Squared Extrapolation Methods (SQUAREM): A New Class of Simple and Efficient Numerical Schemes for Accelerating the Convergence of the EM Algorithm

We derive a new class of iterative schemes for accelerating the convergence of the EM algorithm, by exploiting the connection between fixed point iterations and extrapolation methods. First, we present a general formulation of one-step iterative schemes, which are obtained by cycling with the extrapolation methods. We, then square the one-step schemes to obtain the new class of methods, which we call SQUAREM. Squaring a one-step iterative scheme is simply applying it twice within each cycle of the extrapolation method. Here we focus on the first order or rank-one extrapolation methods for two reasons, (1) simplicity, and (2) computational efficiency. In particular, we study two first order extrapolation methods, the reduced rank extrapolation (RRE1) and minimal polynomial extrapolation (MPE1). The convergence of the new schemes, both one-step and squared, is non-monotonic with respect to the residual norm. The first order one-step and SQUAREM schemes are linearly convergent, like the EM algorithm but they have a faster rate of convergence. We demonstrate, through five different examples, the effectiveness of the first order SQUAREM schemes, SqRRE1 and SqMPE1, in accelerating the EM algorithm. The SQUAREM schemes are also shown to be vastly superior to their one-step counterparts, RRE1 and MPE1, in terms of computational efficiency. The proposed extrapolation schemes can fail due to the numerical problems of stagnation and near breakdown. We have developed a new hybrid iterative scheme that combines the RRE1 and MPE1 schemes in such a manner that it overcomes both stagnation and near breakdown. The squared first order hybrid scheme, SqHyb1, emerges as the iterative scheme of choice based on our numerical experiments. It combines the fast convergence of the SqMPE1, while avoiding near breakdowns, with the stability of SqRRE1, while avoiding stagnations. The SQUAREM methods can be incorporated very easily into an existing EM algorithm. They only require the basic EM step for their implementation and do not require any other auxiliary quantities such as the complete data log likelihood, and its gradient or hessian. They are an attractive option in problems with a very large number of parameters, and in problems where the statistical model is complex, the EM algorithm is slow and each EM step is computationally demanding.

Checking Assumptions in Latent Class Regression Models via a Markov Chain Monte Carlo Estimation Approach: An Application to Depression and Socio-Economic Status

Latent class regression models are useful tools for assessing associations between covariates and latent variables. However, evaluation of key model assumptions cannot be performed using methods from standard regression models due to the unobserved nature of latent outcome variables. This paper presents graphical diagnostic tools to evaluate whether or not latent class regression models adhere to standard assumptions of the model: conditional independence and non-differential measurement. An integral part of these methods is the use of a Markov Chain Monte Carlo estimation procedure. Unlike standard maximum likelihood implementations for latent class regression model estimation, the MCMC approach allows us to calculate posterior distributions and point estimates of any functions of parameters. It is this convenience that allows us to provide the diagnostic methods that we introduce. As a motivating example we present an analysis focusing on the association between depression and socioeconomic status, using data from the Epidemiologic Catchment Area study. We consider a latent class regression analysis investigating the association between depression and socioeconomic status measures, where the latent variable depression is regressed on education and income indicators, in addition to age, gender, and marital status variables. While the fitted latent class regression model yields interesting results, the model parameters are found to be invalid due to the violation of model assumptions. The violation of these assumptions is clearly identified by the presented diagnostic plots. These methods can be applied to standard latent class and latent class regression models, and the general principle can be extended to evaluate model assumptions in other types of models.

Multilevel Latent Class Models with Dirichlet Mixing Distribution

Latent class analysis (LCA) and latent class regression (LCR) are widely used for modeling multivariate categorical outcomes in social sciences and biomedical studies. Standard analyses assume data of different respondents to be mutually independent, excluding application of the methods to familial and other designs in which participants are clustered. In this paper, we develop multilevel latent class model, in which subpopulation mixing probabilities are treated as random effects that vary among clusters according to a common Dirichlet distribution. We apply the Expectation-Maximization (EM) algorithm for model fitting by maximum likelihood (ML). This approach works well, but is computationally intensive when either the number of classes or the cluster size is large. We propose a maximum pairwise likelihood (MPL) approach via a modified EM algorithm for this case. We also show that a simple latent class analysis, combined with robust standard errors, provides another consistent, robust, but less efficient inferential procedure. Simulation studies suggest that the three methods work well in finite samples, and that the MPL estimates often enjoy comparable precision as the ML estimates. We apply our methods to the analysis of comorbid symptoms in the Obsessive Compulsive Disorder study. Our models' random effects structure has more straightforward interpretation than those of competing methods, thus should usefully augment tools available for latent class analysis of multilevel data.

What's Working in Family-Based Services--or, What's Left to Believe in During a Time of Such Doubt?

This article is a qualitative, personal report from the field, designed to highlight current developments in family-based theory and practice that bring hopefulness to workers and clients. The author, an experienced human services consultant and family therapist, draws from his recent experience in a number of states to identify exemplars of practice in the following areas: integrative theory building, functional family assessment, systems change in regard to inter-agency coordination and foster care, community building in low income neighborhoods, developing humility as helpers, and addressing issues of hope and spirituality with clients and with co-workers. Given the turbulent and hostile political environment for family-based services, this article challenges us to remember that effectiveness in helping others is directly related to our feelings of hopefulness about ourselves and our world.

Student Performance in Traditional vs. Online Format: Evidence from an MBA Level Introductory Economics Class

All previous studies comparing online and face-to-face format for instruction of economics compared courses that were either online or face-to-face format and regressed exam scores on selected student characteristics. This approach is subject to the econometric problems of self-selection omitted unobserved variables. Our study uses two methods to deal with these problems. First we eliminate self-selection bias by using students from a course that uses both instruction formats. Second, we use the exam questions as the unit of observation, and eliminate omitted variable bias by using an indicator variable for each student to capture the effect of differences in unobserved student characteristics on learning outcomes. We report the finding that students had a significantly greater chance of answering a question correctly if it came from a chapter covered online.

Follow-up care after a health fair screening in three Houston neighborhoods in 2008

Background. Each year thousands of people participate in mass health screenings for diabetes and hypertension, but little is known about whether or not those who receive higher than normal screening results obtain the recommended follow-up medical care, or what barriers they perceive to doing so. ^ Methods. Study participants were recruited from attendees at three health fairs in low-income neighborhoods in Houston, Texas Potential participants had higher than normal blood pressure (> 90/140 mgHg) or blood glucose readings (100 mm/dL fasting or 140 mm/dL random). Study participants were called at one, two, and three months and asked if they had obtained follow-up medical care; those who had not yet obtained follow-up care were asked to identify barriers. Using a modified Aday-Andersen model of health service access, the independent variables were individual and community characteristics and self-perceived need. The dependent variable was obtaining follow-up care, with barriers to care a secondary outcome. ^ Results. Eighty-two study participants completed the initial questionnaire and 59 participants completed the study protocol. Forty-eight participants (59% under an intent to treat analysis, 81% of those completing the study protocol) obtained follow-up care. Those who completed the initial questionnaire and who reported a regular source of care were significantly more likely to obtain follow-up care. For those who completed the study protocol the relationship between having a regular source of care and obtaining follow-up care approached but did not reach significance. For those who completed the initial questionnaire, self-described health status, when examined as a binary variable (good, very good, excellent, or poor, fair, not sure) was associated with obtaining follow-up care for those who rated their health as poor, fair, or not sure. While the group who completed the study protocol did not reach statistical significance, the same relationship between self-described health status of poor, fair, or not sure and obtaining follow-up care was present. The participants who completed the study protocol and described their blood pressure as OK or a little high were statistically more likely to get follow-up care than those who described it as high or very high. All those on oral medications for hypertension (12/12) and diabetes (4/4) who were told to obtain follow-up care did so; however, the small sample size allows this correlation to be of statistical significance only for those treating hypertension. ^ The variables significantly associated with obtaining follow-up care were having a regular source of care, self-described health status of poor, fair, or not sure, self-described blood pressure of OK or a little high, and taking medication for blood pressure. ^ At the follow-up telephone calls, 34 participants identified barriers to care; cost was a significant barrier reported by 16 participants, and 10 reported that they didn’t have time because they were working long hours after Hurricane Ike. ^ The study included the offer of access assistance: information about nearby safety-net providers, a visit to or information from the Health Information Center at their Neighborhood Center location, or information from Project Safety Net (a searchable web site for safety net providers). Access assistance was offered at the health fairs and then again at follow-up telephone calls to those who had not yet obtained follow-up care. Of the 48 participants who reported obtaining follow-up care, 26 said they had made use of the access assistance to do so. The use of access assistance was associated with being Hispanic, not having health insurance or a regular source of care, and speaking Spanish. It was also associated with being worried about blood glucose. ^ Conclusion. Access assistance, as a community enabling characteristic, may be useful in aiding low-income people in obtaining medical care. ^

The urban middle class in the instability of new democracies

The recent revolts of the middle class in the national capitals of the Philippines and Thailand have raised a new question about democratic consolidation. Why would the urban middle class, which is expected to stabilize democracy, expel the democratically elected leaders through extra-constitutional action? This article seeks to explain such middle class deviation from democratic institutions through an examination of urban primacy and the change in the winning coalition. The authoritarian regime previously in power tended to give considerable favor to the primate city to prevent it revolting against the ruler, because it could have become a menace to his power. But after democratization the new administration shifts policy orientation from an urban to rural bias because it needs to garner support from rural voters to win elections. Such a shift dissatisfies the middle class in the primate city. In this article I take up the Philippines as a case study to examine this theory.

Virtual Excursions: a new way to explore science in class

The educational platform Virtual Science Hub (ViSH) has been developed as part of the GLOBAL excursion European project. ViSH (http://vishub.org/) is a portal where teachers and scientist interact to create virtual excursions to science infrastructures. The main motivation behind the project was to connect teachers - and in consequence their students - to scientific institutions and their wide amount of infrastructures and resources they are working with. Thus the idea of a hub was born that would allow the two worlds of scientists and teachers to connect and to innovate science teaching. The core of the ViSH?s concept design is based on virtual excursions, which allow for a number of pedagogical models to be applied. According to our internal definition a virtual excursion is a tour through some digital context by teachers and pupils on a given topic that is attractive and has an educational purpose. Inquiry-based learning, project-based and problem-based learning are the most prominent approaches that a virtual excursion may serve. The domain specific resources and scientific infrastructures currently available on the ViSH are focusing on life sciences, nano-technology, biotechnology, grid and volunteer computing. The virtual excursion approach allows an easy combination of these resources into interdisciplinary teaching scenarios. In addition, social networking features support the users in collaborating and communicating in relation to these excursions and thus create a community of interest for innovative science teaching. The design and development phases were performed following a participatory design approach. An important aspect in this process was to create design partnerships amongst all actors involved, researchers, developers, infrastructure providers, teachers, social scientists, and pedagogical experts early in the project. A joint sense of ownership was created and important changes during the conceptual phase were implemented in the ViSH due to early user feedback. Technology-wise the ViSH is based on the latest web technologies in order to make it cross-platform compatible so that it works on several operative systems such as Windows, Mac or Linux and multi-device accessible, such as desktop, tablet and mobile devices. The platform has been developed in HTML5, the latest standard for web development, assuring that it can run on any modern browser. In addition to social networking features a core element on the ViSH is the virtual excursions editor. It is a web tool that allows teachers and scientists to create rich mash-ups of learning resources provided by the e-Infrastructures (i.e. remote laboratories and live webcams). These rich mash-ups can be presented in either slides or flashcards format. Taking advantage of the web architecture supported, additional powerful components have been integrated like a recommendation engine to provide personalized suggestions about educational content or interesting users and a videoconference tool to enhance real-time collaboration like MashMeTV (http://www.mashme.tv/).

On the cup anemometer working condition monitoring

The analysis of the harmonic terms related to the rotational speed of a cup anemometer is a way to detect anomalies such as wear and tear, rotor non-symmetries (rotor damage) or problems at the output signal system. The research already done in this matter at the IDR/UPM Institute is now taken to cup anemometers working on the field. A 1-2 year testing campaign is being carried out in collaboration with Kintech Engineering. 2 Thies First Class Advanced installed at 58 m and 73 m height in a meteorology tower are constantly monitored. The results will be correlated to the anemometer performance evolution studied through several calibrations planned to be performed along the testing campaign.

Occupational class and cause specific mortality in middle aged men in 11 European countries: comparison of population based studies

Objectives: To compare countries in western Europe with respect to class differences in mortality from specific causes of death and to assess the contributions these causes make to class differences in total mortality.