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

Cunen, Céline; Walløe, Lars; Hjort, Nils Lid

doi:10.1214/20-aoas1331

Cited by 9 publications

(12 citation statements)

References 41 publications

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“…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.…”

Section: Discussionmentioning

confidence: 99%

“…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.…”

Section: The Brazilian Datamentioning

confidence: 99%

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

Stoltenberg

Hjort

2020

Scandinavian J Statistics

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We introduce a model for recurrent event data subject to left-, right-, and intermittent-censoring. The observations consist of binary sequences (along with covariates) for each individual under study. These sequences are modeled as generated by latent Ornstein-Uhlenbeck processes being above or below certain thresholds. Features of the latent process and the thresholds are taken as functions of covariates, allowing the researcher to distinguish factors that have an effect on the frailty, from those that have an effect on the variability, of the observational unit. Inference is achieved by a quasi-likelihood approach, for which consistency and asymptotic normality is established. An advantage of our model is that particularities regarding the censoring need not be taken actively into account, and that it is well suited for situations where the individuals under study are irregularly and asynchronously observed. The motivation for our model came from a dataset pertaining to the incidence of diarrhoea among Brazilian children growing up under rather harsh conditions. We analyze these data with our model and contrast the results with an intensity-based counting process analysis of the same data.

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Section: Discussionmentioning

confidence: 99%

Section: The Brazilian Datamentioning

confidence: 99%

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

Stoltenberg

Hjort

2020

Scandinavian J Statistics

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“…Finally, we include random effects, and our regression model falls therefore into the class of mixed-effect models, see Demidenko (2013), Pinheiro and Bates (2000) and Cunen et al (2020). Mixed-effect models are often used when the observations form natural groups, which typically correspond to observations collected at close to the same location or time.…”

Section: Data and Model Buildingmentioning

confidence: 99%

“…The different strategies all have the same goal, but use different mathematical approximation tools, and can therefore have somewhat different forms. In our case, we use the formulae from Cunen et al (2020), which are derived specifically for the class of linear mixed-effects models. All FIC strategies require the biases and variances in (3) to be defined with respect to a wide model.…”

Section: Focused Model Selectionmentioning

confidence: 99%

Decline in body condition in the Antarctic minke whale (Balaenoptera bonaerensis) in the Southern Ocean during the 1990s

Cunen

Walløe

Konishi³

et al. 2021

Polar Biol

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Changes in the body condition of Antarctic minke whales (Balaenoptera bonaerensis) have been investigated in a number of studies, but remain contested. Here we provide a new analysis of body condition measurements, with particularly careful attention to the statistical model building and to model selection issues. We analyse body condition data for a large number (4704) of minke whales caught between 1987 and 2005. The data consist of five different variables related to body condition (fat weight, blubber thickness and girth) and a number of temporal, spatial and biological covariates. The body condition variables are analysed using linear mixed-effects models, for which we provide sound biological motivation. Further, we conduct model selection with the focused information criterion (FIC), reflecting the fact that we have a clearly specified research question, which leads us to a clear focus parameter of particular interest. We find that there has been a substantial decline in body condition over the study period (the net declines are estimated to 10% for fat weight, 7% for blubber thickness and 3% for the girth). Interestingly, there seems to be some differences in body condition trends between males and females and in different regions of the Antarctic. The decline in body condition could indicate major changes in the Antarctic ecosystem, in particular, increased competition from some larger krill-eating whale species.

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“…For comparison with our method, we implement the observed best selective predictor (OBSP) of Sugasawa et al (2019) and study its performance in simulations in Section 6. The issue of accounting for the model selection in the context of LMM has been also mentioned by Cunen et al (2020), but the authors did not approach it in their article.…”

Section: Introductionmentioning

confidence: 99%

Post-selection inference for linear mixed model parameters using the conditional Akaike information criterion

Claeskens,

Reluga,

Sperlich

2021

Preprint

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We investigate the issue of post-selection inference for a fixed and a mixed parameter in a linear mixed model using a conditional Akaike information criterion as a model selection procedure. Within the framework of linear mixed models we develop complete theory to construct confidence intervals for regression and mixed parameters under three frameworks: nested and general model sets as well as misspecified models. Our theoretical analysis is accompanied by a simulation experiment and a post-selection examination on mean income across Galicia's counties. Our numerical studies confirm a good performance of our new procedure. Moreover, they reveal a startling robustness to the model misspecification of a naive method to construct the confidence intervals for a mixed parameter which is in contrast to our findings for the fixed parameters.

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

Cited by 9 publications

References 41 publications

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

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

Decline in body condition in the Antarctic minke whale (Balaenoptera bonaerensis) in the Southern Ocean during the 1990s

Post-selection inference for linear mixed model parameters using the conditional Akaike information criterion

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