Moving Beyond the Homoscedasticity Assumption
Recently while scrolling through social media, I saw an article posting with a catchy name: "Location-Scale Meta-Analysis and Meta-Regression as a Tool to Capture Large-Scale Changes in Biological and Methodological Heterogeneity." I'll admit the title was technical, but the abstract caught my attention immediately. What stood out was that this article was suggesting a modeling approach that addresses the homoscedasticity assumption of simple models – an assumption that has always bothered me in my environmental work.
You see, homoscedasticity (the assumption that variance is constant across your data) is a problem because in biological applications, most of the time we simply can't talk of homoscedasticity. The real world is messy. Some species respond more consistently to pollution than others. Some ecosystems show wildly variable responses to the same disturbance. Traditional statistical approaches treat this variability as a nuisance – something to control for rather than something to understand.
I was surprised to learn that solutions to overcome this assumption have actually been around for quite some time – weighted least squares, robust standard errors, and generalized linear models with specified variance structures have all tried to tackle this issue. Yet somehow these approaches never fully penetrated ecological research. This was my first time seeing an article directly addressing such a problem in a comprehensive framework specifically tailored for biological data. Apparently, this correction has been going on for some time now, with foundational work dating back to Lee and Nelder (1996), but the ecological applications are much more recent.
More Than Just Fixing a Statistical Assumption
This article had some more tricks up its sleeve. What Nakagawa and colleagues (2025) propose isn't just a statistical fix – it's a fundamental rethinking of how we model ecological data. Their location-scale approach models both the mean (location) AND the variance (scale) of your response variables simultaneously.
This approach didn't emerge overnight but evolved through a series of methodological advances. The foundation was laid by Lee and Nelder's (1996) double-hierarchical generalized linear models, but Nakagawa's journey with variance modeling began with his 2011 paper with Cleasby highlighting the importance of heteroscedasticity in behavioral ecology. The approach gained momentum through applications in quantitative genetics (Rönnegård et al., 2010) and behavioral prediction (Cleasby et al., 2015), before Bürkner's (2017) brms package made Bayesian implementation more accessible. Recent extensions by Cinar et al. (2022) incorporated phylogenetic relationships, while Viechtbauer and López-López (2022) focused on meta-analytic applications – all culminating in this comprehensive synthesis that is arguably the latest and most sophisticated version of overcoming the homoscedasticity assumption in ecological and evolutionary research.
Think about what this means for environmental science. When studying how forest disturbance affects pollination, we're not just interested in the average effect – we want to know when and where that effect is most consistent or variable. Traditional approaches might tell you that forest fragmentation reduces pollinator visits by 30% on average, but they miss the critical insight that this effect might be highly consistent in temperate regions but wildly unpredictable in tropical ones.
Revealing Hidden Patterns in Environmental Data
What's particularly clever about this approach is how it can reveal completely hidden patterns. The authors show examples where:
- Aquatic organisms don't just have different average heat tolerance than terrestrial ones – they also show much more variable responses
- Plant traits don't just change with elevation – they become increasingly unpredictable at higher elevations
- Smaller studies don't just report different effect sizes – they show systematically different levels of variability
For someone working with environmental data, this is revolutionary. How many times have we discarded or ignored patterns in our residuals? How often have we treated heteroscedasticity as merely a statistical problem rather than a biological signal?
Beyond Traditional Meta-Analysis
The framework also extends to meta-analysis, where they propose four types of publication bias rather than the traditional two. Beyond the well-known "small-study effect" and "decline effect," they introduce the "small-study divergence" and "Proteus effect" – patterns in the variance structure that were previously invisible to traditional methods.
Their Bayesian implementation (provided in detailed R code in their tutorial) makes the approach accessible to researchers with intermediate statistical skills. You'll need to understand random effects and be comfortable with R, but the barrier to entry isn't as high as you might fear.
Looking Forward
What excites me most is that this approach treats ecological complexity as information rather than noise. Instead of forcing our messy natural systems into statistical frameworks that demand consistency, we're adapting our statistics to match the reality of nature.
The authors mention that most published ecological and evolutionary meta-analyses could be reanalyzed using this framework – suggesting a treasure trove of new insights hiding in existing data.
Have you encountered location-scale models in your work? Are you considering implementing them? I'd be interested to hear experiences from those who've taken the plunge into modeling variance as a phenomenon of interest rather than just a statistical headache.
Want to learn more? Check out Nakagawa et al.'s 2025 paper in Global Change Biology and their accompanying online tutorial.
References
Bürkner, P. C. (2017). brms: An R package for Bayesian multilevel models using Stan. https://doi.org/10.18637/jss.v080.i01
Çınar, O., Nakagawa, S., & Viechtbauer, W. (2022). Phylogenetic multilevel meta-analysis: A simulation study on the importance of modeling the phylogeny. https://doi.org/10.1111/2041-210X.13760
Cleasby, I. R., & Nakagawa, S. (2011). Neglected biological patterns in the residuals: A behavioural ecologist's guide to co-operating with heteroscedasticity. https://doi.org/10.1007/s00265-011-1254-7
Cleasby, I. R., Nakagawa, S., & Schielzeth, H. (2015). Quantifying the predictability of behaviour: Statistical approaches for the study of between-individual variation in the within-individual variance. https://doi.org/10.1111/2041-210X.12281
Lee, Y., & Nelder, J. A. (1996). Hierarchical generalized linear models. https://doi.org/10.1111/j.2517-6161.1996.tb02105.x
Lee, Y., & Nelder, J. A. (2006). Double hierarchical generalized linear models (with discussion). https://doi.org/10.1111/j.1467-9876.2006.00538.x
Nakagawa, S., Mizuno, A., Morrison, K., Ricolfi, L., Williams, C., Drobniak, S. M., Lagisz, M., & Yang, Y. (2025). Location-scale meta-analysis and meta-regression as a tool to capture large-scale changes in biological and methodological heterogeneity: A spotlight on heteroscedasticity. https://doi.org/10.1111/gcb.70204
Nakagawa, S., Mizuno, A., Williams, C., Lagisz, M., Yang, Y., & Drobniak, S. M. (2025). Quantifying macro-evolutionary patterns of trait mean and variance with phylogenetic location-scale models. Evolution, 79(3), 745-762. https:/doi.org/10.1111/gcb.70204 [Note: This is the tutorial paper referenced in the blog]
Rönnegård, L., Felleki, M., Fikse, F., Mulder, H. A., & Strandberg, E. (2010). Genetic heterogeneity of residual variance-estimation of variance components using double hierarchical generalized linear models. https://doi.org/10.1186/1297-9686-42-8
Viechtbauer, W., & López-López, J. A. (2022). Location-scale models for meta-analysis. https://doi.org/10.1002/jrsm.1562