Merging the Idiographic Filter With Dynamic Factor Analysis to Model Process

Bibliographic Data

ID15029480
AuthorsPeter C M Molenaar (0000-0002-0026-0756, Pennsylvania State University, corresponding author), John R Nesselroade (University of Virginia)
Year2012
Volume16
Issue4
Pages210-219
Publication date2012-10-01
Open AccessNo
TypeARTICLE
VenueApplied Developmental Science (JOURNAL)
Journal identifiersISSN: 1088-8691 • E-ISSN: 1532-480X
PublisherInforma UK Limited (PUBLISHER • GB)
DOI10.1080/10888691.2012.722884
OpenAlexW2046158995
LanguageEN
Citations received28
References cited24

To model processes we propose merging idiographic filter measurement with dynamic factor analysis. This involves testing whether or not the same latent dynamics (concurrent and lagged factor interrelations) can describe different individuals' observed multivariate time series. The methodology allows fitting, across different individuals, dynamic factor models that are invariant with respect to the latent dynamics, but not necessarily the factor loadings (measurement model). This methodology allows the same latent process to manifest differently from one individual to another, thus recognizing that the process is general but its realization in a given person is to some degree idiosyncratic. The approach is illustrated with empirical data. M. Molenaar and Award Number AG034284 from the National Institute on Aging to John R. Nesselroade. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Science Foundation, National Institute on Aging, or the National Institutes of Health. John R. Nesselroade gratefully acknowledges the support of the Max Planck Institute for Human Development, Berlin, Germany. The authors are indebted to Michael W. Browne and Jack McArdle for valuable comments and suggestions regarding identification matters in fitting the models proposed in this article. The authors also thank Manuel Voelkle for suggestions for improving an earlier version of this article. Notes 1The idiographic filter is a very different representation than those allowing for factor loadings that are random variables. The idiographic filter maintains a traditional view of factorial invariance but moves it to a higher order of the factor space. Factor loadings at the primary factor level are parameters of the model that are not constrained to be invariant over individuals, but they are not random variables. 2Use of a superscripted asterisk with Φ i(0) here and subsequently with other matrix symbols is to discriminate matrices that will also appear as submatrices comprising the corresponding block-Toeplitz matrices from those block-Toeplitz matrices. The latter will appear without a superscripted asterisk. 3This can be done using the block-Toeplitz approach previously mentioned and also used by Molenaar (Citation1985) and Nesselroade et al. (Citation2002). We are hopeful that more specialized dynamic factor modeling software [e.g., DyFA (Browne & Zhang, Citation2005)] will soon offer alternative approaches to fitting the DFA-IF model. 4Michael W. Browne alerted us that simply constraining the dynamics to equality across groups (individuals' P-technique data) would not suffice for model estimation. Note. Expected salient loadings are in boldface. *Statistically significant non-salient loading. Note. Expected salient loadings are in boldface. *Statistically significant non-salient loading

Dynamic factor · Econometrics · Epistemology · Factor analysis · Filter (signal processing · Foundation (evidence · Generalization · Identification (biology · Latent variable · Machine learning · Multivariate statistics · Nomothetic and idiographic · Operations research · Political science · Process (computing · Realization (probability · Representation (politics · Statistics · Computer Science · Law · Mathematics · Psychology · Social Psychology · Youth Development and Social Support · Artificial Intelligence

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