A multivariate reduced-rank growth curve model with unbalanced data

Hwang, Heungsun; Takane, Yoshio

doi:10.1007/bf02295840

Cited by 9 publications

(11 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The sample consisted of 221 pairs of children and mothers, who completed interviews at 4 time points. Hwang and Takane (2004) have also analyzed the same data.…”

Section: An Illustrative Applicationmentioning

confidence: 99%

“…Furthermore, Y j is not necessarily identically time-structured or balanced, indicating that all individuals do not need to be measured on J response variables at the same time points, nor the same number of time points. Hwang and Takane (2004) proposed a model that did not include the random-effects term, ΛA, i.e., Y = XBA + E, although their method emphasized rank restrictions on BA. In the multivariate fixed-effects model, however, Σ is unconstrained.…”

Section: The Proposed Methodsmentioning

confidence: 99%

“…Moreover, it can be used to fit the multivariate fixed-effects growth curve model by Hwang and Takane (2004): Given B and A, the ML estimate of the unconstrained Σ is updated byΣ = N −1 V.…”

Section: The Proposed Methodsmentioning

confidence: 99%

“…In (6), A is assumed at most partially known. To maximize (6), we may use an optimization procedure similar to an alternating maximum likelihood (AML) procedure (de Leeuw, 1989;Hwang & Takane, 2004;van der Leeden, 1990). The AML procedure consists of two global steps.…”

Section: The Proposed Methodsmentioning

confidence: 99%

“…As such, he could not examine whether or not both response variables changed in an identical linear pattern over time. Hwang and Takane (2004) also chose the identically constrained linear-trend model as the final model. However, their method cannot investigate whether or not there exist substantial individual differences in the temporal pattern because it is a fixed-effect model.…”

Section: An Illustrative Applicationmentioning

confidence: 99%

See 4 more Smart Citations

An Extended Multivariate Random-Effects Growth Curve Model

Hwang

Takane

2005

Behaviormetrika

Self Cite

View full text Add to dashboard Cite

Two methods are typically used for the analysis of multivariate longitudinal data: multivariate random-effects growth curve models and latent curve models. Despite their popularity, in the former method an entire set of basis functions should a priori be specified and in the latter the estimates of random-effects or latent variable scores are not uniquely determined. An extended multivariate random-effects growth curve model is proposed to overcome the limitations of the two methods. The proposed method extends the existing multivariate random-effects growth curve model in such a way that it does not need to specify all basis functions in advance. It also offers the unique estimates of random-effects. Furthermore, the method can deal with unbalanced response variables, so that they do not have to be measured at the same time points, nor the same number of time points. An example is given to illustrate the method.

show abstract

“…The sample consisted of 221 pairs of children and mothers, who completed interviews at 4 time points. Hwang and Takane (2004) have also analyzed the same data.…”

Section: An Illustrative Applicationmentioning

confidence: 99%

Section: The Proposed Methodsmentioning

confidence: 99%

Section: The Proposed Methodsmentioning

confidence: 99%

Section: The Proposed Methodsmentioning

confidence: 99%

Section: An Illustrative Applicationmentioning

confidence: 99%

See 3 more Smart Citations

An Extended Multivariate Random-Effects Growth Curve Model

Hwang

Takane

2005

Behaviormetrika

Self Cite

View full text Add to dashboard Cite

show abstract

The Growth Curve Model and Reduced-Rank Regression Methods

Reinsel

Velu

Chen

2022

Multivariate Reduced-Rank Regression

View full text Add to dashboard Cite

A Bayesian approach to model individual differences and to partition individuals: case studies in growth and learning curves

2022

View full text Add to dashboard Cite

The first objective of the paper is to implement a two stage Bayesian hierarchical nonlinear model for growth and learning curves, particular cases of longitudinal data with an underlying nonlinear time dependence. The aim is to model simultaneously individual trajectories over time, each with specific and potentially different characteristics, and a time-dependent behavior shared among individuals, including eventual effect of covariates. At the first stage inter-individual differences are taken into account, while, at the second stage, we search for an average model. The second objective is to partition individuals into homogeneous groups, when inter individual parameters present high level of heterogeneity. A new multivariate partitioning approach is proposed to cluster individuals according to the posterior distributions of the parameters describing the individual time-dependent behaviour. To assess the proposed methods, we present simulated data and two applications to real data, one related to growth curve modeling in agriculture and one related to learning curves for motor skills. Furthermore a comparison with finite mixture analysis is shown.

show abstract

A multivariate reduced-rank growth curve model with unbalanced data

Abstract: Multivariate growth curve models, reduced-rank restriction, longitudinal data,

Cited by 9 publications

References 31 publications

An Extended Multivariate Random-Effects Growth Curve Model

An Extended Multivariate Random-Effects Growth Curve Model

The Growth Curve Model and Reduced-Rank Regression Methods

A Bayesian approach to model individual differences and to partition individuals: case studies in growth and learning curves

Contact Info

Product

Resources

About