An incomplete data approach to the analysis of covariance structures

In this paper, linear structural equation models with latent variables are considered. It is shown how many common models arise from incomplete observation of a relatively simple system. Subclasses of models with conditional independence interpretations are also discussed. Using an incomplete data point of view, the relationships between the incomplete and complete data likelihoods, assuming normality, are highlighted. For computing maximum likelihood estimates, the EM algorithm and alternatives are surveyed. For the alternative algorithms, simplified expressions for computing function values and derivatives are given. Likelihood ratio tests based on complete and incomplete data are related, and an example on using their relationship to improve the fit of a model is given.This research forms part of the author's doctoral thesis and was supported by a Commonwealth Postgraduate Research Award. The author also wishes to acknowledge the support of CSIRO during the preparation of this paper and the referees' comments which led to substantial improvements.     

The analysis of multitrait-multimethod matrices via constrained components analysis

Multitrait-Multimethod (MTMM) matrices are often analyzed by means of confirmatory factor analysis (CFA). However, fitting MTMM models often leads to improper solutions, or non-convergence. In an attempt to overcome these problems, various alternative CFA models have been proposed, but with none of these the problem of finding improper solutions was solved completely. In the present paper, an approach is proposed where improper solutions are ruled out altogether and convergence is guaranteed. The approach is based on constrained variants of components analysis (CA). Besides the fact that these methods do not give improper solutions, they have the advantage that they provide component scores which can later on be used to relate the components to external variables. The new methods are illustrated by means of simulated data, as well as empirical data sets.This research has been made possible by a fellowship from the Royal Netherlands Academy of Arts and Sciences to the first author. The authors are obliged to three anonymous reviewers and an associate editor for constructive suggestions on the first version of this paper.     

Using aspiration levels in an interior primal-dual multiobjective linear programming algorithm

We introduce in this paper a new multiple-objective linear programming (MOLP) algorithm. The algorithm is based on the single-objective path-following primal—dual linear programming algorithm and combines it with aspiration levels and the use of achievement scalarizing functions. The resulting algorithm falls in the class of interactive MOLP algorithms, as it requires interaction with the decision maker (DM) during the iterative process to obtain statements of aspirations for levels of objectives of the MOLP problem. The interior point algorithm is then used to trace a path of interates from a current (interior) solution and approach as closely as desired a non-dominated solution corresponding to the optimum of the achievement scalarizing function. The timing of the interaction with the DM is dependent on the progress of the interior algorithm. It can take place every few, pre-specified, iterations or after the duality gap achieved for the stated aspirations has fallen below a certain threshold. It is expected that an interior algorithm will speed up the overall process of searching and finding the most preferred MOLP solution—especially in large-scale problems—by avoiding the need for numerous pivot operations and their corresponding interactive sessions inherent in simplex-based algorithms.     

Recent Developments in the Treatment of Depression

The cognitive and behavioral interventions can be as efficacious as antidepressant medications and more enduring, but some patients will be more likely to respond to one than the other. Recent work has focused on developing sophisticated selection algorithms using machine-learning approaches that answer the question, “What works best for whom?” Moreover, the vast majority of people suffering from depression reside in low- and middle-income countries where access to either psychotherapy or medications is virtually nonexistent. Great strides have been made in training nonspecialist providers (known as task sharing) to overcome this gap. Finally, recent work growing out of evolutionary psychology suggests that antidepressant medications may suppress symptoms at the expense of prolonging the underlying episode so as to increase the risk of relapse whenever someone tries to stop. We address each of these developments and their cumulative implications.     

Regularization of languages by adults and children: A mathematical framework

The fascinating ability of humans to modify the linguistic input and “create” a language has been widely discussed. In the work of Newport and colleagues, it has been demonstrated that both children and adults have some ability to process inconsistent linguistic input and “improve” it by making it more consistent. In Hudson Kam and Newport (2009), artificial miniature language acquisition from an inconsistent source was studied. It was shown that (i) children are better at language regularization than adults and that (ii) adults can also regularize, depending on the structure of the input. In this paper we create a learning algorithm of the reinforcement-learning type, which exhibits patterns reported in Hudson Kam and Newport (2009) and suggests a way to explain them. It turns out that in order to capture the differences between children’s and adults’ learning patterns, we need to introduce a certain asymmetry in the learning algorithm. Namely, we have to assume that the reaction of the learners differs depending on whether or not the source’s input coincides with the learner’s internal hypothesis. We interpret this result in the context of a different reaction of children and adults to implicit, expectation-based evidence, positive or negative. We propose that a possible mechanism that contributes to the children’s ability to regularize an inconsistent input is related to their heightened sensitivity to positive evidence rather than the (implicit) negative evidence. In our model, regularization comes naturally as a consequence of a stronger reaction of the children to evidence supporting their preferred hypothesis. In adults, their ability to adequately process implicit negative evidence prevents them from regularizing the inconsistent input, resulting in a weaker degree of regularization.     

Through neural stimulation to behavior manipulation: a novel method for analyzing dynamical cognitive models

The dynamical systems' approach to cognition (Dynamicism) promises computational models that effectively embed cognitive processing within its more natural behavioral context. Dynamical cognitive models also pose difficult, analytical challenges, which motivate the development of new analytical methodology. We start by illustrating the challenge by applying two conventional analytical methods to a well-known Dynamicist model of categorical perception. We then introduce our own analysis, which works by analogy with neural stimulation methods, and which yields some novel insights into the way the model works. We then extend and apply the method to a second Dynamicist model, which captures the key psychophysical trends that emerge when humans and animals compare two numbers. The results of the analysis-which reveals units with tuning functions that are monotonically related to the magnitudes of the numbers that the agents must compare-offer a clear contribution to the contentious debate concerning the way number information is encoded in the brain.     

Triple Bottomline Many‐Objective‐Based Decision Making for a Land Use Management Problem

A land use many‐objective optimization problem for a 1500‐ha farm with 315 paddocks was formulated with 14 objectives (maximizing sawlog production, pulpwood production, milksolids, beef, sheep meat, wool, carbon sequestration, water production, income and Earnings Before Interest and Tax; and minimizing costs, nitrate leaching, phosphorus loss and sedimentation). This was solved using a modified Reference‐point‐based Non‐dominated Sorting Genetic Algorithm II augmented by simulated epigenetic operations. The search space had complex variable interactions and was based on economic data and several interoperating simulation models. The solution was an approximation of a Hyperspace Pareto Frontier (HPF), where each non‐dominated trade‐off point represented a set of land‐use management actions taken within a 10‐year period and their related management options, spanning a planning period of 50 years. A trade‐off analysis was achieved using Hyper‐Radial Visualization (HRV) by collapsing the HPF into a 2‐D visualization capability through an interactive virtual reality (VR)‐based method, thereby facilitating intuitive selection of a sound compromise solution dictated by the decision makers' preferences under uncertainty conditions. Four scenarios of the HRV were considered emphasizing economic, sedimentation and nitrate leaching aspects—giving rise to a triple bottomline (i.e. the economic, environmental and social complex, where the social aspect is represented by the preferences of the various stakeholders). Highlights of the proposed approach are the development of an innovative epigenetics‐based multi‐objective optimizer, uncertainty incorporation in the search space data and decision making on a multi‐dimensional space through a VR‐simulation‐based visual steering process controlled at its core by a multi‐criterion decision making‐based process. This approach has widespread applicability to many other ‘wicked’ societal problem‐solving tasks. Copyright © 2014 John Wiley & Sons, Ltd.     

Weighted least squares fitting using ordinary least squares algorithms

A general approach for fitting a model to a data matrix by weighted least squares (WLS) is studied. This approach consists of iteratively performing (steps of) existing algorithms for ordinary least squares (OLS) fitting of the same model. The approach is based on minimizing a function that majorizes the WLS loss function. The generality of the approach implies that, for every model for which an OLS fitting algorithm is available, the present approach yields a WLS fitting algorithm. In the special case where the WLS weight matrix is binary, the approach reduces to missing data imputation.This research has been made possible by a fellowship from the Royal Netherlands Academy of Arts and Sciences to the author.     

EM algorithms for ML factor analysis

The details of EM algorithms for maximum likelihood factor analysis are presented for both the exploratory and confirmatory models. The algorithm is essentially the same for both cases and involves only simple least squares regression operations; the largest matrix inversion required is for aq ×q symmetric matrix whereq is the matrix of factors. The example that is used demonstrates that the likelihood for the factor analysis model may have multiple modes that are not simply rotations of each other; such behavior should concern users of maximum likelihood factor analysis and certainly should cast doubt on the general utility of second derivatives of the log likelihood as measures of precision of estimation.     

Sparse distributed memory for ‘conscious’ software agents

In this work we are reporting a case study on the use of SDM as the associative memory for a software agent, CMattie, whose architecture is modeled on human cognition. Sparse distributed memory (SDM) is a content-addressable memory technique that relies on close memory items tending to be clustered together. In this work, we used an enhanced version of SDM augmented with the use of genetic algorithms as an associative memory in our ‘conscious’ software agent, CMattie, who is responsible for emailing seminar announcements in an academic department. Interacting with seminar organizers via email in natural language, CMattie can replace the secretary who normally handles such announcements. SDM is a key ingredient in a complex agent architecture that implements global workspace theory, a psychological theory of consciousness and cognition. In this architecture, SDM, as the primary memory for the agent, provides associations with incoming percepts. These include disambiguation of the percept by removing noise, correcting misspellings, and adding missing pieces of information. It also retrieves behaviors and emotions associated with the percept. These associations are based on previous similar percepts, and their consequences, that have been recorded earlier. SDM also possesses several key psychological features. Some enhancements to SDM including multiple writes of important items, use of error detection and correction, and the use of hashing to map the original information into fixed size keys were used. Test results indicate that SDM can be used successfully as an associative memory in such complex agent architectures. The results show that SDM is capable of recovering a percept based on a part of that percept, and finding defaults for empty perception registers. The evaluation of suggested actions and emotional states is satisfactory. We think that this work opens the door to more scientific and empirical uses for SDM.