Latent variable modelling of longitudinal data: applications of Mplus™ methodologies
(latent class growth and growth mixture models) in epidemiological cohort studies and
household panel data
Presenter:
Dr Tim Croudace, Department of Health Career Scientist Public Health,
And Senior Lecturer (Psychometric Epidemiology)
Department of Psychiatry, University of Cambridge, UK
Co-authors
George B. Ploubidis1, Rosemary A Abbott1, Diana Kuh 2, Peter B. Jones, , Michael E.J. Wadsworth 2,
Felicia A Huppert 1
1
Department of Psychiatry, University of Cambridge, Box 189, Addenbrooke’s Hospital, Hills Road,
Cambridge, CB2 2QQ, UK
2
MRC National Survey of Health and Development, Royal Free & University College Medical School,
Department of Epidemiology and Public Health, 1-19 Torrington Place, London, WC1E 6BT,
UK
§
Corresponding author
Email addresses:
TJC: tjc39@cam.ac.uk
GP: gp287@medschl.cam.ac.uk
RAA: raa25@medschl.cam.ac.uk
PBJ: pbj21@cam.ac.uk
FAH: fah2@cam.ac.uk
DJK: d.kuh@ucl.ac.uk
MW: m.wadsworth@ucl.ac.uk
Abstract
Latent variable frameworks offer a flexible range of analytical models for longitudinal data
(Muthén 1991, 2001, 2004). Analysis potential for applied researchers has been greatly
extended by commercial software developments e.g. Mplus 3.1 (Muthén and Muthén, 19982004; www.statmodel.com) and gllamm procedures (Rabe-Hesketh, Pickles and Skrondal,
2001; www.gllamm.org) implemented in Stata. Here, modelling extensions and new
estimation procedures allow for a comprehensive integration of latent variable models with
random effects, latent classes and structural equations. Modelling can therefore combine
latent class approaches to population heterogeneity modelling with random effects (linear
mixed) modelling of individual’s trajectories. Latent variable approaches to construct scaling
(psychometric models) can also be incorporated to correct for measurement error. Missing
data can be incorporated. Our interest is in a life-course developmental approach to the study
of psychopathology and behaviour (Willet et al, 1998; Kuh and Hardy, 2002). Our
talk/chapter will demonstrate four types of analysis: 1) latent class analysis of binary repeated
measures; 2) latent growth modelling; 3) growth mixture modelling, and 4) parallel process
modelling of two latent, inter-dependent growth processes. We will illustrate the types of
model that can be estimated using high quality epidemiological cohort studies (Croudace et
al, 2002) including birth cohort studies and household panel data. Our first example concerns
latent class analysis of binary repeated measures (Croudace et al, 2002). Here the outcome of
interest is night-time bed-wetting (present or absent) recorded on six occasions (ages
4,6,8,9,11 and 15 years) on children in the Medical Research Council 1946 National Survey
of Health and Development birth cohort study (Wadsworth, 1991; Wadsworth and Kuk, 1997;
Wadsworth et al, 2003). Enuresis as an antecedent of adult health outcomes will be explored.
Other models from the latent variable framework will be exemplified using repeated measures
from the 12-item GHQ (General Health Questionnaire; Goldberg, 1972) recorded by
participants in the BHPS (British Household Panel Survey; Taylor (2004)
http://www.iser.essex.ac.uk/ulsc/bhps). Bivariate outcome modelling will concern trajectories
for positive and negatively worded items. Extensions of these modelling frameworks will be
discussed, and Mplus scripts (input and output) will be mounted on a website prior to the
conference so that participants can use these pedagogical examples to develop their own
modelling skills and ideas.
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