Nicolas S. Müller

Discrepancy Analysis of State Sequences

In this article, the authors define a methodological framework for analyzing the relationship between state sequences and covariates. Inspired by the principles of analysis of variance, this approach looks at how the covariates explain the discrepancy of the sequences. The authors use the pairwise dissimilarities between sequences to determine the discrepancy, which makes it possible to develop a series of statistical significance–based analysis tools. They introduce generalized simple and multifactor discrepancy-based methods to test for differences between groups, a pseudo-R 2 for measuring the strength of sequence-covariate associations, a generalized Levene statistic for testing differences in the within-group discrepancies, as well as tools and plots for studying the evolution of the differences along the time frame and a regression tree method for discovering the most significant discriminant covariates and their interactions. In addition, the authors extend all methods to account for case weights. The scope of the proposed methodological framework is illustrated using a real-world sequence data set.

Extracting and Rendering Representative Sequences

This paper is concerned with the summarization of a set of categorical sequences. More specifically, the problem studied is the determination of the smallest possible number of representative sequences that ensure a given coverage of the whole set, i.e. that have together a given percentage of sequences in their neighbourhood. The proposed heuristic for extracting the representative subset requires as main arguments a pairwise distance matrix, a representativeness criterion and a distance threshold under which two sequences are considered as redundant or, identically, in the neighborhood of each other. It first builds a list of candidates using a representativeness score and then eliminates redundancy. We propose also a visualization tool for rendering the results and quality measures for evaluating them. The proposed tools have been implemented in our TraMineR R package for mining and visualizing sequence data and we demonstrate their efficiency on a real world example from social sciences. The methods are nonetheless by no way limited to social science data and should prove useful in many other domains.

Extracting Knowledge from Life Courses: Clustering and Visualization

This article presents some of the facilities offered by our TraMineR R-package for clustering and visualizing sequence data. Firstly, we discuss our implementation of the optimal matching algorithm for evaluating the distance between two sequences and its use for generating a distance matrix for the whole sequence data set. Once such a matrix is obtained, we may use it as input for a cluster analysis, which can be done straightforwardly with any method available in the R statistical environment. Then we present three kinds of plots for visualizing the characteristics of the obtained clusters: an aggregated plot depicting the average sequential behavior of cluster members; an sequence index plot that shows the diversity inside clusters and an original frequency plot that highlights the frequencies of the nmost frequent sequences. TraMineR was designed for analysing sequences representing life courses and our presentation is illustrated on such a real world data set. The material presented should also be of interest for other kind of sequential data such as DNA analysis or web logs.

Discrepancy Analysis of Complex Objects Using Dissimilarities

In this article we consider objects for which we have a matrix of dissimilarities and we are interested in their links with covariates. We focus on state sequences for which pairwise dissimilarities are given for instance by edit distances. The methods discussed apply however to any kind of objects and measures of dissimilarities. We start with a generalization of the analysis of variance (ANOVA) to assess the link of complex objects (e.g. sequences) with a given categorical variable. The trick is to show that discrepancy among objects can be derived from the sole pairwise dissimilarities, which permits then to identify factors that most reduce this discrepancy.We present a general statistical test and introduce an original way of rendering the results for state sequences. We then generalize the method to the case with more than one factor and discuss its advantages and limitations especially regarding interpretation. Finally, we introduce a new tree method for analyzing discrepancy of complex objects that exploits the former test as splitting criterion. We demonstrate the scope of the methods presented through a study of the factors that most discriminate Swiss occupational trajectories. All methods presented are freely accessible in our TraMineR package for the R statistical environment.

Pluralized life courses? An exploration of the life trajectories of individuals with psychiatric disorders

Background: Most of the existing research relating to the life courses of people with psychiatric symptoms focuses on the occurrence and the impact of non-normative events on the onsets of crises; it usually disregards the more regular dimensions of life, such as work, family and intimate partnerships that may be related to the timing and seriousness of psychiatric problems. An additional reason for empirically addressing life trajectories of individuals with psychiatric problems relates to recent changes of family and occupational trajectories in relation to societal trends such as individualization and pluralization of life courses. Aim: This paper explores the life trajectories of 86 individuals under clinical supervision and proposes a typology of their occupational, co-residence and intimacy trajectories. The results are discussed in light of the life-course paradigm. Method: A multidimensional optimal matching analysis was performed on a sample of 86 individuals under clinical supervision to create a typology of trajectories. The influence of these trajectories on psychiatric disorders, evaluated using a SCL-90-R questionnaire, was then assessed using linear regression modelling. Results: The typologies of trajectories showed that the patients developed a diversity of life trajectories. Individuals who have developed a standard life course with few institutionalization periods reported more symptoms and distress than individuals with an institutionalized life trajectory. Conclusion: The results of this study stress that psychiatric patients are social actors who are influenced by society at large and its ongoing process of change. Therefore, it is essential to take into account the diversity of occupational and family trajectories when dealing with individuals in therapeutic settings.

Converting between Various Sequence Representations

This chapter is concerned with the organization of categorical sequence data. We first build a typology of sequences distinguishing for example between chronological sequences and sequences without time content. This permits to identify the kind of information that the data organization should preserve. Focusing then mainly on chronological sequences, we discuss the advantages and limits of different ways of representing time stamped event and state sequence data and present solutions for automatically converting between various formats, e.g., between horizontal and vertical presentations but also from state sequences into event sequences and reciprocally. Special attention is also drawn to the handling of missing values in these conversion processes.