arXiv subjects

Benjamin M. Bolker

Publications and source records attributed to Benjamin M. Bolker.

11 recordsLinked to original sources

arXiv2026

Meta-analysis with the glmmTMB R package

Two common formulations of meta-analytical models include the standard two-stage normal-normal models, which synthesise estimated effect sizes, and the one-stage generalised linear mixed model (GLMM), which directly model the underlying outcome data across studies. The general-purpose glmmTMB R package provides flexible response distributions and random-effect covariance structures through Template Model Builder (TMB). Its existing functionality can fit one-stage meta-analytic GLMM specifications. However, incorporating known sampling variances and covariances in the conventional two-stage inverse-variance formulation of meta-analysis was previously not easily accomplished in glmmTMB. Here, we introduce equalto, a new covariance structure in glmmTMB that allows users to supply a known sampling error variance-covariance matrix when fitting meta-analytic models. This enables explicit modelling of heteroscedasticity and dependence among sampling errors. Using simulations, we show that glmmTMB produces estimates identical to those from the corresponding metafor package functions for normal-normal models and similar estimates for GLMM specifications. We illustrate these models using published meta-analysis datasets in medicine, evolutionary ecology, and the social sciences. With the addition of the equalto covariance structure, glmmTMB now provides a unified and flexible framework for fitting two-stage normal-normal models and one-stage meta-analytic GLMMs, including multivariate specifications. These models can be fitted using the same glmmTMB() function, expanding the R toolkit available for evidence synthesis.

stat.CO↗

arXiv2026

Fitting Generalized Linear Mixed-Effects Models using lme4

The lme4 R package can be used to fit generalized linear mixed models (GLMMs), which extend the class of linear mixed models (LMMs). The two main extensions provided by GLMMs are (1) allowing for the conditional distribution of the response given the random effects to be non-Gaussian (e.g. binomial, Poisson) and (2) allowing the conditional mean to be a nonlinear function of a linear combination of the fixed and random effect coefficients, via an inverse link function. The conditional mode of the random effects given the observed data, the variance-covariance matrix of the random effects, and the fixed effect parameters are determined using penalized iteratively reweighted least squares. We compute an approximation of the integral over the distributions of the conditional modes to compute the maximum likelihood estimate for a given set of parameters (by default we use the Laplace approximation or, alternatively, the more computationally expensive adaptive Gauss-Hermite quadrature). The package provides all the standard features available for GLMs in base R, including the standard set of accessor functions as well as the possibility of user-specified distributions (within the exponential dispersion family) and link functions.

stat.ME↗

arXiv2026

Too Few or Too Many? Sample Size Estimation for Differential Abundance Studies

Determining an appropriate sample size for a study is a crucial step in planning scientific research. Appropriate sample size planning avoids both inadequate and inflated sample sizes. Inflated sample sizes wastes resources, time and effort of human subjects, and lives of experimental animals. Inadequate sample sizes, a much more common problem, wastes even more resources through the inability to detect biologically meaningful differences and encourages questionable research practices like $p$-hacking. Microbiome studies are particularly challenged by small sample sizes, particularly in studies of human subjects or expensive animal models. In practice, the statistical power of taxa within a differential abundance study is influenced by the effect size (typically quantified as fold change), mean abundance of individual taxa, and the number of samples. We present a novel approach for sample size calculation for differential abundance studies as a function of effect size, mean abundance and statistical power of taxa. Our method is implemented in the power.nb R package, available at https://michaelagronah.com/power.nb/articles/stub.html. We applied our model for sample size calculation using estimates of mean abundance and fold change of taxa obtained from thirty real-world microbiome datasets. Our results showed that differential abundance microbiome studies require larger sample sizes than are currently prevalent in the literature to achieve adequate statistical power. Our framework will help researchers make informed decisions about appropriate sample sizes.

q-bio.QM↗

arXiv2024

Parsimoniously Fitting Large Multivariate Random Effects in glmmTMB

Multivariate random effects with unstructured variance-covariance matrices of large dimensions, $q$, can be a major challenge to estimate. In this paper, we introduce a new implementation of a reduced-rank approach to fit large dimensional multivariate random effects by writing them as a linear combination of $d < q$ latent variables. By adding reduced-rank functionality to the package glmmTMB, we enhance the mixed models available to include random effects of dimensions that were previously not possible. We apply the reduced-rank random effect to two examples, estimating a generalized latent variable model for multivariate abundance data and a random-slopes model.

stat.ME↗

arXiv2023

Toward a comprehensive system for constructing compartmental epidemic models

Compartmental models are valuable tools for investigating infectious diseases. Researchers building such models typically begin with a simple structure where compartments correspond to individuals with different epidemiological statuses, e.g., the classic SIR model which splits the population into susceptible, infected, and recovered compartments. However, as more information about a specific pathogen is discovered, or as a means to investigate the effects of heterogeneities, it becomes useful to stratify models further -- for example by age, geographic location, or pathogen strain. The operation of constructing stratified compartmental models from a pair of simpler models resembles the Cartesian product used in graph theory, but several key differences complicate matters. In this article we give explicit mathematical definitions for several so-called ``model products'' and provide examples where each is suitable. We also provide examples of model stratification where no existing model product will generate the desired result.

q-bio.PE↗

arXiv2022

Evaluating undercounts in epidemics: response to Maruotti et al. 2022

Maruotti et al. 2022 used a mark-recapture approach to estimate bounds on the true number of monkeypox infections in various countries. These approaches are fundamentally flawed; it is impossible to estimate undercounting based solely on a single stream of reported cases. Simulations based on a Richards curve for cumulative incidence show that, for reasonable epidemic parameters, the proposed methods estimate bounds on the ascertainment ratio of $\approx 0.2-0.5$ roughly independently of the true ascertainment ratio. These methods should not be used.

q-bio.PE↗

arXiv2021

Testing and Isolation Efficacy: Insights from a Simple Epidemic Model

Testing individuals for pathogens can affect the spread of epidemics. Understanding how individual-level processes of sampling and reporting test results can affect community- or population-level spread is a dynamical modeling question. The effect of testing processes on epidemic dynamics depends on factors underlying implementation, particularly testing intensity and on whom testing is focused. Here, we use a simple model to explore how the individual-level effects of testing might directly impact population-level spread. Our model development was motivated by the COVID-19 epidemic, but has generic epidemiological and testing structures. To the classic SIR framework we have added a per capita testing intensity, and compartment-specific testing weights, which can be adjusted to reflect different testing emphases -- surveillance, diagnosis, or control. We derive an analytic expression for the relative reduction in the basic reproductive number due to testing, test-reporting and related isolation behaviours. Intensive testing and fast test reporting are expected to be beneficial at the community level because they can provide a rapid assessment of the situation, identify hot spots, and may enable rapid contact-tracing. Direct effects of fast testing at the individual level are less clear, and may depend on how individuals' behaviour is affected by testing information. Our simple model shows that under some circumstances both increased testing intensity and faster test reporting can reduce the effectiveness of control, and allows us to explore the conditions under which this occurs. Conversely, we find that focusing testing on infected individuals always acts to increase effectiveness of control.

q-bio.PE↗

arXiv2021

pcoxtime: Penalized Cox Proportional Hazard Model for Time-dependent Covariates

The penalized Cox proportional hazard model is a popular analytical approach for survival data with a large number of covariates. Such problems are especially challenging when covariates vary over follow-up time (i.e., the covariates are time-dependent). The standard R packages for fully penalized Cox models cannot currently incorporate time-dependent covariates. To address this gap, we implement a variant of gradient descent algorithm (proximal gradient descent) for fitting penalized Cox models. We apply our implementation to real and simulated data sets.

stat.ME↗

arXiv2021

Sensitivity analysis of an integrated climate-economic model

We conduct a sensitivity analysis of a new type of integrated climate-economic model recently proposed in the literature, where the core economic component is based on the Goodwin-Keen dynamics instead of a neoclassical growth model. Because these models can exhibit much richer behaviour, including multiple equilibria, runaway trajectories and unbounded oscillations, it is crucial to determine how sensitive they are to changes in underlying parameters. We focus on four economic parameters (markup rate, speed of price adjustments, coefficient of money illusion, growth rate of productivity) and two climate parameters (size of upper ocean reservoir, equilibrium climate sensitivity) and show how their relative effects on the outcomes of the model can be quantified by methods that can be applied to an arbitrary number of parameters.

econ.GN↗

arXiv2019

A note on observation processes in epidemic models

Many disease models focus on characterizing the underlying transmission mechanism but make simple, possibly naive assumptions about how infections are reported. In this note, we use a simple deterministic Susceptible-Infected-Removed (SIR) model to compare two common assumptions about disease incidence reports: individuals can report their infection as soon as they become infected or as soon as they recover. We show that incorrect assumptions about the underlying observation processes can bias estimates of the basic reproduction number and lead to overly narrow confidence intervals.

q-bio.PE↗

arXiv2018

I can see clearly now: reinterpreting statistical significance

Null hypothesis significance testing remains popular despite decades of concern about misuse and misinterpretation. We believe that much of the problem is due to language: significance testing has little to do with other meanings of the word "significance". Despite the limitations of null-hypothesis tests, we argue here that they remain useful in many contexts as a guide to whether a certain effect can be seen clearly in that context (e.g. whether we can clearly see that a correlation or between-group difference is positive or negative). We therefore suggest that researchers describe the conclusions of null-hypothesis tests in terms of statistical "clarity" rather than statistical "significance". This simple semantic change could substantially enhance clarity in statistical communication.

stat.OT↗