Model Selection via Focused Information Criteria for Complex Data in Ecology and Evolution

Abstract

Datasets encountered when examining deeper issues in ecology and evolution are often complex. This calls for careful strategies for both model building, model selection, and model averaging. Our paper aims at motivating, exhibiting, and further developing focused model selection criteria. In contexts involving precisely formulated interest parameters, these versions of FIC, the focused information criterion, typically lead to better final precision for the most salient estimates, confidence intervals, etc. as compared to estimators obtained from other selection methods. Our methods are illustrated with real case studies in ecology; one related to bird species abundance and another to the decline in body condition for the Antarctic minke whale.

Models and inference for on–off data via clipped Ornstein–Uhlenbeck processes

“…In many situations the research question concerns a clearly specified statistical quantity, and the statistical model works as a vehicle in providing inference about this specified quantity. The focused information criterion ( fic ) (Claeskens et al, 2019; Claeskens & Hjort, 2003, 2008; Cunen et al, 2020; Jullum & Hjort, 2017) takes this into account and aims at selecting the optimal model in terms of mean squared error for a prespecified statistical quantity. fic ‐theory can be developed for the quasi‐likelihood worked with in this paper, as well as for the general composite likelihood case (Varin et al, 2011), thus yielding the possibility of focused model selection in cases where the full likelihood is computationally infeasible.…”

“…For comparative purposes, we briefly present the model of Borgan et al (2007) and fit one such to the data, thereafter, we fit three different latent Ornstein–Uhlenbeck process models. The adequacy of the Ornstein–Uhlenbeck process models compared to the linear hazard models may be evaluated using the focused information criterion introduced in Jullum and Hjort (2017), and extended to regression models in Cunen, Walløe, and Hjort (2020) and Claeskens, Cunen, and Hjort (2019). Since such comparisons must be rather elaborate and would lead us too far afield, we do not pursue such a study of different model classes here.…”

Confidence Distributions for FIC Scores

“…This framework, having started with Hjort and Claeskens (2003a) and Claeskens and Hjort (2003), has been demonstrated to be very useful, leading to various FIC procedures in the literature, and now also to the extended and finessed FIC procedures of the present paper. A different and in some situations more satisfactory framework involves starting with a fixed wide model, and with no 'local asymptotics' involved; see the review paper Claeskens et al (2019) for general regression models and Cunen et al (2020) for classes of linear mixed models. The key results involve different approximations to mse quantities, along the lines of…”

“…Later extensions include Claeskens et al (2007) for time series models, Gueuning and Claeskens (2018) for high-dimensional setups, Hjort and Claeskens (2006) and for semiparametric and nonparametric survival regression models, Zhang and Liang (2011) for generalised additive models, Zhang et al (2012) for tobit models, Ko et al (2019) for copulae with two-stage estimation methods. Recent methodological extensions and advances also include setups centred on a fixed wide model, with large-sample approximations not depending on the local asymptotics methods; see Claeskens et al (2019); Hjort (2017, 2019), along with Cunen et al (2020) for linear mixed models. There is a growing list of application domains where FIC is finding practical and context-relevant use, such as finance and economics (Behl et al 2012;Brownlees and Gallo 2008), peace research and political science (Cunen et al 2020), sociology (Zhang et al 2012), marine science (Hermansen et al 2016), etc.…”

Focused model selection for linear mixed models with an application to whale ecology

“…Our last remark is to point out that crucially, the methodology developed here can be extended to FIC model selection methods also for several other classes of candidate models, in different regression frameworks, see Claeskens, Cunen and Hjort (2019). As long as there is a fixed wide model, under which results for each candidate model corresponding to (4.9) and (4.11) can be reached, then only few more steps are required to reach a FIC in that framework.…”