Matrix analysis of identifiability of some finite markov models

Methods developed by Bernbach [1966] and Millward [1969] permit increased generality in analyses of identifiability. Matrix equations are presented that solve part of the identifiability problem for a class of Markov models. Results of several earlier analyses are shown to involve special cases of the equations developed here. And it is shown that a general four-state chain has the same parameter space as an all-or-none model if and only if its representation with an observable absorbing state is lumpable into a Markov chain with three states.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45730/1/11336_2005_Article_BF02291365.pd

An analysis of some conditions for representing N state Markov processes as general all or none models

Recently Markov learning models with two unidentifiable presolution success states, an error state, and an absorbing learned state, have been suggested to handle certain aspects of data better than the three state Markov models of the General All or None model type. In attempting to interpret psychologically, and evaluate statistically the adequacy of various classes of Markov models, a knowledge of the relationship between the classes of models would be helpful. This paper considers some aspects of the relationship between the class of General All or None models and the class of Stationary Absorbing Markov models with N error states, and M presolution success states.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45728/1/11336_2005_Article_BF02290602.pd

Equivalence classes of functions of finite Markov chains

A matrical representation of a Markov chain consists of the initial vector and transition matrix of the chain, along with matrices that specify which observable response occurs for each state. The likelihood function based on a Markov model can be stated in a general way using the components of the model's matrical representation. It follows directly from that statement that two models are equivalent in likelihood if they are related through matrix operations that constitute a change of basis of the matrical representation. Two necessary properties of a change matrix associating two Markov models that are members of the same equivalence class with respect to likelihood are derived. Examples are provided, involving use of the results in analyzing identifiability of Markov models, including a useful application of diagonalization that provides a connection between the problem of identifiability and the eigenvalue problem.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/22239/1/0000675.pd

The fundamental cycle of concept construction underlying various theoretical frameworks

In this paper, the development of mathematical concepts over time is considered. Particular reference is given to the shifting of attention from step-by-step procedures that are performed in time, to symbolism that can be manipulated as mental entities on paper and in the mind. The development is analysed using different theoretical perspectives, including the SOLO model and various theories of concept construction to reveal a fundamental cycle underlying the building of concepts that features widely in different ways of thinking that occurs throughout mathematical learning

An academic health center cost analysis of screening mammography

BACKGROUND The current study sought to determine the institutional financial impact of a screening mammography (SM) program in the context of an integrated cancer center. METHODS Using administrative databases, 10,048 women were identified as receiving screening mammograms in fiscal year 1999 and the first one-half of fiscal year 2000. The utilization of breast care resources was followed for an average of 1208 days. The University of Michigan cost accounting system was then used to determine overall margin (revenues − total costs) and contribution margin (revenues − actual costs) of the SM program, as well as other breast care services. RESULTS The percentage of variable costs to total costs for the SM program was 24%. The overall facility losses in the breast care line were $1.7 million with a positive contribution margin of$2.0 million. The annual yield of nonscreening/diagnostic mammographic procedures was 0.9%. All types of radiologic activity failed to cover their total costs, but did provide a positive contribution margin. Overall margins for surgery procedures were approximately even, and adjuvant medical and radiotherapy services were net positive. Modeling helped to identify overhead limits necessary to achieve margin targets associated with increased activity. CONCLUSIONS The current study showed that SM programs are unlikely to succeed financially without careful selection of those screened to increase the yield of diagnostic and therapeutic procedures. Based on favorable contribution margins, SM programs were viable when viewed as incremental business. Cancer 2004. © 2004 by the American Cancer Society.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/34389/1/20476_ftp.pd

Konstruktivistische Ansätze in der Erwachsenenbildung und Weiterbildung

Theoretical approaches in the field of further education and advanced vocational training have to face multifaceted demands: the analysis of knowledge aquisition and knowledge transfer and its instructional support as well as the revealment of the mechanisms which influence further education on an organisational level in companies. This article describes, that herefore especially moderate constructivistic approaches are useful. After an introduction to the philosophical tradition of these approaches and important characteristics of adult learning, two examples of constructivistic models are being described particularly: The theory of situated learning environments and career counseling. Concluding it is shown, that a moderate constructive perspective fulfils important criteria for the theoretic modelling of further education processes.Theoretische Ansätze in der Erwachsenen- und insbesondere in der beruflichen Weiterbildung müssen sich vielfältigen Ansprüchen stellen: der Analyse des Wissenserwerbs und Wissenstransfers und seiner instruktionalen Unterstützung ebenso wie der Aufdeckung der Mechanismen, die in den Betrieben auf organisatorischer Ebene die Weiterbildung beeinflussen. In diesem Beitrag wird die Auffassung vertreten, daß dafür insbesondere liberalisierte konstruktivistische Ansätze gut geeignet sind. Nach einer Einführung in die philosophische Tradition dieser Ansätze und wichtiger Merkmale des Lernens im Erwachsenenalter werden zwei Beispiele konstruktivistischer Modelle genauer beschrieben: die Theorie situierter Lernumgebungen und das career counseling. Abschließend wird gezeigt, daß eine liberalisierte konstruktivistische Perspektive wichtige Kriterien für die theoretische Modellierung von Weiterbildungsprozessen erfüllt

Do student perceptions of teaching predict the development of representational competence and biological knowledge?

Dealing with representations is a crucial skill for students and such representational competence is essential for learning science. This study analysed the relationship between representational competence and content knowledge, student perceptions of teaching practices concerning the use of different representations, and their impact on students’ outcome over a teaching unit. Participants were 931 students in 51 secondary school classes. Representational competence and content knowledge were interactively related. Representational aspects were only moderately included in teaching and students did not develop rich representational competence although content knowledge increased significantly. Multilevel regression showed that student perceptions of interpreting and constructing visual-graphical representations and active social construction of knowledge predicted students’ outcome at class level, whereas the individually perceived amount of terms and use of symbolic representations influenced the students’ achievement at individual level. Methodological and practical implications of these findings are discussed in relation to the development of representational competence in classrooms