### Abstract

Longitudinal structural equation modeling has generally addressed the time-dependent covariance structure of a relatively small number of repeated measures, T, observed in a relatively large representative sample, N. In contrast, the literature on autoregressive moving average modeling is usually directed at a single realization comprising many observations, that is, N = 1, and T > 50. This article deals with autoregressive moving average-based structural equation modeling of time series data, in the situation that N is small, T is intermediate, and T > N. The aims of this article are to (a) give a brief overview of the development of alternative formulations of the likelihood function to obtain estimates of autoregressive moving average parameters, in particular the formulation that lies at the basis of Mélard's algorithm; (b) show the equivalence between the likelihood function to obtain estimates for these parameters, and the raw data likelihood method that can be used in structural equation modeling programs like Mx, and demonstrate this equivalence through simulation experiments; and (c) provide illustrations of this use of Mx with real data.

Original language | English (US) |
---|---|

Pages (from-to) | 352-379 |

Number of pages | 28 |

Journal | Structural Equation Modeling |

Volume | 10 |

Issue number | 3 |

DOIs | |

State | Published - Dec 1 2003 |

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### All Science Journal Classification (ASJC) codes

- Decision Sciences(all)
- Modeling and Simulation
- Sociology and Political Science
- Economics, Econometrics and Finance(all)

### Cite this

*Structural Equation Modeling*,

*10*(3), 352-379. https://doi.org/10.1207/S15328007SEM1003_2

}

*Structural Equation Modeling*, vol. 10, no. 3, pp. 352-379. https://doi.org/10.1207/S15328007SEM1003_2

**ARMA-Based SEM When the Number of Time Points T Exceeds the Number of Cases N : Raw Data Maximum Likelihood.** / Hamaker, Ellen L.; Dolan, Conor V.; Molenaar, Peter.

Research output: Contribution to journal › Article

TY - JOUR

T1 - ARMA-Based SEM When the Number of Time Points T Exceeds the Number of Cases N

T2 - Raw Data Maximum Likelihood

AU - Hamaker, Ellen L.

AU - Dolan, Conor V.

AU - Molenaar, Peter

PY - 2003/12/1

Y1 - 2003/12/1

N2 - Longitudinal structural equation modeling has generally addressed the time-dependent covariance structure of a relatively small number of repeated measures, T, observed in a relatively large representative sample, N. In contrast, the literature on autoregressive moving average modeling is usually directed at a single realization comprising many observations, that is, N = 1, and T > 50. This article deals with autoregressive moving average-based structural equation modeling of time series data, in the situation that N is small, T is intermediate, and T > N. The aims of this article are to (a) give a brief overview of the development of alternative formulations of the likelihood function to obtain estimates of autoregressive moving average parameters, in particular the formulation that lies at the basis of Mélard's algorithm; (b) show the equivalence between the likelihood function to obtain estimates for these parameters, and the raw data likelihood method that can be used in structural equation modeling programs like Mx, and demonstrate this equivalence through simulation experiments; and (c) provide illustrations of this use of Mx with real data.

AB - Longitudinal structural equation modeling has generally addressed the time-dependent covariance structure of a relatively small number of repeated measures, T, observed in a relatively large representative sample, N. In contrast, the literature on autoregressive moving average modeling is usually directed at a single realization comprising many observations, that is, N = 1, and T > 50. This article deals with autoregressive moving average-based structural equation modeling of time series data, in the situation that N is small, T is intermediate, and T > N. The aims of this article are to (a) give a brief overview of the development of alternative formulations of the likelihood function to obtain estimates of autoregressive moving average parameters, in particular the formulation that lies at the basis of Mélard's algorithm; (b) show the equivalence between the likelihood function to obtain estimates for these parameters, and the raw data likelihood method that can be used in structural equation modeling programs like Mx, and demonstrate this equivalence through simulation experiments; and (c) provide illustrations of this use of Mx with real data.

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UR - http://www.scopus.com/inward/citedby.url?scp=33846477146&partnerID=8YFLogxK

U2 - 10.1207/S15328007SEM1003_2

DO - 10.1207/S15328007SEM1003_2

M3 - Article

VL - 10

SP - 352

EP - 379

JO - Structural Equation Modeling

JF - Structural Equation Modeling

SN - 1070-5511

IS - 3

ER -