Ecological-Inference-Based Latent Growth
Models: Modeling Changes of Alienation
, CHIH-CHIANG YANG
Graduate School of Educational Measurement & Statistics, National Taichung Teachers Col-
lege, Taichung 403, Taiwan;
L.L. Thurstone Psychometric Laboratory, Department of Psy-
chology, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA;
Department of Elementary Education, National Taipei Teachers College, Taipei, Taiwan;
Institute of Ethnology, Academia Sinica, Taipei, Taiwan
Abstract. Ecological-inference-based statistical methods employ aggregated (ecological) data
to approximately infer individual-level structures of interests when individual-level data were
not available. Under the same conceptual frames, we introduce the ecological-inference-based
latent growth model (EI-LGM) to analyze cross-years latent trends of a general population
when longitudinally collected data were not available. We showed both the substantive values
and methodological feasibilities of EI-LGMs. Substantively, we analyze results from several
Taiwan Social Change Surveys (TSCS) to show the cross-years latent trends using a subscale
of alienation psychological characteristics. Not only the cross-years movements of measure-
ment constructs of the scale were shown, the trends of latent factors were revealed as well.
More importantly, these trends can be formally tested under the frameworks of EI-LGMs.
Statistically, EI-LGMs were implemented under the weighted least square (WLS) approaches
because of the dichotomous outcomes of the subscale. We demonstrate some of the estimation
methods as well as some cautions of interpreting EI-LGMs using the estimated results.
Key words: Ecological-inference, latent growth model, Structural equation models, categorical
Ecological inference (EI), as deﬁned by King et al. (1999), is a process of
inferring about discrete individual-level behavior by analyzing group data.
Part of this paper was presented at the Fourth Survey Research Conference held at the
Academia Sinica, Taipei, August 29–August 30, 2002.
Author for Correspondence Address: Chih-Chien Yang, Graduate School of Educational
Measurement & Statistics, National Taichung Teachers College, 140 MinSheng Road,
Taichung 403, Taiwan. Tel.: (886)-4-2226-3181 ext. 401; Fax: (886)-4-2222-1526; E-mail:
Quality & Quantity (2005) 39: 125–135 Ó Springer 2005