作为表达的模型

通常认为,模型在科学知识的组织和获得过程中起中心作用,大多数模型以某种方式表达了它们的目标系统。本文试图探讨的问题是关于模型如何表达它的目标系统。首先本文将引入模型的表达理论必须面对的两个基本问题,接下来将试图评述理论的语义观的解决方案所面临的问题及其原因,最后本文将对在何种方向上寻求模型的表达理论提出意见。     

Multidimensional Item Response Theory Models with Collateral Information as Poisson Regression Models

Multiple choice items on tests and Likert items on surveys are ubiquitous in educational, social and behavioral science research; however, methods for analyzing of such data can be problematic. Multidimensional item response theory models are proposed that yield structured Poisson regression models for the joint distribution of responses to items. The methodology presented here extends the approach described in Anderson, Verkuilen, and Peyton (2010) that used fully conditionally specified multinomial logistic regression models as item response functions. In this paper, covariates are added as predictors of the latent variables along with covariates as predictors of location parameters. Furthermore, the models presented here incorporate ordinal information of the response options thus allowing an empirical examination of assumptions regarding the ordering and the estimation of optimal scoring of the response options. To illustrate the methodology and flexibility of the models, data from a study on aggression in middle school (Espelage, Holt, and Henkel 2004) is analyzed. The models are fit to data using SAS.     

Metric Models for Random Graphs

Many problems entail the analysis of data that are independent and identically distributed random graphs. Useful inference requires flexible probability models for such random graphs; these models should have interpretable location and scale parameters, and support the establishment of confidence regions, maximum likelihood estimates, goodness-of-fit tests, Bayesian inference, and an appropriate analogue of linear model theory. Banks and Carley (1994) develop a simple probability model and sketch some analyses; this paper extends that work so that analysts are able to choose models that reflect application-specific metrics on the set of graphs. The strategy applies to graphs, directed graphs, hypergraphs, and trees, and often extends to objects in countable metric spaces.     

Modelling Experiments as Mediating Models

Syntactic and structural models specify relationships between their constituents but cannot show what outcomes their interaction would produce over time in the world. Simulation consists in iterating the states of a model, so as to produce behaviour over a period of simulated time. Iteration enables us to trace the implications and outcomes of inference rules and other assumptions implemented in the models that make up a theory. We apply this method to experiments which we treat as models of the particular aspects of reality they are designed to investigate. Scientific experiments are constantly designed and re-designed in the context of implementation and use. They mediate between theoretical understanding and the practicalities of engaging with the empirical and social world. In order to model experiments we need to identify and represent features that all experiments have in common. We treat these features as parameters of a general model of experiment so that by varying these parameters different types of experiment can be modelled.

Axiomatization and Models of Scientific Theories

In this paper we discuss two approaches to the axiomatization of scientific theories in the context of the so called semantic approach, according to which (roughly) a theory can be seen as a class of models. The two approaches are associated respectively to Suppes’ and to da Costa and Chuaqui’s works. We argue that theories can be developed both in a way more akin to the usual mathematical practice (Suppes), in an informal set theoretical environment, writing the set theoretical predicate in the language of set theory itself or, more rigorously (da Costa and Chuaqui), by employing formal languages that help us in writing the postulates to define a class of structures. Both approaches are called internal, for we work within a mathematical framework, here taken to be first-order ZFC. We contrast these approaches with an external one, here discussed briefly. We argue that each one has its strong and weak points, whose discussion is relevant for the philosophical foundations of science.     

Functional PCA and Base-Line Logit Models

In many statistical applications data are curves measured as functions of a continuous parameter as time. Despite of their functional nature and due to discrete-time observation, these type of data are usually analyzed with multivariate statistical methods that do not take into account the high correlation between observations of a single curve at nearby time points. Functional data analysis methodologies have been developed to solve these type of problems. In order to predict the class membership (multi-category response variable) associated to an observed curve (functional data), a functional generalized logit model is proposed. Base-line category logit formulations will be considered and their estimation based on basis expansions of the sample curves of the functional predictor and parameters. Functional principal component analysis will be used to get an accurate estimation of the functional parameters and to classify sample curves in the categories of the response variable. The good performance of the proposed methodology will be studied by developing an experimental study with simulated and real data.     

Visual Models in Analogical Problem Solving

Visual analogy is believed to be important in human problem solving. Yet, there are few computational models of visual analogy. In this paper, we present a preliminary computational model of visual analogy in problem solving. The model is instantiated in a computer program, called Galatea, which uses a language for representing and transferring visual information called Privlan. We describe how the computational model can account for a small slice of a cognitive-historical analysis of Maxwell’s reasoning about electromagnetism.     

Incorporating Student Covariates in Cognitive Diagnosis Models

In educational measurement, cognitive diagnosis models have been developed to allow assessment of specific skills that are needed to perform tasks. Skill knowledge is characterized as present or absent and represented by a vector of binary indicators, or the skill set profile. After determining which skills are needed for each assessment item, a model is specified for the relationship between item responses and skill set profiles. Cognitive diagnosis models are often used for diagnosis, that is, for classifying students into the different skill set profiles. Generally, cognitive diagnosis models do not exploit student covariate information. However, investigating the effects of student covariates, such as gender, SES, or educational interventions, on skill knowledge mastery is important in education research, and covariate information may improve classification of students to skill set profiles. We extend a common cognitive diagnosis model, the DINA model, by modeling the relationship between the latent skill knowledge indicators and covariates. The probability of skill mastery is modeled as a logistic regression model, possibly with a student-level random intercept, giving a higher-order DINA model with a latent regression. Simulations show that parameter recovery is good for these models and that inclusion of covariates can improve skill diagnosis. When applying our methods to data from an online tutor, we obtain reasonable and interpretable parameter estimates that allow more detailed characterization of groups of students who differ in their predicted skill set profiles.     

对运气解释模型的批判性考察

知识与运气的关系自柏拉图时代就被提起。但在当代西方知识论中,研究的重心却一直在知识的这一方,对运气的研究就没有那么深入和丰富。文章通过总结归纳学者们对运气的解释模型或观点,即重要性论题、缺乏控制力观点、概率性观点、模态解释和形而上学的解释,进行批判性考察。并借鉴其中的优点,发展出一个新的解释。     

Theory of Knowledge in System Dynamics Models

Having entered into the problem structuring methods, system dynamics (SD) is an approach, among systems’ methodologies, which claims to recognize the main structures of socio-economic behaviors. However, the concern for building or discovering strong philosophical underpinnings of SD, undoubtedly playing an important role in the modeling process, is a long-standing issue, in a way that there is a considerable debate about the assumptions or the philosophical foundations of it. In this paper, with a new perspective, we have explored theory of knowledge in SD models and found strange similarities between classic epistemological concepts such as justification and truth, and the mechanism of obtaining knowledge in SD models. In this regard, we have discussed related theories of epistemology and based on this analysis, have suggested some implications for moderating common problems in the modeling process of SD. Furthermore, this research could be considered a reword of system dynamics modeling principles in terms of theory of knowledge.     

Parsimonious Classification Via Generalized Linear Mixed Models

We devise a classification algorithm based on generalized linear mixed model (GLMM) technology. The algorithm incorporates spline smoothing, additive model-type structures and model selection. For reasons of speed we employ the Laplace approximation, rather than Monte Carlo methods. Tests on real and simulated data show the algorithm to have good classification performance. Moreover, the resulting classifiers are generally interpretable and parsimonious.     

Identifiablity of Models for Clusterwise Linear Regression

The model choice and the interpretation of the parameters are discussed as well as the use of the identifiability concept for fixed partition models. The concept is generalized to "partial identifiability".     

GME Estimation of Spatial Structural Equations Models

The objective of this paper is to develop a GME formulation for the class of spatial structural equations models (S-SEM). In this respect, two innovatory aspects are introduced: (i) the formalization of the GME estimation approach for structural equations models that account for spatial heterogeneity and spatial dependence; (ii) the extension of the methodology to a panel data framework. We also present an application of the method to real data finalized to investigate disparities of unemployment rates in OECD countries over the period 1998-2006.     

Mechanistic Explanations and Models in Molecular Systems Biology

Mechanistic models in molecular systems biology are generally mathematical models of the action of networks of biochemical reactions, involving metabolism, signal transduction, and/or gene expression. They can be either simulated numerically or analyzed analytically. Systems biology integrates quantitative molecular data acquisition with mathematical models to design new experiments, discriminate between alternative mechanisms and explain the molecular basis of cellular properties. At the heart of this approach are mechanistic models of molecular networks. We focus on the articulation and development of mechanistic models, identifying five constraints which guide the articulation of models in molecular systems biology. These constraints are not independent of one another, with the result that modeling becomes an iterative process. We illustrate the use of these constraints in the modeling of the mechanism for bistability in the lac operon.     

Mathematical Models and Reality: A Constructivist Perspective

To explore the relation between mathematical models and reality, four different domains of reality are distinguished: observer-independent reality (to which there is no direct access), personal reality, social reality and mathematical/formal reality. The concepts of personal and social reality are strongly inspired by constructivist ideas. Mathematical reality is social as well, but constructed as an autonomous system in order to make absolute agreement possible. The essential problem of mathematical modelling is that within mathematics there is agreement about ‘truth’, but the assignment of mathematics to informal reality is not itself formally analysable, and it is dependent on social and personal construction processes. On these levels, absolute agreement cannot be expected. Starting from this point of view, repercussion of mathematical on social and personal reality, the historical development of mathematical modelling, and the role, use and interpretation of mathematical models in scientific practice are discussed.