Analysis of Longitudinal Data.

Correspondence analysis is an exploratory tool for the analysis of associations between categorical variables, the results of which may be displayed graphically. For longitudinal data, two types of analysis can be distinguished: the first focuses on transitions, whereas the second investigates trends. For transitional analysis with two time points, an analysis of the transition matrix (showing the relative frequencies for pairs of categories) provides insight into the structure of departures from independence in the transitions. Transitions between more than two time points can also be studied simultaneously. In trend analyses often the trajectories of different groups are compared. Examples for all these analyses are provided. Correspondence analysis is an exploratory tool for the analysis of association(s) between categorical variables. Usually, the results are displayed in a graphical way. There are many interpretations of correspondence analysis. Here, we make use of two of them. A first interpretation is that the observed categorical data are collected in a matrix, and correspondence analysis approximates this matrix by a matrix of lower rank[1]. This lower rank approximation of, say, rank M + 1 is then displayed graphically in an M-dimensional representation in which each row and each column of the matrix is displayed as a point. The difference in rank between the rank M + 1 matrix and the rank M representation is matrix of rank 1, and this matrix is the product of the marginal counts of the matrix, that is most often considered uninteresting. This brings us to the second interpretation, that is, that when the two-way matrix is a contingency table, correspondence analysis decomposes the departure from a matrix where the row and column variables are independent[2,3]. Thus, correspondence analysis is a tool for residual analysis. This interpretation holds because for a contingency table estimates under the independence model are obtained from the product of the margins of the table divided by the total sample size. Longitudinal data are data where observations (e.g., individuals) are measured at least twice using the same variables. We consider here only categorical (i.e., nominal or ordinal) variables, as only this kind of variables is analyzed in standard applications of correspondence analysis[4]. We first discuss correspondence analysis for the analysis of transitions. Thereafter, we consider analysis of trends with canonical correspondence analysis. 1 Leiden University, Leiden, The Netherlands 2 Utrecht University, Utrecht, The Netherlands Update based on original article by Peter G. M. Van Der Heijden, Wiley StatsRef: Statistics Reference Online, © 2014, John Wiley & Sons, Ltd Wiley StatsRef: Statistics Reference Online, © 2014–2015 John Wiley & Sons, Ltd. This article is © 2015 John Wiley & Sons, Ltd. DOI: 10.1002/9781118445112.stat05497.pub2 1 Correspondence Analysis of Longitudinal Data 1 Transitional Analysis