Merging multiple longitudinal studies with study-specific missing covariates: A joint estimating function approach

Biometrics ◽  
2015 ◽  
Vol 71 (4) ◽  
pp. 929-940 ◽  
Author(s):  
Fei Wang ◽  
Peter X.-K. Song ◽  
Lu Wang
Keyword(s):  
Longitudinal Studies ◽  
Function Approach ◽  
Missing Covariates ◽  
Estimating Function

An estimating function approach to linkage heterogeneity

2013 ◽  
Vol 92 (3) ◽  
pp. 413-421
Author(s):  
HE GAO ◽  
YING ZHOU ◽  
WEIJUN MA ◽  
HAIDONG LIU ◽  
LINAN ZHAO
Keyword(s):  
Function Approach ◽  
Estimating Function

scholarly journals Estimation for Wrapped Zero Inflated Poisson and Wrapped Poisson Distributions

2016 ◽  
Vol 5 (3) ◽  
pp. 1 ◽  
Author(s):  
Aerambamoorthy Thavaneswaran ◽  
Saumen Mandal ◽  
Dharini Pathmanathan
Keyword(s):  
Closed Form ◽  
Information Matrix ◽  
Score Function ◽  
Function Approach ◽  
Closed Form Expression ◽  
Characteristic Functions ◽  
Model Parameters ◽  
Estimating Function ◽  
Method Of Moment ◽  
Poisson Distributions

There has been a growing interest in discrete circular models such as wrapped zero inflated Poisson and wrapped Poisson distributions and the trigonometric moments (see Brobbey et al., 2016 and Girija et al., 2014). Also, characteristic functions of stable processes have been used to study the estimation of the model parameters using estimating function approach (see Thavaneswaran et al., 2013). One difficulty in estimating the circular mean and the resultant mean length parameter of wrapped Poisson (WP) or wrapped zero inflated Poisson (WZIP) is that neither the likelihood of WP/WZIP random variable nor the score function is available in closed form, which leads one to use either trigonometric method of moment estimation (TMME) or an estimating function approach. In this paper, we study the estimation of WZIP distribution and WP distribution using estimating functions and obtain the closed form expression of the information matrix. We also derive the asymptotic distribution of the tangent of the mean direction for both the WZIP and WP distributions.

scholarly journals Extended Poisson–Tweedie: Properties and regression models for count data

2017 ◽  
Vol 18 (1) ◽  
pp. 24-49 ◽  
Author(s):  
Wagner H. Bonat ◽  
Bent Jørgensen ◽  
Célestin C. Kokonendji ◽  
John Hinde ◽  
Clarice G. B. Demétrio
Keyword(s):  
Count Data ◽  
Linear Models ◽  
Negative Binomial ◽  
Function Approach ◽  
Estimating Function ◽  
Estimating Functions ◽  
Unified Framework ◽  
Dispersion Parameters ◽  
Computational Implementation ◽  
Heavy Tailed

We propose a new class of discrete generalized linear models based on the class of Poisson–Tweedie factorial dispersion models with variance of the form [Formula: see text], where [Formula: see text] is the mean and [Formula: see text] and [Formula: see text] are the dispersion and Tweedie power parameters, respectively. The models are fitted by using an estimating function approach obtained by combining the quasi-score and Pearson estimating functions for the estimation of the regression and dispersion parameters, respectively. This provides a flexible and efficient regression methodology for a comprehensive family of count models including Hermite, Neyman Type A, Pólya–Aeppli, negative binomial and Poisson-inverse Gaussian. The estimating function approach allows us to extend the Poisson–Tweedie distributions to deal with underdispersed count data by allowing negative values for the dispersion parameter [Formula: see text]. Furthermore, the Poisson–Tweedie family can automatically adapt to highly skewed count data with excessive zeros, without the need to introduce zero-inflated or hurdle components, by the simple estimation of the power parameter. Thus, the proposed models offer a unified framework to deal with under-, equi-, overdispersed, zero-inflated and heavy-tailed count data. The computational implementation of the proposed models is fast, relying only on a simple Newton scoring algorithm. Simulation studies showed that the estimating function approach provides unbiased and consistent estimators for both regression and dispersion parameters. We highlight the ability of the Poisson–Tweedie distributions to deal with count data through a consideration of dispersion, zero-inflated and heavy tail indices, and illustrate its application with four data analyses. We provide an R implementation and the datasets as supplementary materials.

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