×

Multivariate regression models for discrete and continuous repeated measurements. (English) Zbl 0825.62179

Summary: A general class of multivariate regression models is considered for repeated measurements with discrete and continuous outcome variables. The proposed model is based on the seemingly unrelated regression model (Zellner, 1962) and an extension of the model of Park and Woolson (1992). The regression parameters of the model are consistently estimated using the two-stage least squares method. When the outcome variables are multivariate normal, the two-stage estimator reduces to Zellner’s two- stage estimator. As a special case, we consider the marginal distribution described by Liang and Zeger (1986). Under this distributional assumption, we show that the two-stage estimator has similar asymptotic properties and comparable small sample properties to Liang and Zeger’s estimator. Since the proposed approach is based on the least squares method, however, any distributional assumption is not required for outcome variables. As a result, the proposed estimator is more robust to the marginal distribution of outcomes.

MSC:

62-XX Statistics
Full Text: DOI

References:

[1] DOI: 10.2307/2682808 · Zbl 0573.62061 · doi:10.2307/2682808
[2] DOI: 10.2307/2684488 · doi:10.2307/2684488
[3] DOI: 10.2307/2530695 · Zbl 0625.62052 · doi:10.2307/2530695
[4] Karim M.R., GRR1 PC SAS (1989)
[5] DOI: 10.2307/2285876 · doi:10.2307/2285876
[6] DOI: 10.2307/2529876 · Zbl 0512.62107 · doi:10.2307/2529876
[7] DOI: 10.1093/biomet/73.1.13 · Zbl 0595.62110 · doi:10.1093/biomet/73.1.13
[8] DOI: 10.2307/2347629 · Zbl 0825.62613 · doi:10.2307/2347629
[9] DOI: 10.1093/biomet/78.1.153 · doi:10.1093/biomet/78.1.153
[10] Lipsitz S.R., Communications in Statistics-Simulation and Computation 19 pp 821– (1990)
[11] McCullagh P., Generalized linear models (1989) · Zbl 0588.62104 · doi:10.1007/978-1-4899-3242-6
[12] DOI: 10.2307/2531484 · Zbl 0707.62250 · doi:10.2307/2531484
[13] Paik M.C., Communications in Statistics-Theory and Method 17 pp 1155– (1988)
[14] DOI: 10.1080/03610919208813059 · Zbl 0775.62197 · doi:10.1080/03610919208813059
[15] DOI: 10.2307/2531733 · Zbl 0715.62145 · doi:10.2307/2531733
[16] DOI: 10.1093/biomet/73.3.707 · Zbl 0621.62104 · doi:10.1093/biomet/73.3.707
[17] DOI: 10.1093/biomet/63.3.581 · Zbl 0344.62034 · doi:10.1093/biomet/63.3.581
[18] DOI: 10.2307/2682829 · doi:10.2307/2682829
[19] DOI: 10.1093/biomet/75.1.172 · Zbl 0635.62070 · doi:10.1093/biomet/75.1.172
[20] DOI: 10.1093/biomet/75.1.129 · Zbl 0636.62073 · doi:10.1093/biomet/75.1.129
[21] DOI: 10.2307/2289285 · doi:10.2307/2289285
[22] DOI: 10.1002/sim.4780070115 · doi:10.1002/sim.4780070115
[23] DOI: 10.1093/biomet/77.3.642 · doi:10.1093/biomet/77.3.642
[24] DOI: 10.2307/2281644 · Zbl 0113.34902 · doi:10.2307/2281644
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.