maternal postnatal care using Bayesian multilevel analysis using 7,192 mothers aged between 15-49 of EDHS 2016 data. Descriptive statistics revealed that 675 (9.4%) women received postnatal care. The Bayesian multilevel model used to analyze postnatal care utilization of woman. The predictor variables like mother's age, region, place of residence, media exposure, religion, wealth index, parents' education level, and mothers' occupation were found to be significant determinants of variation in women postnatal care utilization in Ethiopia. The Bayesian multilevel logistic regression analysis also estimates the variance of random effect at the regional level. Thus, the value of var (u0j) = δ2= 0.127 is significant at the 5% level of significance. In order to convey policies, it is important not only to comprehend the effect of reforms on the issues, but also on the how it diverges with demographic and economic characteristics.

Conditional Model Selection in Mixed-Effects Models with cAIC4

Model selection in mixed models based on the conditional distribution is appropriate for many practical applications and has been a focus of recent statistical research. In this paper we introduce the R package cAIC4 that allows for the computation of the conditional Akaike information criterion (cAIC). Computation of the conditional AIC needs to take into account the uncertainty of the random effects variance and is therefore not straightforward. We introduce a fast and stable implementation for the calculation of the cAIC for (generalized) linear mixed models estimated with lme4 and (generalized) additive mixed models estimated with gamm4. Furthermore, cAIC4 offers a stepwise function that allows for an automated stepwise selection scheme for mixed models based on the cAIC. Examples of many possible applications are presented to illustrate the practical impact and easy handling of the package.

The BepiColombo solar conjunction experiments revisited

BepiColombo ESA/JAXA mission is currently in its 7 year cruise phase towards Mercury. The Mercury orbiter radioscience experiment (MORE), one of the 16 experiments of the mission, will start its scientific investigation during the superior solar conjunction (SSC) in March 2021 with a test of general relativity (GR). Other solar conjunctions will follow during the cruise phase, providing several opportunities to improve the results of the first experiment. MORE radio tracking system allows to establish precise ranging and Doppler measurements almost at all solar elongation angles (up to 7–8 solar radii), thus providing an accurate measurement of the relativistic time delay and frequency shift experienced by a radio signal during an SSC. The final objective of the experiment is to place new limits to the accuracy of the GR as a theory of gravity in the weak-field limit. As in all gravity experiments, non-gravitational accelerations acting on the spacecraft are a major concern. Because of the proximity to the Sun, the spacecraft will undergo severe solar radiation pressure acceleration, and the effect of the random fluctuations of the solar irradiance may become a significant source of spacecraft buffeting. In this paper we address the problem of a realistic estimate of the outcome of the SSC experiments of BepiColombo, by including in the dynamical model the effects of random variations in the solar irradiance. We propose a numerical method to mitigate the impact of the variable solar radiation pressure on the outcome of the experiment. Our simulations show that, with different assumptions on the solar activity and observation coverage, the accuracy attainable in the estimation of γ lays in the range [–] ×10−6.

Is the source of domestic water associated with the risk of malaria infection? Spatial variability and a mixed-effects multilevel analysis

BackgroundThere is a dearth of information on the relationship between domestic water source and malaria infection in malaria-endemic regions such as Tanzania. This study examined the geospatial variability and association between domestic water source and malaria prevalence in Tanzania. MethodsWe analyzed data from a sample of 6707 children, aged 6–59 months, from the 2017 Tanzania Malaria Indicator Survey. The outcome variable was the result of malaria testing (positive or negative) and the main explanatory variable was domestic water source (piped or non-piped). Random effect variables were administrative region and geographical zone. ArcGIS 10.7 was used to create geospatial distribution maps. A STATA MP 14.0 was used to fit a mixed-effects multilevel logistic regression to examine the factors associated with malaria prevalence. ResultsThe prevalence of malaria and non-piped domestic water source was respectively 7.3% and 59.6%. The regions and zones with a higher prevalence of malaria also had a higher percentage of non-piped water. There was a statistically significant variation in the risk of malaria across the regions (variance = 1.27; 95% CI, 0.40−4.07) and zones (variance = 4.75; 95% CI, 1.46−15.46). The final fixed-effects model showed that non-piped domestic water was significantly associated with malaria prevalence (adjusted odds ratio (AOR) = 2.18; 95% CI, 1.64−2.89; P < 0.001). ConclusionsA non-piped source of domestic water was independently associated with positive testing for malaria. Moreover, regions with a high percentage of non-piped domestic water had a correspondingly high prevalence of malaria.

Association between different types of within-farm worker movements and number of pigs weaned per sow in U.S. Swine farms

The integration and intensification of modern swine production has amplified the importance of biosecurity, as diseases are more easily able to spread and persist in large swine farms, resulting in economic losses. Advancements in accessible technology and computational methods offer new applications for precision livestock farming, such as monitoring internal movements to better understand biosecurity compliance on farm. In this study, a beacon-sensor based internal movement system (PigChamp Pro Europa®) was utilized to investigate the association between weekly within-farm movements of workers and an important production parameter: average weekly number of pigs weaned per sow (PWS), on three US swine farms. Sensors were installed in each room of each farm and Bluetooth-based beacons were distributed individually to farm employees. Movement data was collected for approximately one year and production data was extracted from each farm retrospectively. A linear mixed effects model was fit in STATA 15 with the primary outcome as the average weekly number of pigs weaned per sow and farm included as a random effect. The main predictors included the weekly frequency of three movement types thought to be risky with respect to disease transmission and maintenance in the herd. The frequency values of the three movements were categorized based on the tertile values for each farm. The movement with the highest average frequency was between farrowing rooms for all three farms. The medium frequency of movements category between farrowing rooms the two-weeks preceding the outcome was significantly associated with a decrease in PWS by nearly 1-pig for every 5-sows after controlling for farm, pre-weaning mortality, PWS the week prior, and season (p = 0.03). The random effect variance estimate for the model was 0.21 with a standard error of 0.18. The intraclass correlation coefficient was 0.67 with a standard error of 0.19, indicating that 67% of the unexplained variability in PWS could be attributed to the farm level. This study demonstrates the application of beacon-sensor technology to monitor internal personnel movements in swine production.Technological applications to monitoring trends of within farm movements of farm personnel, such as the system used here, may have the potential to identify specific movements related to farm-specific biosecurity protocol allowing corrective measures and facilitating focused efforts on disease control and mitigation; in turn maintaining productivity and improving overall animal health.

Variance constraints strongly influenced model performance in growth mixture modeling: a simulation and empirical study

BackgroundGrowth Mixture Modeling (GMM) is commonly used to group individuals on their development over time, but convergence issues and impossible values are common. This can result in unreliable model estimates. Constraining variance parameters across classes or over time can solve these issues, but can also seriously bias estimates if variances differ. We aimed to determine which variance parameters can best be constrained in Growth Mixture Modeling.MethodsTo identify the variance constraints that lead to the best performance for different sample sizes, we conducted a simulation study and next verified our results with the TRacking Adolescent Individuals’ Lives Survey (TRAILS) cohort.ResultsIf variance parameters differed across classes and over time, fitting a model without constraints led to the best results. No constrained model consistently performed well. However, the model that constrained the random effect variance and residual variances across classes consistently performed very poorly. For a small sample size (N = 100) all models showed issues. In TRAILS, the same model showed substantially different results from the other models and performed poorly in terms of model fit.ConclusionsIf possible, a Growth Mixture Model should be fit without any constraints on variance parameters. If not, we recommend to try different variance specifications and to not solely rely on the default model, which constrains random effect variances and residual variances across classes. The variance structure must always be reported Researchers should carefully follow the GRoLTS-Checklist when analyzing and reporting trajectory analyses.

Computation of green’s tensor and wave propagation in the random granular elastic medium

A linear differential operator equation involving randomly variable field parameters, characterising the heterogeneous granular elastic medium is considered. The appropriate Green’s tensor is evaluated for the non-deterministic operator equations in the form of Fourier integrals in the frequency space; the exact evaluation is carried out to obtain the 36 components of Green’s tensor. The problem of wave propagation in the random granular elastic medium is then carried out with the help of the associated Green’s tensor. The effect of random variation of parameters on wave propagation in the granular elastic medium is examined. Dispersion equations have been analysed in details.

Disentangling the Effects of HLA DRB1*15:01 and DQB1*06:02 to Establish the True HLA Risk Allele for Inhibitor Development in the Treatment of Hemophilia A

The HLA haplotype DRB1*15:01/DQB1*06:02 has been shown to be associated with the development of inhibitory antibodies ("inhibitors") against therapeutic FVIII (tFVIII) proteins in Hemophilia A (HA) patients. Moreover, this same haplotype has also been implicated with an increased risk for the development of multiple sclerosis, narcolepsy, and drug-induced-hypersensitivity and -liver-injury. Recent reports in the literature have indicated that the alleles of this haplotype may have differential effects on immunogenicity despite the fact that they are in strong linkage disequilibrium (LD). Thus, the question arises as to which of the two constituent alleles of this haplotype is the true HLA risk allele. To address this question we analyzed peptidomic profiling data on HLA-class-II (HLAcII)-presented peptides from dendritic cell (DC)-protein processing and presentation assays (PPPAs) performed in two independent experiments performed by Peyron et al. (2018) and Diego et al. (2020) which reported results on both the HLA-DQ and -DR isomers. The tFVIII in both experiments is full-length recombinant FVIII (FL-rFVIII). We performed log-linear mixed model analyses under two models, where the dependent variable in both models is the logarithm of the expected peptide count. Under Model 1, we analyzed in the fixed effect component of the model a single HLA allele predictor variable consisting of 10 levels represented by distinct DRB1 and DQB1 alleles (4 and 6 levels, respectively). Under this model, we analyzed in the random effects component of the model variables for individuals (8 and 9 levels from Peyron et al. and Diego et al., respectively), experiments (2 levels for Peyron et al. and Diego et al.), and HLA isomers (2 levels for DQ and DR). The random effects component of the model serves to reduce the error (or "noise") in our estimation of the predictive effect of HLA alleles for the peptide counts by accounting for the clustering due to individuals, experiments, and isomers. This approach therefore can be understood as maximizing the signal-to-noise ratio. Model 2 was more focused in that the single HLA allele predictor variable in the fixed effect component consisted of only DQB1*06:02 and DRB1*15:01. Model 2 was also simpler in that we only accounted for two random effect variables, namely for individuals (in this case 2 and 6 levels for Peyron et al. and Diego et al., respectively) and experiments. Thus, Model 2 is a direct head-to-head comparison of the two main HLA alleles of interest. The Model 1 results are reported in Figure 1A and B, where it can be seen that relative to the baseline reference allele provided by DQB1*02:01, both DQB1*06:02 and DRB1*15:01 are at significantly increased risk of contributing to the overall peptide count. Results are reported as risk ratios (RRs) and their associated 95% confidence interval lower and upper bounds (95% CI LB and 95% CI UB). For DQB1*06:02 and DRB1*15:01 respectively, we found a RR (95% CI LB, 95% CI UB) of 1.76 (1.24, 2.50) and 14.16 (10.38, 19.33). Because they are compared to the same baseline, the two RRs may also be directly compared, thus showing that DRB1*15:01 contributes significantly more to the overall peptide count than DQB1*06:02. Under Model 2 (the head-to-head comparison), the RR for the DRB1*15:01 allele against the baseline DQB1*06:02 allele is 7.00 (5.80, 8.44) (Figure 2A and B). These results contribute to the field of precision medicine because they demonstrate that even in the case of alleles in tight LD, their effects can be effectively disentangled by a DC-PPPA and a log-linear mixed model analysis. Our results support the conclusion that in regard to the well-known risk haplotype of DQB1*06:02/DRB1*15:01, the true HLA risk allele seems to be DRB1*15:01. Disclosures Luu: Haplogenics Corporation: Current Employment. Hofmann:CSL Behring: Current Employment. Powell:Haplogenics Corporation: Membership on an entity's Board of Directors or advisory committees. Dinh:Haplogenics Corporation: Current Employment. Escobar:National Hemophilia Foundation: Consultancy, Membership on an entity's Board of Directors or advisory committees; Takeda: Consultancy, Membership on an entity's Board of Directors or advisory committees; Sanofi: Consultancy, Membership on an entity's Board of Directors or advisory committees; Genentech, Inc.: Consultancy, Membership on an entity's Board of Directors or advisory committees; Novo Nordisk: Consultancy, Membership on an entity's Board of Directors or advisory committees; Pfizer: Consultancy, Membership on an entity's Board of Directors or advisory committees. Maraskovsky:CSL Behring: Current Employment. Howard:Haplogenics Corporation: Membership on an entity's Board of Directors or advisory committees.

Comparative Effectiveness of CABG versus PCI in Patients with Ischemic Heart Disease: insights from SWEDEHEART Registry

Abstract Background Several studies have compared CABG to PCI as revascularization treatment in patients with ischemic heart disease (IHD). However, it remains unclear which revascularization strategy carries survival benefits in the long-term. Methods We used data from the SWEDEHEART (Swedish Web-System for Enhancement and Development of Evidence-Based Care in Heart Disease Evaluated According to Recommended Therapies) registry for all hospital admissions at 13 cardiac care centers within Västra Götaland County in Sweden (∼20% of all SWEDEHEART data). The database contains &amp;gt;1000 clinical variables documenting the entire process of acute coronary hospital care. All patients hospitalized for stable angina or NSTE-ACS during the period 2000–2018 were included in the analysis. We used a propensity score-adjusted Cox proportional-hazards regression with hospitals as random-effect variables. We adjusted for patients' demographics, socio-economic status, traditional risk factors, comorbidities, the severity of coronary artery disease, left ventricular function, calendar year and medication at discharge. For sensitivity analysis, we used the instrumental variable estimator for the Cox proportional-hazards model (with treating hospital as a treatment-preference instrument) to simultaneously deal with the problems of unmeasured confounding and censoring of the outcome. The primary outcome was all-cause mortality. Results In total, 11,896 patients were included in the study. Of these, 3,129 (26.3%) were women. 20.4% had diabetes and 10.4% had a previous myocardial infarction. The mean age was 66.7±10.7, and 42.9% were &amp;gt;70 years old. 61.5% had three-vessel and/or left main disease. Median follow-up time was 5.7 years (range 1 day-18.2 years). Revascularization therapy after coronary angiography was PCI in 9449 (79.4%) and CABG in 2,447 (20.6%) patients. CABG patients were more likely to have diabetes, left main/multivessel disease and heart failure. The number of revascularized patients with PCI increased by 6.4% per calendar year (P&amp;lt;0.001). There were 2,481 (20.9%) deaths. CABG was associated with a lower risk of death compared to PCI (HR 0.81; 95% CI 0.69–0.95; P=0.011. We found no evidence for treatment heterogeneity between the revascularization strategy and age, gender, diabetes, heart failure and indication for revascularization (all P-interaction &amp;gt;0.05). Results from the sensitivity analysis support the conclusions from the primary model. Conclusions In hospitalized patients due to IHD, revascularization with CABG was associated with superior long-term survival compared to PCI. Funding Acknowledgement Type of funding source: Foundation. Main funding source(s): Heart and Lung Foundation, ALF Västra Götaland, Swedish Scientific Council

Influence of aggregate geometry and material fabric on tensile cracking in concrete

A recently developed discrete element capability is used to understand the effect of random variations in aggregate shape and size on tensile cracking in concrete. A procedure to reconstruct the three-dimensional crack surface, and characterize its tortuosity, is proposed. The role of anisotropy in the material fabric, induced by variations in aggregate shape, is studied. Both tensile and compressive strength are seen to be affected by fabric anisotropy, but to different extents and in different ways. Post-peak behaviour in tension is linked to dispersion in the local fabric, characterized by a proposed local fabric tensor. The influence of aggregate shape on fracture process zone geometry is investigated. Overall, aggregate shape appears to be the dominant factor in determining the post-peak response. However aggregate size appears to affect the tensile strength more strongly while its influence on the fracture energy is complicated and subject to two opposing trends.

Multinomial Logistic Mixed Models for Clustered Categorical Data in a Complex Survey Sampling Setup

In a finite/survey population setup, where categorical/multinomial responses are collected from individuals belonging to a cluster, in a recent study Skinner (International Statistical Review, 87, S64-S78 2019) has modeled the means of the clustered categorical responses as a function of regression parameters, and suggested a ‘working’ correlations based GEE (generalized estimating equations) approach for the estimation of the regression parameters. However, this mean model involving only regression parameters is not justified for clustered multinomial responses because of the fact that these responses share a common cluster effect which compels the clustered correlation parameter to enter into the mean function on top of the regression parameters. Consequently, the so-called GEE approach, which requires the means to be free of correlations, is not applicable for regression analysis in the clustered multinomial setup. As a remedy, in this paper we consider a multinomial mixed model which accommodates the clustered correlation parameter in the mean functions. For inferences in the present finite population setup, as the GQL (generalized quasi-likelihood) approach is known to produce consistent and more efficient estimate than the MM (method of moments) approach in an infinite population setup, we estimate the regression parameters of primary interest by using the first order response based survey weighted GQL (WGQL) approach. For the estimation of the random effects variance (also known as clustered correlation) parameter, as it is of secondary interest, we use the second order response based survey weighted MM (WMM) approach, which is simpler than the corresponding WGQL estimation approach. The estimation steps are presented clearly for the benefit to the practitioners. Also because, in practice, survey practitioners such as statistical agencies frequently deal with a large health or socio-economic data set at national or state levels, for example, we make sure for their benefit that our proposed WGQL and WMM estimators are consistent. Thus, the asymptotic properties such as asymptotic unbiasedness and consistency for both regression and clustered correlation parameters are studied in details. The asymptotic normality property, for the benefit of constructing confidence interval for the main regression parameters, is also studied.

Comparing three approaches for handling a fourth level of nesting structure in cluster-randomized trials

This study compared three approaches for handling a fourth level of nesting when analyzing cluster-randomized trial (CRT) data. Although CRT data analyses may include repeated measures, individual, and cluster levels, there may be an additional fourth level that is typically ignored. This study examined the impact of ignoring this fourth level, accounting for it using a model-based approach, and accounting for it using a design-based approach on parameter and standard error (SE) estimates. Several fixed effect and random effect variance parameters and SEs were biased across all three models. Results suggest if a meaningful fourth level exists, researchers should acknowledge it using a design-based approach. If the fourth level is not practically important, researchers may ignore it altogether, resulting in more accurate parameter and SE estimates.

An unbalanced multidimensional latent effects-based logistic mixed model and GQL estimation for spatial binary data

Spatial correlation structure is the most essential tool in a spatial data analysis. However, the difficulty of modelling spatial correlations between two responses collected from two neighbouring locations is a challenge, when it is known that each of the responses may also be influenced by certain visible and/or invisible effects of other neighbouring locations. Further difficulties arise when one deals with spatial binary data as opposed to linear spatial data. In this paper, we resolve this correlation model issue for spatial binary data by using a mixed logits model approach where pair-wise correlations are computed by accommodating both within and between correlations for paired-responses. For inferences, we use the true correlation based generalized quasi-likelihood (GQL) approach. The asymptotic normality of the estimators of the main regression and random effects variance parameters are studied. The model and estimation methodology used are illustrated by a finite sample-based simulation study.

Effective transformation-based variable selection under two-fold subarea models in small area estimation

Abstract We present a simple yet effective variable selection method for the two-fold nested subarea model, which generalizes the widely-used Fay-Herriot area model. The twofold subarea model consists of a sampling model and a linking model, which has a nested-error model structure but with unobserved responses. To select variables under the two-fold subarea model, we first transform the linking model into a model with the structure of a regular regression model and unobserved responses. We then estimate an information criterion based on the transformed linking model and use the estimated information criterion for variable selection. The proposed method is motivated by the variable selection method of Lahiri and Suntornchost (2015) for the Fay-Herriot model and the variable selection method of Li and Lahiri (2019) for the unit-level nested-error regression model. Simulation results show that the proposed variable selection method performs significantly better than some naive competitors, especially when the variance of the area-level random effect in the linking model is large.

Robustness of linear mixed‐effects models to violations of distributional assumptions

Abstract Linear mixed‐effects models are powerful tools for analysing complex datasets with repeated or clustered observations, a common data structure in ecology and evolution. Mixed‐effects models involve complex fitting procedures and make several assumptions, in particular about the distribution of residual and random effects. Violations of these assumptions are common in real datasets, yet it is not always clear how much these violations matter to accurate and unbiased estimation. Here we address the consequences of violations in distributional assumptions and the impact of missing random effect components on model estimates. In particular, we evaluate the effects of skewed, bimodal and heteroscedastic random effect and residual variances, of missing random effect terms and of correlated fixed effect predictors. We focus on bias and prediction error on estimates of fixed and random effects. Model estimates were usually robust to violations of assumptions, with the exception of slight upward biases in estimates of random effect variance if the generating distribution was bimodal but was modelled by Gaussian error distributions. Further, estimates for (random effect) components that violated distributional assumptions became less precise but remained unbiased. However, this particular problem did not affect other parameters of the model. The same pattern was found for strongly correlated fixed effects, which led to imprecise, but unbiased estimates, with uncertainty estimates reflecting imprecision. Unmodelled sources of random effect variance had predictable effects on variance component estimates. The pattern is best viewed as a cascade of hierarchical grouping factors. Variances trickle down the hierarchy such that missing higher‐level random effect variances pool at lower levels and missing lower‐level and crossed random effect variances manifest as residual variance. Overall, our results show remarkable robustness of mixed‐effects models that should allow researchers to use mixed‐effects models even if the distributional assumptions are objectively violated. However, this does not free researchers from careful evaluation of the model. Estimates that are based on data that show clear violations of key assumptions should be treated with caution because individual datasets might give highly imprecise estimates, even if they will be unbiased on average across datasets.