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Additional resources for Advances in data analysis: proceedings of the 30th Annual Conference of The Gesellschaft fur Klassifikation e.V., Freie Universitat Berlin, March 8-10, 2006
18 Adriana Climescu-Haulica 3. Find y1 , y2 , . . ym , the eigenvectors of L, chosen to be orthogonal to each other in the case of repeated eigenvalues and form the matrix Y = [y1 y2 . . ym ] ∈ IRm×m by stacking the eigenvectors in columns. 4. Compute the Fourier transform of Y column by column and construct W the matrix corresponding to the absolute values of matrix elements. 5. Assign, in increasing order, the maximal value of each column from W to the vector U ∈ IR+ called envelope intensity.
We included the most commonly used information criteria in applied research for this type of longitudinal model-based clustering approach. This ﬁrst attempt to understand the behavior of information criteria for the mixture of Markov chains model points out the need for detailed replications of these results, which are restricted to S = 2 and have to be extended to a larger number of components. On the other hand for a larger number of components the level of separation of components is even harder to set.
28 Jos´e G. Dias Table 2. 000 A second objective of the study was the comparison of these criteria across the design factors. Increasing the sample size always improves the performance of the information criteria, and reduces underﬁtting. However, for AIC increas- Model Selection for Mixtures of Markov Chains 29 ing the sample size tends to increase the overﬁtting. Increasing the number of time points (T + 1) improves the performance of the information criteria and reduces the underﬁtting. Increasing the state space (K) reduces the underﬁtting, and improves the performance of the information criteria.