Finite Mixtures of Hidden Markov Models for Longitudinal Responses Subject to Drop out

Abstract

Drop out is a typical issue in longitudinal studies. When the missingness is non-ignorable, inference based on the observed data only may be biased. This paper is motivated by the Leiden 85+ study, a longitudinal study conducted to analyze the dynamics of cognitive functioning in the elderly. We account for dependence between longitudinal responses from the same subject using time-varying random effects associated with a heterogeneous hidden Markov chain. As several participants in the study drop out prematurely, we introduce a further random effect model to describe the missing data mechanism. The potential dependence between the random effects in the two equations (and, therefore, between the two processes) is introduced through a joint distribution specified via a latent structure approach. The application of the proposal to data from the Leiden 85+ study shows its effectiveness in modeling heterogeneous longitudinal patterns, possibly influenced by the missing data process. Results from a sensitivity analysis show the robustness of the estimates with respect to misspecification of the missing data mechanism. A simulation study provides evidence for the reliability of the inferential conclusions drawn from the analysis of the Leiden 85+ data.     

States Are Not Basic Structures: Against State-Centric Political Theory

Abstract

Contemporary political philosophy often operates on a ‘two-tiered’ theoretical treatment of global politics, on which domestic political systems and the principles governing their internal dynamics constitute one tier, and on which the relationships between states and governing multinational institutions constitute a second. One way of grounding and justifying this approach, preferred by Rawls, is called constructivism. Constructivists describe the world as containing specific domains and domain-types of political and social interaction, and relativizes principles of justice to important versions of these—states, in the case of contemporary two-tiered political philosophy. In this paper I argue against the specifically Rawlsian account of uniting these three commitments (two-tiered political theory, constructivism, and statism) and gesture towards a general argument against the coherence of this bundle of views.     

Expository Texts in First-Grade Classroom Libraries: Issues in Teacher Selection

Abstract

In 2010, the Common Core State Standards (CCSS) were adopted by most states in the US. The authors of these standards called for a shift from previous standards by recommending that young children experience a 50-50 balance between informational and literary reading. For this mixed-methods study, researchers examined the contents of 23 first-grade classroom libraries 8?years after the implementation of the CCSS to determine the percentage of expository texts found in these libraries and if these percentages differed based on the SES of the school or the number of years a teacher had been teaching. In addition, researchers interviewed twelve selected classroom teachers to gain an understanding of how they selected books for their libraries and what influenced their decisions. Results indicated that 22.8% of the texts found in first-grade classroom libraries were expository and there was no difference based on SES of the school or years a teacher had been in the classroom. Teacher interviews indicated that book cost, reading level, student interest, and genre (both narrative and expository/nonfiction) influenced their library text selections. Only two teachers indicated that the CCSS impacted their book choices.     

How to separate coordinate and categorical spatial relation components in integrated spatial representations: A new methodology for analysing sketch maps

Spatial relations between landmarks can be represented by means of categories and coordinates. In the present research, this paradigm was applied to sketch maps based on information acquired in goal-directed behaviour of exploration of a university campus area. The first aim was to investigate whether categorical and coordinate information can be considered conceptually independent in sketch maps. The second aim was to assess which kind of distance measure served better to represent coordinate information in the present case study, and finally to assess the factorial structure of coordinate and categorical data. Analytic methodology as well as statistical analysis were found to confirm that separating coordinate and categorical components was formally as well as empirically appropriate. A series of confirmatory factor analyses showed the best fit for the model with two correlated components, as well as an acceptable reliability of measures emerged. The two components were moderately correlated. Moreover, the adoption of Manhattan distance seemed to be the most effective method to represent coordinate spatial relations in spatial sketch maps of areas acquired through navigation.