Improving the Lavallée and Hidiroglou algorithm for stratification of skewed populations

Gunning, Patricia; Horgan, Jane M.

doi:10.1080/10629360600569170

Cited by 12 publications

(16 citation statements)

References 5 publications

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“…This happened less frequently (6%) for Sethi's algorithm with geometric and iterated initial values as compared to the initial strata of equal size (7%). This agrees with the findings of Gunning & Horgan (2007).…”

Section: Experimental Comparison Of Several Stratification Algorithmssupporting

confidence: 93%

A General Algorithm for Univariate Stratification

Baillargeon¹,

Rivest²

2009

Int Statistical Rev

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This paper presents a general algorithm for constructing strata in a population using "X", a univariate stratification variable known for all the units in the population. Stratum "h" consists of all the units with an "X" value in the interval ["b" "h" - 1 , "b h") . The stratum boundaries {"b h"} are obtained by minimizing the anticipated sample size for estimating the population total of a survey variable "Y" with a given level of precision. The stratification criterion allows the presence of a take-none and of a take-all stratum. The sample is allocated to the strata using a general rule that features proportional allocation, Neyman allocation, and power allocation as special cases. The optimization can take into account a stratum-specific anticipated non-response and a model for the relationship between the stratification variable "X" and the survey variable "Y". A loglinear model with stratum-specific mortality for "Y" given "X" is presented in detail. Two numerical algorithms for determining the optimal stratum boundaries, attributable to Sethi and Kozak, are compared in a numerical study. Several examples illustrate the stratified designs that can be constructed with the proposed methodology. All the calculations presented in this paper were carried out with stratification , an R package that will be available on CRAN (Comprehensive R Archive Network). Copyright (c) 2009 The Authors. Journal compilation (c) 2009 International Statistical Institute.

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Section: Experimental Comparison Of Several Stratification Algorithmssupporting

confidence: 93%

A General Algorithm for Univariate Stratification

Baillargeon¹,

Rivest²

2009

Int Statistical Rev

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“…Gunning and Horgan (2007) also proposed a new approach to generate initial boundaries to the Lavallée and Hidiroglou algorithm, in order to improve the rate of convergence to the optimal solution, often resulting in smaller sample sizes.…”

Section: Stratified Random Samplingmentioning

confidence: 99%

An iterative local search approach applied to the optimal stratification problem

Brito¹,

Ochi²,

Montenegro³

et al. 2010

Int Trans Operational Res

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Stratified sampling is a technique that consists in separating the elements of a population into nonoverlapping groups, called strata. This paper describes a new algorithm to solve the one-dimensional case, which reduces the stratification problem to just determining strata boundaries. Assuming that the number L of strata and the total sample size n are predetermined, we obtain the strata boundaries by taking into consideration an objective function associated with the variance. In order to solve this problem, we have implemented an algorithm based on the iterative local search metaheuristic. Computational results obtained from a real data set are presented and discussed.

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“…The geometric procedure may provide good starting points for optimisation‐based stratification (e.g. Kozak & Verma, ; Gunning & Horgan, ; Gunning et al. , ).…”

Section: Discussionmentioning

confidence: 99%

“…Gunning & Horgan () proposed an even simpler method, which they labelled geometric stratification; it was later used and described in various additional sources (e.g. Gunning & Horgan, ; Gunning et al. , ; Horgan, ).…”

Section: Introductionmentioning

confidence: 99%

Stratification of Skewed Populations: A Comparison of Optimisation‐based versus Approximate Methods

Hidiroglou

Kozak

2017

Int Statistical Rev

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Summary Survey statisticians use either approximate or optimisation‐based methods to stratify finite populations. Examples of the former are the cumrootf (Dalenius & Hodges, ) and geometric (Gunning & Horgan, ) methods, while examples of the latter are Sethi () and Kozak () algorithms. The approximate procedures result in inflexible stratum boundaries; this lack of flexibility results in non‐optimal boundaries. On the other hand, optimisation‐based methods provide stratum boundaries that can simultaneously account for (i) a chosen allocation scheme, (ii) overall sample size or required reliability of the estimator of a studied parameter and (iii) presence or absence of a take‐all stratum. Given these additional conditions, optimisation‐based methods will result in optimal boundaries. The only disadvantage of these methods is their complexity. However, in the second decade of 21st century, this complexity does not actually pose a problem. We illustrate how these two groups of methods differ by comparing their efficiency for two artificial populations and a real population. Our final point is that statistical offices should prefer optimisation‐based over approximate stratification methods; such a decision will help them either save much public money or, if funds are already allocated to a survey, result in more precise estimates of national statistics.

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Improving the Lavallée and Hidiroglou algorithm for stratification of skewed populations

Cited by 12 publications

References 5 publications

A General Algorithm for Univariate Stratification

A General Algorithm for Univariate Stratification

An iterative local search approach applied to the optimal stratification problem

Stratification of Skewed Populations: A Comparison of Optimisation‐based versus Approximate Methods

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