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Asymptotic Inferences in a Multinomial Logit Mixed Model for Spatial Categorical Data

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  • Brajendra C. Sutradhar

    (Memorial University)

  • R. Prabhakar Rao

    (Sri Sathya Sai Institute of Higher Learning)

Abstract

There exist many studies on regression analysis for spatial binary data, espsecially in ecological, environmental and socio-economic setups, where spatial responses from neighboring locations within a given threshold distance are correlated. However, in some of these studies, it could be more natural to consider a spatial regression analysis for categorical response data with more than two categories, as an improvement over the spatial binary analysis. But, this type of regression analysis for spatial categorical/multinomial data is not adequately addressed in the literature. One of the main reasons is the difficulty of modeling the spatial familial correlations for categorical data, where a spatial family is generated within the threshold distance for each of the two selected neighboring locations. Also, some of the locations from two families may be pair-wise correlated. Unlike the existing studies, in this paper we propose a familial random effects based multinomial logits mixed (MLM) effects model which accommodates both within and between familial correlations for spatial multinomial data. In this context, the proposed spatial multinomial correlations are contrasted with existing longitudinal multinomial correlations so that the longitudinal correlation models are avoided for spatial multinomial data. Both regression effects and the random effects influence parameters are estimated using the generalized quasi-likelihood approach, whereas the random effects variance and correlation parameters are estimated by the well known method of moments. The large sample properties such as consistency of the proposed estimators are studied analytically. The asymptotic normality of the regression estimators is also studied for the convenience of constructing the confidence intervals when needed. The devirations and proofs are given in details, as opposed to conducting a limited simulation study, to justify the validity and convergence properties of the proposed estimators. The estimating equations those produced consistent estimates are clearly formulated for the computational benefit to the practitioners.

Suggested Citation

  • Brajendra C. Sutradhar & R. Prabhakar Rao, 2023. "Asymptotic Inferences in a Multinomial Logit Mixed Model for Spatial Categorical Data," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 885-930, February.
    • Handle: RePEc:spr:sankha:v:85:y:2023:i:1:d:10.1007_s13171-022-00282-7
    DOI: 10.1007/s13171-022-00282-7
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    References listed on IDEAS

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    1. Sutradhar, Brajendra C., 2021. "Block-band behavior of spatial correlations: An analytical asymptotic study in a spatial exponential family data setup," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    2. Hensley H Mariathas & Brajendra C Sutradhar, 2016. "Variable Family Size Based Spatial Moving Correlations Model," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 78(1), pages 1-38, May.
    3. Pushpakanthie Wijekoon & Alwell Oyet & Brajendra C. Sutradhar, 2019. "Pair-Wise Family-Based Correlation Model for Spatial Count Data," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 133-184, June.
    4. Barry Boots, 2003. "Developing local measures of spatial association for categorical data," Journal of Geographical Systems, Springer, vol. 5(2), pages 139-160, August.
    5. Thomas R. Ten Have & Alfredo Morabia, 1999. "Mixed Effects Models with Bivariate and Univariate Association Parameters for Longitudinal Bivariate Binary Response Data," Biometrics, The International Biometric Society, vol. 55(1), pages 85-93, March.
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