Mixed effects: a unifying framework for statistical modelling in fisheries biology

Preventing invasive species establishment is a global conservation priority, yet limited management resources oftentimes restrict sites to target for prevention or monitoring. Risk assessments based on habitat suitability can identify sites most vulnerable to invasion that should be prioritized for preventative actions. Since habitat suitability is the result of interactions between environmental and organismal attributes, analyses should incorporate individual variability in demographics expected in an invasive population. Individual‐based models (IBMs) can predict habitat suitability by accounting for interactions between environmental conditions and individual‐level variability. We developed an IBM to predict suitability of rivers in the northern United States to the invasive fishes silver carp (Hypophthalmichthys molitrix) and bighead carp (H. nobilis) and explored the projected effects of climate change on habitat suitability. All rivers supported adult survival, although complete survival of all adult demographics and positive growth only occurred in approximately 45% (17 of 38) of rivers for silver carp and 26% (10 of 38) of rivers for bighead carp. Only the largest individuals at the time of introduction survived in rivers where adult mortality occurred. Most rivers were unsuitable for young‐of‐year (89% and 92% of rivers for silver carp and bighead carp respectively). Climate change simulations had relatively little effect on adult habitat suitability but resulted in up to four times the number of rivers being suitable for young‐of‐year by the late‐21st century and greatly extended the viable spawning season by up to an additional 65 days for silver carp and 77 days for bighead carp. Synthesis and applications. Our approach of using individual‐based models as a risk assessment tool informs proactive conservation planning by identifying sites for invasive species early detection monitoring, promoting the development of contingency response plans and allowing for proactive prevention efforts. Model predictions also provide specific management guidance regarding the size and life stages to target for monitoring efforts, which capture gears to use, and the most effective time to sample for early detection monitoring.

Pharmacokinetic-Pharmacodynamic Modeling and Simulation

A general multivariate mixed effect linear model is introduced. Special cases of the model include the multivariate nested error covariance component regression and the random coefficient repeated measure model. Discussion is given on modeling the random effect structure and its effect on statistical inference. A procedure for testing certain class of hypotheses concerning the random effect structure is developed. The procedure is based on a statistic in a readily computable form, facilitating the use at the model building stage. 1. The Model. This paper is concerned with introducing a general multivariate mixed effect model, and with developing a procedure for testing hypotheses concerning the random effect structure in such a model. For simplicity we concentrate here on mixed models with the one-way random effect structure, i.e., with the random effect (other than the error term) involving one unknown covariance matrix. To introduce our general model, first consider the most widely used univariate mixed effect model with the one-way classification random effect or with the nested error structure. The response yij and the k ? 1 explanatory variable Xij for the j-th individual in the z-th group are assumed to satisfy

In the previous chapters, we discussed autoregressive linear mixed effects models. In this section, we discuss the relationships between the autoregressive linear mixed effects models and nonlinear mixed effects models, growth curves, and differential equations. The autoregressive model shows a profile approaching an asymptote, where the change is proportional to the distance remaining to the asymptote. Autoregressive models in discrete time correspond to monomolecular curves in continuous time. Autoregressive linear mixed effects models correspond to monomolecular curves with random effects in the baseline and asymptote, and special error terms. The autoregressive coefficient is a nonlinear parameter, but all random effects parameters in the model are linear. Therefore, autoregressive linear mixed effects models are nonlinear mixed effects models without nonlinear random effects and have a closed form of likelihood. When there are time-dependent covariates, autoregressive linear mixed effects models are represented by a differential equation and random effects. The monomolecular curve is one of the popular growth curves. We introduce other growth curves, such as the logistic curves and von Bertalanffy curves, and generalizations of growth curves. Re-parameterization is often performed in nonlinear models, and various representations of re-parameterization in monomolecular and other curves are provided herein.

Many statistical models have been proposed in the literature for the analysis of longitudinal data. One may propose to model two or more correlated longitudinal processes simultaneously, with a goal of understanding their association over time. Joint modeling is then required to carefully study the association structure among the outcomes as well as drawing joint inferences about the different outcomes. In this study, we sought to model the associations among six nutrition outcomes while circumventing the computational challenge posed by their clustered and high-dimensional nature. We analyzed data from a 2 2 randomized crossover trial conducted in Kenya, to compare the effect of high-dose and low-dose iodine in household salt on systolic blood pressure (SBP) and diastolic blood pressure (DBP) in women of reproductive age and their household matching pair of school-aged children. Two additional outcomes, namely, urinary iodine concentration (UIC) in women and children were measured repeatedly to monitor the amount of iodine excreted through urine. We extended the model proposed by Mwangi etal. (2021, Communications in Statistics: Case Studies, Data Analysis and Applications, 7(3), 413-431) allowing flexible piecewise joint models for six outcomes to depend on separate random effects, which are themselves correlated. This entailed fitting 15 bivariate general linear mixed models and deriving inference for the joint model using pseudo-likelihood theory. We analyzed the outcomes separately and jointly using piecewise linear mixed-effects (PLME) model and further validated the results using current state-of-the-art Jones and Kenward methodology (JKME model) used for analyzing randomized crossover trials. The results indicate that high-dose iodine in salt significantly reduced blood pressure (BP) compared to low-dose iodine in salt. Estimates for the random effects and residual error components showed that SBP and DBP had strong positive correlation, with effect of the random slope indicating that significantly related outcomes are strongly associated in their evolution. There was a moderately strong inverse relationship between evolutions of UIC and BP both in women and children. These findings confirmed the original hypothesis that high-dose iodine salt has significant lowering effect on BP. We further sought to evaluate the performance of our proposed PLME model against the widely used JKME model, within the multivariate joint modeling framework through a simulation study mimicking a crossover design. From our findings, the multivariate joint PLME model performed exceptionally well both in estimation of random-effects matrix (G) and Hessian matrix (H), allowing satisfactory model convergence during estimation. It allowed a more complex fit to the data with both random intercepts and slopes effects compared to the multivariate joint JKME model that allowed for random intercepts only. When a hierarchical viewpoint is adopted, in the sense that outcomes are specified conditionally upon random effects, the variance-covariance matrix of the random effects must be positive definite. In some cases, additional random effects could explain much variability in the data, thus improving precision in estimation of the estimands (effect size) parameters. The key highlight in this evaluation shows that multivariate joint JKME model is a powerful tool especially while fitting mixed models with random intercepts only, in crossover design settings. Addition of random slopes may lead to model complexities in most cases, resulting in unsatisfactory model convergence during estimation. To circumvent convergence pitfalls, extention of JKME model to PLME model allows a more flexible fit to the data (generated from crossover design settings), especially in the multivariate joint modelingframework.

Mixed effects models and Berkson measurement error models are widely used. They share features which the author uses to develop a unified estimation framework. He deals with models in which the random effects (or measurement errors) have a general parametric distribution, whereas the random regression coefficients (or unobserved predictor variables) and error terms have nonparametric distributions. He proposes a second‐order least squares estimator and a simulation‐based estimator based on the first two moments of the conditional response variable given the observed covariates. He shows that both estimators are consistent and asymptotically normally distributed under fairly general conditions. The author also reports Monte Carlo simulation studies showing that the proposed estimators perform satisfactorily for relatively small sample sizes. Compared to the likelihood approach, the proposed methods are computationally feasible and do not rely on the normality assumption for random effects or other variables in the model.

Summary We propose a general family of nonparametric mixed effects models. Smoothing splines are used to model the fixed effects and are estimated by maximizing the penalized likelihood function. The random effects are generic and are modelled parametrically by assuming that the covariance function depends on a parsimonious set of parameters. These parameters and the smoothing parameter are estimated simultaneously by the generalized maximum likelihood method. We derive a connection between a nonparametric mixed effects model and a linear mixed effects model. This connection suggests a way of fitting a nonparametric mixed effects model by using existing programs. The classical two-way mixed models and growth curve models are used as examples to demonstrate how to use smoothing spline analysis-of-variance decompositions to build nonparametric mixed effects models. Similarly to the classical analysis of variance, components of these nonparametric mixed effects models can be interpreted as main effects and interactions. The penalized likelihood estimates of the fixed effects in a two-way mixed model are extensions of James–Stein shrinkage estimates to correlated observations. In an example three nested nonparametric mixed effects models are fitted to a longitudinal data set.

Characterization of the suitability or potentiality of a territory for forest tree species is an important source of information for forest planning and managing. In this study, we compared a relatively simple methodology to generate potential habitat distribution areas that has been traditionally used in Spain (the potential index model) with a statistical modelling approach (generalized linear model). We modelled the potential distribution of mountain pine (Pinus uncinata) in the Iberian peninsula as a working example. The potential index model generated a map of habitat suitability according to the values of an index of potentiality, whose distribution has usually divided into four categories based on quartiles (from optimum to low suitability). Considering all values of the index of potentiality as presences of mountain pine resulted in a low to moderate degree of agreement between the potential index model and the generalized linear model according to the kappa coefficient. Using the cut-off value of the index of potentiality that maximized the degree of agreement between both modelling approaches resulted in a substantial similarity between the maps of the predicted distribution of mountain pine. This cut-off value did lie in the upper-third quartile of the potential index distribution (high suitability category), and roughly coincided with the upper 30th percentile. The use of statistical techniques, which have proved to be powerful and versatile for species distribution modelling, is recommended. However, the potential index model, together with the adjustments proposed here, could be a reasonably simple methodology to predict the potential distribution of forest tree species that forest managers should take into account when evaluating forestation and afforestation projects.

ABSTRACTPhysical habitat models are used to relate the availability of suitable habitat to river flows by describing the combined availability of depths, velocities and substrates deemed suitable for a species. Field data are often used to calibrate hydraulic models and therefore calculate availability of suitable physical habitat over a range of flows at a site. This paper describes and tests a parameterize-then-cluster-then-predict strategy that extends physical habitat models across New Zealand. Mixed-effects models were used to represent habitat–flow relationships at 274 sites for each of 17 sets of habitat suitability criteria. Parameter values for each set of habitat suitability criteria and for each formulation were clustered into groups. Cluster membership was related to catchment characteristics. Cross-validated generalized habitat predictions were tested for their ability to predict: (1) availability of suitable physical habitat across a range of flows; and (2) loss of suitable physical habitat between two reference flows. Of the 17 sets of habitat suitability criteria, 12 had predicted habitat–flow patterns that exceeded a set of a priori defined performance criteria, providing evidence that predictions were able to distinguish between-site patterns in relationships between availability of suitable physical habitat and flow at unvisited sites.

Fast-growing Eucalyptus spp. forest plantations and their resultant wood products are economically important and may provide a low-cost means to sequester carbon for greenhouse gas reduction. The development of advanced and optimized frameworks for estimating forest plantation attributes from lidar remote sensing data combined with statistical modeling approaches is a step towards forest inventory operationalization and might improve industry efficiency in monitoring and managing forest resources. In this study, we first developed and tested a framework for modeling individual tree attributes in fast-growing Eucalyptus forest plantation using airborne lidar data and linear mixed-effect models (LME) and assessed the gain in accuracy compared to a conventional linear fixed-effects model (LFE). Second, we evaluated the potential of using the tree-level estimates for determining tree attribute uniformity across different stand ages. In the field, tree measurements, such as tree geolocation, species, genotype, age, height (Ht), and diameter at breast height (dbh) were collected through conventional forest inventory practices, and tree-level aboveground carbon (AGC) was estimated using allometric equations. Individual trees were detected and delineated from lidar-derived canopy height models (CHM), and crown-level metrics (e.g., crown volume and crown projected area) were computed from the lidar 3-D point cloud. Field and lidar-derived crown metrics were combined for ht, dbh, and AGC modeling using an LME. We fitted a varying intercept and slope model, setting species, genotype, and stand (alone and nested) as random effects. For comparison, we also modeled the same attributes using a conventional LFE model. The tree attribute estimates derived from the best LME model were used for assessing forest uniformity at the tree level using the Lorenz curves and Gini coefficient (GC). We successfully detected 96.6% of the trees from the lidar-derived CHM. The best LME model for estimating the tree attributes was composed of the stand as a random effect variable, and canopy height, crown volume, and crown projected area as fixed effects. The %RMSE values for tree-level height, dbh, and AGC were 8.9%, 12.1%, and 23.7% for the LFE model and improved to 7.3%, 7.1%, and 13.6%, respectively, for the LME model. Tree attributes uniformity was assessed with the Lorenz curves and tree-level estimations, especially for the older stands. All stands showed a high level of tree uniformity with GC values approximately 0.2. This study demonstrates that accurate detection of individual trees and their associated crown metrics can be used to estimate Ht, dbh, and AGC stocks as well as forest uniformity in fast-growing Eucalyptus plantations forests using lidar data as inputs to LME models. This further underscores the high potential of our proposed approach to monitor standing stock and growth in Eucalyptus—and similar forest plantations for carbon dynamics and forest product planning.

Outcomes of primary versus revision TLIF following decompression alone in degenerative spondylolisthesis: a retrospective propensity score matched study.

The goal of this paper is to develop a double penalized hierarchical likelihood (DPHL) with a modified Cholesky decomposition for simultaneously selecting fixed and random effects in mixed effects models. DPHL avoids the use of data likelihood, which usually involves a high-dimensional integral, to define an objective function for variable selection. The resulting DPHL-based estimator enjoys the oracle properties with no requirement on the convexity of loss function. Moreover, a two-stage algorithm is proposed to effectively implement this approach. An H-likelihood-based Bayesian information criterion (BIC) is developed for tuning parameter selection. Simulated data and a real data set are examined to illustrate the efficiency of the proposed method.

Modeling of Clostridium perfringens vegetative cell inactivation in beef-in-sauce products: A meta-analysis using mixed linear models

Purpose: To describe and demonstrate methods for analyzing longitudinal correlated eye data with a continuous outcome measure. Methods: We described fixed effects, mixed effects and generalized estimating equations (GEE) models, applied them to data from the Complications of Age-Related Macular Degeneration Prevention Trial (CAPT) and the Age-Related Eye Disease Study (AREDS). In CAPT (N = 1052), we assessed the effect of eye-specific laser treatment on change in visual acuity (VA). In the AREDS study, we evaluated effects of systemic supplement treatment among 1463 participants with AMD category 3. Results: In CAPT, the inter-eye correlations (0.33 to 0.53) and longitudinal correlations (0.31 to 0.88) varied. There was a small treatment effect on VA change (approximately one letter) at 24 months for all three models (p = .009 to 0.02). Model fit was better with the mixed effects model than the fixed effects model (p < .001). In AREDS, there was no significant treatment effect in all models (p > .55). Current smokers had a significantly greater VA decline than non-current smokers in the fixed effects model (p = .04) and the mixed effects model with random intercept (p = .0003), but marginally significant in the mixed effects model with random intercept and slope (p = .08), and GEE models (p = .054 to 0.07). The model fit was better with the fixed effects model than the mixed effects model (p < .0001). Conclusion: Longitudinal models using the eye as the unit of analysis can be implemented using available statistical software to account for both inter-eye and longitudinal correlations. Goodness-of-fit statistics may guide the selection of the most appropriate model.

In order to predict the remaining useful life of rail train wheels progressively under dependent measurement errors, an extended mixed effect degradation model and Bayesian parameter update framework is proposed. The heteroscedastic and correlated structure of error terms are considered in the modeling process, and the spectral decomposition of the error effect matrix is used to realize the independent conversion of online monitoring data. Based on the Bayesian method, the online monitoring data is merged with historical knowledge for parameter updating, and remaining useful life prediction and reliability evaluation are performed. The case study results show that the proposed method considering dependent measurement errors could provide adequate degradation modeling and improve the accuracy of remaining useful life prediction. These results will help the development of prognostic and health management of train wheel.