Mark-recapture models are extensively used in quantitative population ecology, providing estimates of population vital rates, such as survival, that are difficult to obtain using other methods. Vital rates are commonl...Mark-recapture models are extensively used in quantitative population ecology, providing estimates of population vital rates, such as survival, that are difficult to obtain using other methods. Vital rates are commonly modeled as functions of explanatory covariates, adding considerable flexibility to mark-recapture models, but also increasing the subjectivity and complexity of the modeling process. Consequently, model selection and the evaluation of covariate structure remain critical aspects of mark-recapture modeling. The difficulties involved in model selection are compounded in Cormack-Jolly-Seber models because they are composed of separate sub-models for survival and recapture probabilities, which are conceptualized independently even though their parameters are not statistically independent. The construction of models as combinations of sub-models, together with multiple potential covariates, can lead to a large model set. Although desirable, estimation of the parameters of all models may not be feasible. Strategies to search a model space and base inference on a subset of all models exist and enjoy widespread use. However, even though the methods used to search a model space can be expected to influence parameter estimation, the assessment of covariate importance, and therefore the ecological interpretation of the modeling results, the performance of these strategies has received limited investigation. We present a new strategy for searching the space of a candidate set of Cormack-Jolly-Seber models and explore its performance relative to existing strategies using computer simulation. The new strategy provides an improved assessment of the importance of covariates and covariate combinations used to model survival and recapture probabilities, while requiring only a modest increase in the number of models on which inference is based in comparison to existing techniques.展开更多
For semiparametric regression model selection, based on a model selection criterion there is no finite order (or number of parameters) of the nonparametric part to be estimated consistently, but there is a finite orde...For semiparametric regression model selection, based on a model selection criterion there is no finite order (or number of parameters) of the nonparametric part to be estimated consistently, but there is a finite order (or number of predictor variables) of the linear part to be estimated consistently. The models selected by using AIC and AICC are not consistent estimates of linear part of the true model. In this paper, we study the consistency in model selection by investigating the asymptotic properties of AIC* and AICC*, the modified versions of AIC and AICC respectively, which were proposed by a referee of the reference Shi and Tsai. Under some regular conditions, we prove that the parametric models of the semiparametric regression selected with AIC* and AICC* converge to the true model in probability. In addition, in terms of the mean integrated squared error plus a penalty, these two criteria can also provide an asymptotically efficient selection.展开更多
文摘Mark-recapture models are extensively used in quantitative population ecology, providing estimates of population vital rates, such as survival, that are difficult to obtain using other methods. Vital rates are commonly modeled as functions of explanatory covariates, adding considerable flexibility to mark-recapture models, but also increasing the subjectivity and complexity of the modeling process. Consequently, model selection and the evaluation of covariate structure remain critical aspects of mark-recapture modeling. The difficulties involved in model selection are compounded in Cormack-Jolly-Seber models because they are composed of separate sub-models for survival and recapture probabilities, which are conceptualized independently even though their parameters are not statistically independent. The construction of models as combinations of sub-models, together with multiple potential covariates, can lead to a large model set. Although desirable, estimation of the parameters of all models may not be feasible. Strategies to search a model space and base inference on a subset of all models exist and enjoy widespread use. However, even though the methods used to search a model space can be expected to influence parameter estimation, the assessment of covariate importance, and therefore the ecological interpretation of the modeling results, the performance of these strategies has received limited investigation. We present a new strategy for searching the space of a candidate set of Cormack-Jolly-Seber models and explore its performance relative to existing strategies using computer simulation. The new strategy provides an improved assessment of the importance of covariates and covariate combinations used to model survival and recapture probabilities, while requiring only a modest increase in the number of models on which inference is based in comparison to existing techniques.
基金This research supported in part by Postdoctoral Science Foundation and NSF of China.
文摘For semiparametric regression model selection, based on a model selection criterion there is no finite order (or number of parameters) of the nonparametric part to be estimated consistently, but there is a finite order (or number of predictor variables) of the linear part to be estimated consistently. The models selected by using AIC and AICC are not consistent estimates of linear part of the true model. In this paper, we study the consistency in model selection by investigating the asymptotic properties of AIC* and AICC*, the modified versions of AIC and AICC respectively, which were proposed by a referee of the reference Shi and Tsai. Under some regular conditions, we prove that the parametric models of the semiparametric regression selected with AIC* and AICC* converge to the true model in probability. In addition, in terms of the mean integrated squared error plus a penalty, these two criteria can also provide an asymptotically efficient selection.
