Spatial Autocorrelation and Qualitative Sampling: The Case of Snowball Type Sampling Designs

Abstract

Hidden populations are defined as subsets of a larger population that are hard to target with traditional (e.g., random) sampling methods. For qualitative research, difficulties of achieving a good sample could include the time of day surveys are conducted, the safety of interviewers in areas with high crime rates, or the unwillingness of members in a hidden population to interact with researchers. Various chain-driven methods, such as snowball sampling (SS) and respondent-driven sampling (RDS), have been developed as techniques to reach hidden populations. Such methodologies have been implemented in previous research for investigations into the networks of people associated with illicit drug use and other risky behavior. To date, some of these studies have considered the contribution to variance inflation attributed to the effects of social network (SN) autocorrelation but not to spatial autocorrelation. This article implements a probabilistic simulation based on two RDS network data sets: one from Rio de Janeiro and another from the Colorado Springs metropolitan region. The network configurations are studied with respect to their associated geographic landscapes and a set of selected census variables. The results of the simulations demonstrate a lack of bias on the mean of the demographic variables and impacts on sample-to-sample variability attributed to both SN autocorrelation and spatial autocorrelation in the presence of other sources of excess variance. Findings reported in this article offer insights into designing future studies using network-based sampling strategies.

隐藏人口, 定义为难以运用传统 (例如随机) 抽样方法瞄准的较大型人口对象。对质化研究而言, 难以取得好的样本之原因, 可能包含一日之中进行调查的时间, 访问者在高犯罪率地区中的安危, 或是隐藏人口的成员不愿与研究者进行互动。诸多链传动的方法, 例如滚雪球抽样 (SS) 和受访者驱动的抽样 (RDS), 已发展成为接触隐藏人口的技巧。这些方法, 已运用于过往探讨与非法毒品使用和其它高风险行为相关的人口网络之研究。至今, 这些研究已有部分考量社会网络 (SN) 自相关效应所导致的变异数膨胀, 但却未考量空间自相关。本文执行根据两个 RDS 网络数据集的或然性模拟：一个来自里约热内卢, 另一个则来自科罗拉多泉的大都会区域。本文研究网络结构及相关的地理地景和一系列选择的人口变项。模拟的结果, 证实人口变项的平均数没有偏误, 以及其他超额变异数来源存在时, 对于同时归因于 SN 自相关和空间自相关的样本间的变异性之影响。本文所报导的研究发现, 为未来运用以网络为基础的抽样策略之研究设计提供洞见。

Las poblaciones ocultas son definidas como subconjuntos de una población más grande que son difíciles de abocar con métodos de muestreo tradicionales (e.g., el aleatorio). En lo que a la investigación cualitativa se refiere, las dificultades para lograr una buena muestra podrían incluir el momento del día cuando se efectúan los estudios, la seguridad de los entrevistadores en áreas de altas tasas de criminalidad, o la falta de voluntad de los miembros de una población oculta de interactuar con los investigadores. Varios métodos orientados por encadenamiento, tales como muestreo bola de nieve (SS) y el muestreo centrado en los entrevistados (RDS), han sido desarrollados como técnicas con las cuales llegar a las poblaciones ocultas. Esas metodologías han sido implementadas en investigación precedente en estudios de las redes de personas asociadas con el uso de drogas ilícitas y otras conductas riesgosas. Hasta el momento, algunos de estos estudios han considerado la contribución a la inflación de varianza atribuida a los efectos de autocorrelación de red social (SN), pero no para la autocorrelación espacial. Este artículo puso en práctica una simulación probabilística basada en dos conjuntos de datos de redes RDS: uno de Río de Janeiro y el otro de la región metropolitana de Colorado Springs. Las configuraciones de redes son estudiadas con respecto a sus paisajes geográficos asociados y a un conjunto de variables censales selectas. Los resultados de las simulaciones mostraron una falta de sesgo en la media de las variables demográficas, e impactos sobre la variabilidad de muestra a muestra atribuida a la autocorrelación SN y a la autocorrelación espacial en presencia de otras fuentes de exceso de varianza. Los hallazgos que se reportan en este artículo ofrecen una contribución inteligente para el diseño de estudios futuros que utilicen estrategias de muestreo basadas en redes.

Key Words:

• respondent-driven sampling
• snowball sampling
• social network
• spatial autocorrelation

关键词：:

• 受访者驱动的抽样
• 滚雪球抽样
• 社会网络
• 空间自相关。

Palabras clave:

• muestreo centrado en el entrevistado
• muestreo bola de nieve
• red social
• autocorrelación espacial

Acknowledgments

We thank Dr. Francisco Inacio Bastos (Oswaldo Cruz Foundation) and Stephen Q. Muth (Director, Quintus-ential Solutions) for providing the Rio de Janeiro and Colorado Springs social network data, respectively, facilitating this research and Dr. Parmanand Sinah for his initial work on retrieving the social network data.

Funding

This research was conducted with support from the U.S. National Science Foundation, Grant BCS-1262717. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

Notes

1. This numerical intensity is one reason why only a single year of the Colorado Springs data has been used as a basis for a simulation experiment. Because this study furnishes a demonstration of concept, this simplification is reasonable.

2. A single year of data was employed because of the sizes of these matrices. The analytical nature of the eigenvectors used in the simulation experiment indicates that expanding the study to multiple years would add detail, but not alter implications. Replicating the analysis with two different geographic landscapes furnishes better comparative results than comparing analyses for two different years for a single geographic landscape. This latter case would yield correlated outcomes.

Additional information

Notes on contributors

Daniel A. Griffith

DANIEL A. GRIFFITH is Asbhel Smith Professor of Geospatial Information Sciences, in the School of Economic, Political, and Policy Sciences at the University of Texas at Dallas, Richardson, TX 75080. E-mail: [email protected]. His research interests include spatial statistics, spatial interaction, spatial demography, spatial epidemiology, urban economic geography, and urban public health.

E Scott Morris

E SCOTT MORRIS is a Research Data Scientist with Monsanto in St. Louis, MO. E-mail: [email protected]. He currently is working within agricultural analytics. His research interests also include fractal geometries within urban settings.

Vaishnavi Thakar

VAISHNAVI THAKAR is a PhD Candidate in the Geospatial Information Sciences Program in the School of Economic, Political, and Policy Sciences at the University of Texas at Dallas, Richardson, TX 75080. E-mail: [email protected]. Her research interests include spatial statistics, geocomputation, and the development of spatial optimization techniques for disaster mitigation and management.