Estimation of parameters under a generalized growth curve model

Katarzyna Filipiak and Daniel Klein

Journal of Multivariate Analysis, 2017, vol. 158, issue C, 73-86

Abstract: This paper concerns multi-level multivariate data. Such data can be presented in the form of a multi-index matrix (tensor) Y. First the third-order normally distributed tensor of observations, Y∈Rn×p×q, is discussed with the mean structured in the form of a generalized growth curve model, [[X;A,B,C]], with multiplication in all three directions of the third-order tensor X of unknown parameters by the known matrices A, B and C. The paper is focused on the estimation of an unknown tensor X of direct effects and a separable and doubly separable variance–covariance matrix. Since the resulting estimators of unknown parameters cannot be presented in an explicit form, the estimates are obtained approximately. The uniqueness of the so-called ‘flip-flop’ algorithm is also discussed, and the use of the algorithm is illustrated on a real data example. Finally, possible extensions of the third-order generalized growth curve model to more levels are considered.

Keywords: Generalized growth curve model; Maximum likelihood estimators; Separable covariance structure (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.jmva.2017.04.005

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