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PubMed1972

Maintenance of genetic variation with a frequency-dependent selection model as compared to the overdominant model.

A frequency-dependent selection model proposed by Huang, Singh and Kojima (1971) was found to be more effective at maintaining genetic variation in a finite population than the overdominant model. The fourth moment parameter of the distribution of unfixed states showed that there was a more platykurtic distribution for the frequency-dependent model. This agreed well with the expected gene frequency change found for an infinite population.

Analysis of Variance↗

PubMed1997

Discriminant analysis using the unweighted sum of binary variables: a comparison of model selection methods.

Many clinical decision-making rules are equivalent to linear discriminant functions that involve the unweighted sum of binary variables (SBV). We briefly consider the geometry of this restriction and then propose a number of methods for forward stepwise selection of SBV models. Using a simulation study, we compare the performance of these methods under a wide range of plausible conditions and show that no single method is uniformly superior for selecting models of a fixed size. Factors of general importance in relative method performance are the ratio of sample size to the number of candidate variables and the class-conditional moment structure of the data. We conclude by offering some practical strategies for SBV model construction.

Computer Simulation↗

PubMed1992

A worst-case optimal parameter selection model of cancer chemotherapy.

An optimal parameter selection model of cancer chemotherapy in which two system parameters are unknown is formulated as a worst-case optimal parameter selection model. The model assumes that the unknown parameters lie within a known set. The system constraints must be satisfied over this entire set, and the objective function minimized in the worst case. The continuous dependence of the objective function and the system constraints upon the unknown parameters can be removed, making a numerical solution tractable. For the data considered it is proven that a cure is impossible no matter what the values of the unknown parameters in the parameter set. The optimal policy is shown to be relatively low dose intensity for the majority of the treatment, with the remaining drug delivered towards the end of the treatment interval.

Humans↗

PubMed2001

Model selection in non-nested hidden Markov models for ion channel gating.

An important task in the application of Markov models to the analysis of ion channel data is the determination of the correct gating scheme of the ion channel under investigation. Some prior knowledge from other experiments can reduce significantly the number of possible models. If these models are standard statistical procedures nested like likelihood ratio testing, provide reliable selection methods. In the case of non-nested models, information criteria like AIC, BIC, etc., are used. However, it is not known if any of these criteria provide a reliable selection method and which is the best one in the context of ion channel gating. We provide an alternative approach to model selection in the case of non-nested models with an equal number of open and closed states. The models to choose from are embedded in a properly defined general model. Therefore, we circumvent the problems of model selection in the non-nested case and can apply model selection procedures for nested models.

Animals↗

PubMed1991

Tests and model selection for the general growth curve model.

The model considered here is a generalized multivariate analysis of variance model useful especially for many types of growth curve problems including biological growth and technology substitution. It is defined as Yp x N = Xp x m tau m x r Ar x N + epsilon p x N, where tau is unknown, and X and A are known design matrices of ranks m less than p and r less than N, respectively. Furthermore, the columns of epsilon are independent p-variate normal with mean vector 0 and common covariance matrix sigma. In general, p is the number of time (or spatial) points observed on each of the N cases, (m - 1) is the degree of polynomial in time, and r is the number of groups. The main focus of this paper is the selection of models for the general growth curve model with regard to the covariance matrix sigma. Likelihood ratio tests and selection procedures based on sample reuse and predictions are proposed. Special emphasis is on the serial covariance structure for sigma, which has been shown to be quite important in the prediction of biological data and technology substitution data. One-population and K-population problems are considered. Some of the results are illustrated with two sets of biological data.

Animals↗

PubMed1995

Model selection for extended quasi-likelihood models in small samples.

We develop a small sample criterion (AICc) for the selection of extended quasi-likelihood models. In contrast to the Akaike information criterion (AIC). AICc provides a more nearly unbiased estimator for the expected Kullback-Leibler information. Consequently, it often selects better models than AIC in small samples. For the logistic regression model, Monte Carlo results show that AICc outperforms AIC, Pregibon's (1979, Data Analytic Methods for Generalized Linear Models. Ph.D. thesis. University of Toronto) Cp*, and the Cp selection criteria of Hosmer et al. (1989, Biometrics 45, 1265-1270). Two examples are presented.

Age Factors↗

PubMed2001

Best harmony, unified RPCL and automated model selection for unsupervised and supervised learning on Gaussian mixtures, three-layer nets and ME-RBF-SVM models.

After introducing the fundamentals of BYY system and harmony learning, which has been developed in past several years as a unified statistical framework for parameter learning, regularization and model selection, we systematically discuss this BYY harmony learning on systems with discrete inner-representations. First, we shown that one special case leads to unsupervised learning on Gaussian mixture. We show how harmony learning not only leads us to the EM algorithm for maximum likelihood (ML) learning and the corresponding extended KMEAN algorithms for Mahalanobis clustering with criteria for selecting the number of Gaussians or clusters, but also provides us two new regularization techniques and a unified scheme that includes the previous rival penalized competitive learning (RPCL) as well as its various variants and extensions that performs model selection automatically during parameter learning. Moreover, as a by-product, we also get a new approach for determining a set of 'supporting vectors' for Parzen window density estimation. Second, we shown that other special cases lead to three typical supervised learning models with several new results. On three layer net, we get (i) a new regularized ML learning, (ii) a new criterion for selecting the number of hidden units, and (iii) a family of EM-like algorithms that combines harmony learning with new techniques of regularization. On the original and alternative models of mixture-of-expert (ME) as well as radial basis function (RBF) nets, we get not only a new type of criteria for selecting the number of experts or basis functions but also a new type of the EM-like algorithms that combines regularization techniques and RPCL learning for parameter learning with either least complexity nature on the original ME model or automated model selection on the alternative ME model and RBF nets. Moreover, all the results for the alternative ME model are also applied to other two popular nonparametric statistical approaches, namely kernel regression and supporting vector machine. Particularly, not only we get an easily implemented approach for determining the smoothing parameter in kernel regression, but also we get an alternative approach for deciding the set of supporting vectors in supporting vector machine.

Algorithms↗

PubMed1998

The application of sample selection models to outcomes research: the case of evaluating the effects of antidepressant therapy on resource utilization.

Non-randomized studies of treatment effects have come under criticism because of their failure to control for potential biases introduced by unobserved variables correlated with treatment selection and outcomes. This paper describes the basic concepts of sample selection models--a technique used widely in the economics evaluation literature for nearly two decades--and discusses the potential role of these models in outcomes research. In addition, it presents a case study of the application of the sample selection modelling approach to evaluation of the effects of antidepressant therapies on medical expenditures for physician services. This case study presents empirical comparisons of alternative model specifications and discusses practical issues in evaluation of sample selection models. We demonstrate that, in this particular case, sample selection models yield very different conclusions regarding treatment effects than traditional ordinary least squares regression.

Antidepressive Agents↗

PubMed1988

A general asymptotic property of two-locus selection models.

It is shown that any two-locus, two-allele model of selection with constant fitnesses has at least one polymorphic equilibrium for which the linkage association measure, D, is arbitrarily close to zero for large enough recombination, R. As R----+/- infinity, D----0 in such a way that the product l = RD----a non-zero finite constant. There may be 1, 3, or 5 distinct asymptotic equilibria, depending upon fitness parameters.

Alleles↗

PubMed1996

Cooperative selection of movements: the optimal selection model.

How one selects a movement when faced with alternative ways of doing a task is a central problem in human motor control. Moving the fingertip a short distance can be achieved with any of an infinite number of combinations of knuckle, wrist, elbow, shoulder, and hip movements. The question therefore arises: how is a unique combination chosen? In our model, choice is achieved by consideration of the similarity between the task requirements and the optimal biomechanical performance of each limb segment. Two variants of the model account for the movements that are selected when subjects freely oscillate the fingertip and when they tap against an obstacle. An important feature of both is that the impulse of collision with an obstacle (as in drumming with the hand or tapping with the finger) is assumed to be controlled in part by aiming for a point beyond the surface being struck. Thus, a force-related control variable may be represented and controlled spatially.

Arm↗

PubMed1999

Computing minimum description length for robust linear regression model selection.

A minimum description length (MDL) and stochastic complexity approach for model selection in robust linear regression is studied in this paper. Computational aspects and implementation of this approach to practical problems are the focuses of the study. Particularly, we provide both algorithms and a package of S language programs for computing the stochastic complexity and proceeding with the associated model selection. A simulation study is then presented for illustration and comparing the MDL approach with the commonly used AIC and BIC methods. Finally, an application is given to a physiological study of triathlon athletes.

Algorithms↗

PubMed2000

Counting probability distributions: differential geometry and model selection.

A central problem in science is deciding among competing explanations of data containing random errors. We argue that assessing the "complexity" of explanations is essential to a theoretically well-founded model selection procedure. We formulate model complexity in terms of the geometry of the space of probability distributions. Geometric complexity provides a clear intuitive understanding of several extant notions of model complexity. This approach allows us to reconceptualize the model selection problem as one of counting explanations that lie close to the "truth." We demonstrate the usefulness of the approach by applying it to the recovery of models in psychophysics.

Models, Theoretical↗

PubMedDate not supplied

The multifocused faculty selection model: a design for hiring the best faculty.

The multifocused faculty selection model is designed to assist the faculty search committee in two ways. First, this model organizes the stages for obtaining information about the applicant's abilities related to faculty performance. Second, the model provides a consistent method for faculty selection as the membership of the department's search committee changes. The applicant selection techniques used in this model include descriptive interviewing, computer assisted data, and the teaching demonstration.

Faculty, Nursing↗

PubMed1975

General kin selection models for genetic evolution of sib altruism in diploid and haplodiploid species.

A population genetic approach is presented for general analysis and comparison of kin selection models of sib and half-sib altruism. Nine models are described, each assuming a particular mode of inheritance, number of female inseminations, and Mendelian dominance of the altruist gene. In each model, the selective effects of altruism are described in terms of two general fitness functions, A(beta) and S(beta), giving respectively the expected fitness of an altruist and a nonaltruist as a function of the fraction of altruists beta in a given sibship. For each model, exact conditions are reported for stability at altruist and nonaltruist fixation. Under the Table 3 axions, the stability conditions may then be partially ordered on the basis of implications holding between pairs of conditions. The partial orderings are compared with predictions of the kin selection theory of Hamilton.

Biological Evolution↗

PubMed1999

Selection models and pattern-mixture models for incomplete data with covariates.

Most models for incomplete data are formulated within the selection model framework. This paper studies similarities and differences of modeling incomplete data within both selection and pattern-mixture settings. The focus is on missing at random mechanisms and on categorical data. Point and interval estimation is discussed. A comparison of both approaches is done on side effects in a psychiatric study.

Biometry↗

PubMed1984

Evolutionarily stable strategies in food selection models with fitness sets.

Most current models for optimal food selection apply to ecological and behavioural optimization. In this paper optimal food selection theory is extended to apply to evolutionary optimization. A general evolutionary model for optimal food selection must incorporate the concept of fitness sets--or that variables, changing as a result of natural selection in evolutionary time, cannot, in general, vary independently of each other. A "Charnov type" optimal food selection model with a fitness set is investigated, and evolutionarily stable strategy (ESS) solutions of the evolutionary variables (i.e., the efficiencies of using available food types) are found. From this analysis it follows that the relative frequency of various food types in the environment may, under specified conditions, influence the evolutionarily optimal diet. Secondly, the analysis demonstrates that a food type not in the optimal diet may, in evolutionary time, be added to this by becoming more abundant. Thirdly, it follows from the analysis that the ecological result of MacArthur and Pianka, that food types are worth eating even if there is competition for them, is not generally applicable when referring to an evolutionary time scale. Finally, it is pointed out that for the diet to be an ESS, it is necessary that the consumer's density is stable and that the consumer's population dynamics are subjected to some density-dependent factor.

Animals↗

PubMed1998

Pedigree analysis package (PAP) vs. MORGAN: model selection and hypothesis testing on a large pedigree.

The MORGAN package of programs is compared to a commonly used package, PAP, with respect to model selection in segregation analysis of a quantitative trait. MORGAN uses Monte Carlo Markov chain (MCMC) methods to estimate the likelihood, whereas both versions of PAP used employ an approximation to the likelihood for the mixed model. Comparisons are done by using results obtained from simulated data. All simulations were done on the same 232-member pedigree using data generated under each of several variations of models, which included different combinations of environmental, polygenic, and major gene components. PAP, version 4.0, and MORGAN gave similar results with respect to model selection for the majority of situations, suggesting that MCMC methods provide a computationally tractable approach for analysis of more complex models that cannot be analyzed by more direct computational methods. PAP, version 3.0, gave somewhat more disparate results compared with either PAP version 4.0 or MORGAN. Both MORGAN and the two versions of PAP confirmed that the major gene component is much easier to detect in the presence of some dominance. All three packages frequently falsely accepted the polygenic model when there was high residual heritability.

Computer Simulation↗

PubMed2000

Model Selection Based on Minimum Description Length.

We introduce the minimum description length (MDL) principle, a general principle for inductive inference based on the idea that regularities (laws) underlying data can always be used to compress data. We introduce the fundamental concept of MDL, called the stochastic complexity, and we show how it can be used for model selection. We briefly compare MDL-based model selection to other approaches and we informally explain why we may expect MDL to give good results in practical applications. Copyright 2000 Academic Press.

Journal Article↗