Identifiability of parameters in longitudinal correlated Poisson and inflated beta regression model with non-ignorable missing mechanism. (English) Zbl 1440.62289

Summary: The identifiability of a statistical model is an essential and necessary property. When a model is not identifiable, even an infinite number of observations cannot determine the true parameter. Non-identifiablity problem in generalized linear models with and without random effects is very common. Also it can occur in such models when the response variable has non-ignorably missing. Since the structure of the beta regression model is similar to that of the generalized linear models and identifiability of many commonly used models such as the beta regression model has not been investigated in the literature, we establish a study about identifiability of some types of the beta regression models such as beta regression model with non-ignorable missing mechanism, zero and one inflated beta regression model, zero and one inflated beta regression model with non-ignorable missing mechanism, longitudinal beta regression model, longitudinal zero and one inflated beta regression model, longitudinal zero and one inflated beta regression model with non-ignorable missing mechanism, and longitudinal correlated bivariate Poisson and zero and one inflated beta regression model with non-ignorable missing mechanism. We construct estimators for the parameters in all mentioned models based on the EM algorithm and the likelihood-based approach. Simulation results and two applications of the Facebook network and FBI datasets are also presented.


62J12 Generalized linear models (logistic models)
62J02 General nonlinear regression
62H11 Directional data; spatial statistics
62D10 Missing data
62P25 Applications of statistics to social sciences
Full Text: DOI


[1] Casella, G.; Berger, RL., Statistical inference, II (2002), Pacific Grove (CA): Duxbury, Pacific Grove (CA)
[2] Martin, ES; Quintana, F., Consistency and identifiability revisited, Braz J Probab Stat, 16, 99-106 (2002) · Zbl 1049.62003
[3] Demidenko, E., Mixed models: theory and applications with R (2013), New York (NY): Wiley, New York (NY) · Zbl 1276.62049
[4] Wang, W., Identifiability of linear mixed effects models, Electron J Stat, 7, 244-263 (2013) · Zbl 1337.62182
[5] Bahrami Samani, E., Sensitivity analysis for the identifiability with application to latent random effect model for the mixed data, J Appl Stat, 41, 12, 2761-2776 (2014)
[6] Miao, W.; Ding, P.; Geng, Z., Identifiability of normal and normal mixture models with nonignorable missing data, J Am Stat Assoc, 111, 516, 1673-1683 (2016)
[7] Cui, X.; Guo, J.; Yang, G., On the identifiability and estimation of generalized linear models with parametric nonignorable missing data mechanism, Comput Stat Data Anal, 107, 64-80 (2017) · Zbl 1466.62050
[8] Kieschnick, R.; McCullough, BD., Regression analysis of variates observed on (0, 1): percentages, proportions and fractions, Stat Model, 3, 193-213 (2003) · Zbl 1070.62056
[9] Ferrari, S.; Cribari-Neto, F., Beta regression for modelling rates and proportions, J Appl Stat, 31, 7, 799-815 (2004) · Zbl 1121.62367
[10] Johnson, NL; Kotz, S.; Balakrishnan, N., Continuous univariate distributions, I (1994), New York (NY): Wiley, New York (NY)
[11] Verkuilen, J.; Smithson, M., Mixed and mixture regression models for continuous bounded responses using the beta distribution, J Educ Behav Stat, 37, 1, 82-113 (2012)
[12] Smithson, M.; Verkuilen, J., A better lemon squeezer? maximum-likelihood regression with beta-distributed dependent variables, Psychol Methods, 11, 1, 54 (2006)
[13] Hunger, M.; Döring, A.; Holle, R., Longitudinal beta regression models for analyzing health-related quality of life scores over time, BMC Med Res Methodol, 12, 1, 144 (2012)
[14] Ospina, R.; Ferrari, SL., A general class of zero-or-one inflated beta regression models, Comput Stat Data Anal, 56, 6, 1609-1623 (2012) · Zbl 1243.62099
[15] Tu, W.Zero-inflated data. Wiley StatsRef: statistics reference online; 2002,
[16] Papadopoulos, A.; Li, G., A note on goodness of fit test using moments, Statistica, 62, 1, 71-86 (2007) · Zbl 1188.62158
[17] Tabrizi, E, Samani, EB, Ganjali, M, Joint modezling of mixed zero-inflated count and (k, l)-inflated beta longitudinal responses with nonignorable missing values for social network analysis. Submitted to the Multivariate Behavioral Research. 2020.
[18] Tabrizi, E.; Samani, EB; Ganjali, M., Analysis of mixed correlated bivariate zero-inflated count and (k, l)-inflated beta responses with application to social network datasets, Commun Stat-Theory Methods, 48, 1-31 (2018)
[19] Viswanath, B, Mislove, A, Cha, M, Gummadi, KP, On the evolution of user interaction in facebook. In Proceedings of the 2nd ACM workshop on Online social networks; Barcelona; 2009. p. 37-42.
[20] Patil, K., Validation of beta distribution for spectrum usage using Kolmogorov-Smirnov test, Int J Comput Appl, 144, 9, 23-26 (2016)
[21] Tabrizi, E, Samani, EB, Ganjali, M, A note on the identi ability of latentvariable models for mixed longitudinal data. Minor Revision to statistics and probability letters. 2020.
[22] Wang, S.; Shao, J.; Kim, JK., An instrumental variable approach for identification and estimation with nonignorable nonresponse, Stat Sin, 24, 1097-1116 (2014) · Zbl 06431822
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