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.This research was supported by the U.S. Public Health Service under Grant MH-12717 to Indiana University and Grant GM-1231 to the University of Michigan.Now at the University of Texas, Austin.     

Identifiability and statistical properties of two-stage learning with no successes in the initial stage

A model is considered for learning where there is an initial stage with only errors, an intermediate state with errors and correct responses, and an absorbing state with only correct responses. A model with observable states is constructed, and sufficient identifiable parameters are given for the original model. Distribution statistics and other properties of data are derived as functions of the identifiable parameters. Informal estimates and sufficient statistics are given for the identifiable parameters. A number of testable hypotheses about the theoretical parameters are described. Some identifying restrictions for the model are given, along with the estimates for the unrestricted free parameters which follow. An application is made to data from a pairedassociate learning experiment.This research was sponsored by NSF Grant GB2791 and by PHS Grant MH12717. Part of the work was done while the author held a visiting faculty appointment at Stanford University.     

The Effectiveness of Models and Prompts on Waste Diversion: A Field Experiment on Composting by Cafeteria Patrons

This study investigated whether or not visual prompts and human models influence compost‐supportive behavior by individuals in a cafeteria setting. Waste disposal behavior of cafeteria patrons was observed (N = 1,060) after the introduction of (1) pro‐composting signs, and (2) models who demonstrated appropriate composting behavior. Ideal composting significantly increased relative to the baseline with the introduction of the signs (from 12.5% to 20.5%). A further increase (to 42%) was observed when two (but not one) individuals modeled the behavior, and this increase was sustained even after the models were removed. Informational and normative influences may explain the increase in composting. This study further supports the use of prompts and models as a strategy for encouraging pro‐environmental behaviors.     

Searching for a two-factor model of marriage duration: commentary on Gottman and Levenson

Gottman and Levenson (2002) report a number of post hoc ordinary least squares regressions to "predict" the length of marriage, given that divorce has occurred. We argue that the type of statistical model they use is inappropriate for answering clinically relevant questions about the causes and timing of divorce, and present several reasons why an alternative family of models called duration models would be more appropriate. The distribution of marriage length is not bimodal, as Gottman and Levenson suggest, and their search for a two-factor model for explaining marriage length is misguided. Their regression models omit many variables known to affect marriage length, and instead use variables that were pre-screened for their predictive ability. Their final model is based on data for only 15 cases, including one unusual case that has undue influence on the results. For these and other technical reasons presented in the text, we believe that Gottman and Levenson's results are not replicable, and that they should not be used to guide interventions for couples in clinical settings.     

A Model of Competence for Counting

A theoretical framework Is presented that distinguishes among three knowledge sources that form the basis for generative performance. The three knowledge sources, termed conceptual, procedural, and utilizational competence, were implemented as a computational model that derives plans for counting procedures. In a previous analysis, Greeno, Riley, and Gelman (1984) developed a characterization of the conceptual competence (implicit understanding of general concepts and principles) associated with the skill of counting and related conceptual competence to various models of performance. In the current work all three knowledge sources are formalized in a computer program (COUNTPLAN) that generates planning nets of counting procedures. The sufficiency of COUNTPLAN's knowledge components is demonstrated through its capacity to generate new plans for counting in novel settings from a core of conceptual competence. The utility of COUNTPLAN to facilitate the distinction between hypotheses of competence and hypotheses of performance is discussed.     

Effects of meaningfulness and organization on problem solving and computability judgments

When subjects were required to calculate answers for computable problems and answer questions, an interaction was found corresponding to that obtained by Kieras and Greeno (1975) from judgments of computability. With nonsense formulas, much longer times were required to identify noncomputable problems than to compute answers, with a much smaller difference when formulas consisted of meaningful concepts. The better performance on noncomputable problems and questions with meaningful formulas corroborates an interpretation that those items test the connection of algorithms with general conceptual knowledge. Finally, it was found that for relatively complex problems, solution times and time to judge computability were longer if nonsense formulas were learned in separate sets than if they were learned in a single set; however, no such effect was found with meaningful formulas. It was concluded that learning conditions influenced the integration of cognitive structure in the case of nonsense formulas, while subjects were able to adjust organization of the meaningful formulas.     

Time to read semantically related sentences*

Ss read sentences specifying relations among concepts, with the sentences related to each other in different hierarchical structures. In the case where sentences had implicative relationships, time to read sentences low in the hierarchy was less if sentences higher in the hierarchy had been read previously, and sentences inconsistent with expectations based on earlier items took longer. However, when structural relations did not involve implication about content, time to read the sentences was not very different regardless of whether related sentences had been read previously.     

Goodness-of-fit tests for models of latency and choice

A goodness-of-fit test based on the maximum likelihood criterion is derived for use in evaluating models of choice reaction time that predict choice probabilities and means and variances of latency. Special cases of the test involving models that predict only one or two of these statistics are considered and shown to be asymptotically identical to the traditional goodness-of-fit tests appropriate for these special cases.