Discrepancy Analysis of State Sequences

Abstract

In this article we define a methodological framework for analyzing the relationship between state sequences and covariates. Inspired by the ANOVA principles, our approach looks at how the covariates explain the discrepancy of the sequences. We use the pairwise dissimilarities between sequences to determine the discrepancy which makes it then possible to develop a series of statistical-significancebased analysis tools. We introduce generalized simple and multi-factor 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 timeframe and a regression tree method for discovering the most significant discriminant covariates and their interactions. In addition, we extend all methods to account for case weights. The scope of the proposed methodological framework is illustrated using a real-world sequence dataset.

Continuous Data Integration for Land Use and Transportation Planning and Modeling

“…To achieve this goal, four sequential steps are proposed: 1) representing an individual's activity diary as a sequence of characters; 2) performing sequence alignment to produce a pairwise distance matrix among all activity sequences; 3) conducting discrepancy analysis to examine the association between activity sequences characterized by the distance matrix and one or more categorical predictors; and 4) building an induction tree to help interpret how activity sequences change with the predictors. All of these steps are implemented in R with the TraMineR package Studer et al, 2011).…”

“…The importance of this finding is substantial because, unlike the Euclidean distances, the calculation of a central location for non-Euclidean distances, such as a pairwise distance matrix resulting from sequence alignments, is often problematic. Further, Studer et al (2011) demonstrate that if the distance measure is non-Euclidean, the non-Euclidean distances do not need to be squared before summing them. In short, the new method generalizes the notion of "sum of squares" in ANOVA to non-Euclidean measures of dissimilarity.…”

“…Consequently, we need a direct analysis of the association between pairwise dissimilarity measures and explanatory variables without any prior clustering. Inspired from the work of Studer et al (2011), this paper proposes a new combination of sequence alignment with ANOVA-like tools, not with cluster analysis. The proposed method was originally developed in ecology under the name of a non-parametric MANOVA (Anderson, 2001), and recently introduced into sociology with the name of discrepancy analysis and ANODI (the Analysis of Dissimilarity) (Bonetti et al, 2013).…”

“…Fourth, from this distribution, the p-value of the observed pseudo F-ratio statistic (Fobserved) is assessed by evaluating the proportion of Fpermuted that are higher than Fobserved. Since the number of all possible permutations is often huge, it is usually practical to perform 1,000 permutations for tests with a 5% significance level (Anderson, 2001;Studer et al, 2011). …”

“…The procedure is repeated at every new node until certain stopping criteria are met. As building a tree with state sequences is very rare in existing literature, however, this study follows the instructions suggested by Studer et al (2011). Their tree is slightly different than popular tree algorithms, such as CHi-squared Automatic Interaction Detection (CHAID), in several aspects.…”