Mixture Model Analysis of Partially Rank‐Ordered Set Samples: Age Groups of Fish from Length‐Frequency Data

Hatefi, Armin; Jozani, Mohammad Jafari; Öztürk, Ömer

doi:10.1111/sjos.12140

Cited by 23 publications

(19 citation statements)

References 20 publications

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“…However, one can easily see that

L_{IJPS}^{com1} false(boldΨ false| \cdot false)

still has a very complex form, due to the presence of functions of the following forms in f ( h : H ) (·; Ψ ), when h varies in {1,…, H },

f (\cdot; Ψ) = \sum_{j = 1}^{M} π_{j} f_{j} (\cdot; {bold-italicθ}_{j}), {\{F (\cdot; Ψ)\}}^{a} = {\{\sum_{j = 1}^{M} π_{j} F_{j} (\cdot; {bold-italicθ}_{j})\}}^{a} and {\{\bar{F} (\cdot; Ψ)\}}^{b} = {\{\sum_{j = 1}^{M} π_{j} {\bar{F}}_{j} (\cdot; {bold-italicθ}_{j})\}}^{b},

with a , b ∈ {1,…, H }. To obtain an easier to use complete‐data likelihood function and proceed with a suitable EM algorithm, as described in the supplementary document, we define further latent vectors to obtain a new set of complete‐data denoted by

bold-italicY = false{false({boldΔ}_{i}^{false[h false]}, {bold-italicZ}_{i}^{false[h false]}, {bold-italicW}_{i}^{false[h false]}, {bold-italicV}_{i}^{false[h false]} false), i = 1, 2, …, n; h = 1, …, H false}

. The complete‐data likelihood function associated with Y is given below as the joint distribution of { X ∗ , Y } and will be used to estimate Ψ , …”

Section: Maximum Likelihood Estimation For Fmms Using Jps Designmentioning

confidence: 99%

“…In the standard methods of modeling and inference for FMMs, samples are often obtained using the SRS design. Recently, finite mixture modeling based on other sampling designs such as RSS is considered in the literature and it is shown that RSS‐based estimators of FMM parameters are more efficient than their SRS counterparts . In spite of several successful applications of RSS, practitioners are still reluctant to use RSS in many practical problems, as they often prefer to have samples from the underlying population that can be used for multiple purposes.…”

Section: Introductionmentioning

confidence: 99%

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Judgment post‐stratification in finite mixture modeling: An example in estimating the prevalence of osteoporosis

Omidvar

Jozani

Nematollahi

2018

Statistics in Medicine

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Judgment post-stratification is used to supplement observations taken from finite mixture models with additional easy to obtain rank information and incorporate it in the estimation of model parameters. To do this, sampled units are post-stratified on ranks by randomly selecting comparison sets for each unit from the underlying population and assigning ranks to them using available auxiliary information or judgment ranking. This results in a set of independent order statistics from the underlying model, where the number of units in each rank class is random. We consider cases where one or more rankers with different ranking abilities are used to provide judgment ranks. The judgment ranks are then combined to produce a strength of agreement measure for each observation. This strength measure is implemented in the maximum likelihood estimation of model parameters via a suitable expectation maximization algorithm. Simulation studies are conducted to evaluate the performance of the estimators with or without the extra rank information. Results are applied to bone mineral density data from the third National Health and Nutrition Examination Survey to estimate the prevalence of osteoporosis in adult women aged 50 and over.

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“…However, one can easily see that

L_{IJPS}^{com1} false(boldΨ false| \cdot false)

still has a very complex form, due to the presence of functions of the following forms in f ( h : H ) (·; Ψ ), when h varies in {1,…, H },

f (\cdot; Ψ) = \sum_{j = 1}^{M} π_{j} f_{j} (\cdot; {bold-italicθ}_{j}), {\{F (\cdot; Ψ)\}}^{a} = {\{\sum_{j = 1}^{M} π_{j} F_{j} (\cdot; {bold-italicθ}_{j})\}}^{a} and {\{\bar{F} (\cdot; Ψ)\}}^{b} = {\{\sum_{j = 1}^{M} π_{j} {\bar{F}}_{j} (\cdot; {bold-italicθ}_{j})\}}^{b},

bold-italicY = false{false({boldΔ}_{i}^{false[h false]}, {bold-italicZ}_{i}^{false[h false]}, {bold-italicW}_{i}^{false[h false]}, {bold-italicV}_{i}^{false[h false]} false), i = 1, 2, …, n; h = 1, …, H false}

. The complete‐data likelihood function associated with Y is given below as the joint distribution of { X ∗ , Y } and will be used to estimate Ψ , …”

Section: Maximum Likelihood Estimation For Fmms Using Jps Designmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Judgment post‐stratification in finite mixture modeling: An example in estimating the prevalence of osteoporosis

Omidvar

Jozani

Nematollahi

2018

Statistics in Medicine

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show abstract

“…These sampling designs are techniques to obtain more representative samples from the underlying population where measurement of the units is costly and/or time-consuming. In such sampling designs, sampling units are ordered fairly accurately by using available auxiliary information which may be costly to some extent (see [3]).…”

Section: Introductionmentioning

confidence: 99%

Improved Kaplan-Meier Estimator in Survival Analysis Based on Partially Rank-Ordered Set Samples

Nematolahi

Nazari

Shayan

et al. 2020

Computational and Mathematical Methods in Medicine

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This study presents a novel methodology to investigate the nonparametric estimation of a survival probability under random censoring time using the ranked observations from a Partially Rank-Ordered Set (PROS) sampling design and employs it in a hematological disorder study. The PROS sampling design has numerous applications in medicine, social sciences and ecology where the exact measurement of the sampling units is costly; however, sampling units can be ordered by using judgment ranking or available concomitant information. The general estimation methods are not directly applicable to the case where samples are from rank-based sampling designs, because the sampling units do not meet the identically distributed assumption. We derive asymptotic distribution of a Kaplan-Meier (KM) estimator under PROS sampling design. Finally, we compare the performance of the suggested estimators via several simulation studies and apply the proposed methods to a real data set. The results show that the proposed estimator under rank-based sampling designs outperforms its counterpart in a simple random sample (SRS).

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“…Since the introduction of RSS, it has attracted significant attention from researchers and has generated both theory and methodology, as well as a wide range of applications in many different fields (e.g., Chen, Bai & Sinha, 2003;Wolfe, 2012, and references therein). Recent RSS development includes Frey, Ozturk & Deshpande (2007), Li & Balakrishnan (2008), Ghosh & Tiwari (2008), Ozturk (2013), Haq et al (2014), Ozturk & Jozani (2014), Hatefi, Jozani & Ziou (2014), Frey & Wang (2014), Hatefi, Jozani & Ozturk (2015), Ozturk (2015), Frey & Zhang (2017), , Zamanzade & Mahdizadeh (2018) and so on.…”

Section: Introductionmentioning

confidence: 99%

Using ranked set sampling with binary outcomes in cluster randomized designs

Wang

Lim

et al. 2019

Can J Statistics

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We study the use of ranked set sampling (RSS) with binary outcomes in cluster‐randomized designs (CRDs), where a generalized linear mixed model (GLMM) is used to model the hierarchical data structure involved. Under the GLMM‐based framework, we propose three different approaches to estimate the treatment effect, including the nonparametric (NP), maximum likelihood (ML) and pseudo likelihood (PL) estimators. We investigate their asymptotic properties and examine their finite‐sample performance via simulation. Based on these three RSS estimators, we further develop procedures for testing the existence of the treatment effect. We examine the power and size of our proposed RSS tests and compare them with existing tests based on simple random sampling (SRS). All the proposed RSS estimation and test methods are illustrated with two data examples, one for rare events and the other for non‐extreme events. Throughout our investigations, we also consider the possible effect of imperfect ranking. Among the proposed methods, we provide recommendations on whether to use RSS rather than SRS with binary outcomes in CRDs and, if yes, when to use which RSS method. The Canadian Journal of Statistics 48: 342–365; 2020 © 2019 Statistical Society of Canada

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Mixture Model Analysis of Partially Rank‐Ordered Set Samples: Age Groups of Fish from Length‐Frequency Data

Cited by 23 publications

References 20 publications

Judgment post‐stratification in finite mixture modeling: An example in estimating the prevalence of osteoporosis

Judgment post‐stratification in finite mixture modeling: An example in estimating the prevalence of osteoporosis

Improved Kaplan-Meier Estimator in Survival Analysis Based on Partially Rank-Ordered Set Samples

Using ranked set sampling with binary outcomes in cluster randomized designs

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