A Parameter Dimension-Split Based Asymptotic Regression Estimation Theory for a Multinomial Panel Data Model

In this paper we revisit the so-called non-stationary regression models for repeated categorical/multinomial data collected from a large number of independent individuals. The main objective of the study is to obtain consistent and efficient regression estimates after taking the correlations of the...

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Vydané v:Sankhya. Series. A Ročník 80; číslo 2; s. 301 - 329
Hlavný autor: Sutradhar, Brajendra C
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New Delhi Springer Science + Business Media 01.08.2018
Springer India
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Mathematics and Statistics
Statistical Theory and Methods
Statistics
Statistics and Computing/Statistics Programs
Primary 62H12, 62F12
Partially estimated likelihood function
Asymptotic properties
Dynamic dependence parameters
Time-dependent covariates
Secondary 60650, 62F10
Lag 1 transitional multinomial probabilities
Regression parameters
Product multinomial for independent groups
ISSN:0976-836X, 0976-8378
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Abstract In this paper we revisit the so-called non-stationary regression models for repeated categorical/multinomial data collected from a large number of independent individuals. The main objective of the study is to obtain consistent and efficient regression estimates after taking the correlations of the repeated multinomial data into account. The existing (1) ‘working’ odds ratios based GEE (generalized estimating equations) approach has both consistency and efficiency drawbacks. Specifically, the GEE-based regression estimates can be inconsistent which is a serious limitation. Some other existing studies use a MDL (multinomial dynamic logits) model among the repeated responses. As far as the estimation of the regression effects and dynamic dependence (i.e., correlation) parameters is concerned, they use either (2) a marginal or (3) a joint likelihood approach. In the marginal approach, the regression parameters are estimated for known correlation parameters by solving their respective marginal likelihood estimating equations, and similarly the correlation parameters are estimated by solving their likelihood equations for known regression estimates. Thus, this marginal approach is an iterative approach which may not provide quick convergence. In the joint likelihood approach, the regression and correlation parameters are estimated simultaneously by searching the maximum value of the likelihood function with regard to these parameters together. This approach may encounter computational drawback, specially when the number of correlation parameters gets large. In this paper, we propose a new estimation approach where the likelihood function for the regression parameters is developed from the joint likelihood function by replacing the correlation parameter with a consistent estimator involving unknown regression parameters. Thus the new approach relaxes the dimension issue, that is, the dimension of the correlation parameters does not affect the estimation of the main regression parameters. The asymptotic properties of the estimates of the main regression parameters (obtained based on consistent estimating functions for correlation parameters) are studied in detail.
AbstractList In this paper we revisit the so-called non-stationary regression models for repeated categorical/multinomial data collected from a large number of independent individuals. The main objective of the study is to obtain consistent and efficient regression estimates after taking the correlations of the repeated multinomial data into account. The existing (1) ‘working’ odds ratios based GEE (generalized estimating equations) approach has both consistency and efficiency drawbacks. Specifically, the GEE-based regression estimates can be inconsistent which is a serious limitation. Some other existing studies use a MDL (multinomial dynamic logits) model among the repeated responses. As far as the estimation of the regression effects and dynamic dependence (i.e., correlation) parameters is concerned, they use either (2) a marginal or (3) a joint likelihood approach. In the marginal approach, the regression parameters are estimated for known correlation parameters by solving their respective marginal likelihood estimating equations, and similarly the correlation parameters are estimated by solving their likelihood equations for known regression estimates. Thus, this marginal approach is an iterative approach which may not provide quick convergence. In the joint likelihood approach, the regression and correlation parameters are estimated simultaneously by searching the maximum value of the likelihood function with regard to these parameters together. This approach may encounter computational drawback, specially when the number of correlation parameters gets large. In this paper, we propose a new estimation approach where the likelihood function for the regression parameters is developed from the joint likelihood function by replacing the correlation parameter with a consistent estimator involving unknown regression parameters. Thus the new approach relaxes the dimension issue, that is, the dimension of the correlation parameters does not affect the estimation of the main regression parameters. The asymptotic properties of the estimates of the main regression parameters (obtained based on consistent estimating functions for correlation parameters) are studied in detail.
Author Sutradhar, Brajendra C
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10.1080/01621459.1995.10476649
10.1093/biomet/78.1.153
10.1198/jasa.2010.tm08551
10.1111/j.1751-5823.2001.tb00463.x
10.1002/sim.4780131106
10.1214/aos/1032894462
10.1007/978-1-4939-2137-9
10.1111/j.1467-9892.2012.00781.x
10.1214/aos/1176350254
10.1198/016214502388618889
10.1289/ehp.8563241
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Issue 2
Keywords Primary 62H12, 62F12
Partially estimated likelihood function
Asymptotic properties
Dynamic dependence parameters
Time-dependent covariates
Secondary 60650, 62F10
Lag 1 transitional multinomial probabilities
Regression parameters
Product multinomial for independent groups
Language English
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Statistics and Computing/Statistics Programs
Title A Parameter Dimension-Split Based Asymptotic Regression Estimation Theory for a Multinomial Panel Data Model
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