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ISSN : 1229-067X
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잠재성장모형의 사용을 위한 표본크기 결정
Determining sample size requirements in Latent Growth Models
석혜은 (이화여자대학교)
초록
시간의 흐름에 따른 행동변화를 분석하기 위한 방법으로서 잠재성장모형은 최근 교육학이나 심리학 등의 여러 학문 분야에서 활발하게 사용되고 있다. 하지만 지난 수년간 성장모형에서의 여러 발전적 연구가 진행되어 왔음에도 불구하고, 모형의 적절한 표본크기를 결정하는 문제는 여전히 충분한 연구가 존재하지 않는다. 본 연구에서는 세 가지 활발하게 이용되는 잠재성장모형(선형모형, 2차 함수모형, 요인부하추정모형)을 이용하여 다양한 조건에서 시뮬레이션을 실시하였고, 각 모형의 모수를 정확히 추정하기 위해 요구되는 최소한의 표본크기에 대한 가이드라인을 제공하고자 하였다. 시뮬레이션 결과, 측정시점의 수가 적고 결측치가 존재하며 이분형 결과변수가 모형 안에 포함되었을 때 큰 표본크기가 필요하였다. 특히 모형을 복잡하게 만드는 조건들이 동시에 발생했을 때(예를 들어, 모형추정을 위한 최소한의 측정시점을 가진 상태에서 결측치 및 이분형 결과변수가 동시에 존재할 때), 각 조건들이 서로 상호작용을 일으켜 매우 큰 표본크기에서도 정확한 모수추정이 가능하지 않은 경우도 발생하였다. 또한 추가적인 성장요인(growth factor)을 가지는 2차 함수 성장모형은 선형모형이나 요인부하추정모형에 비해 눈에 띄게 큰 표본을 필요로 하였음을 발견하였다. 마지막으로 다양한 조건하에서 이루어진 시뮬레이션의 결과를 이용해 이를 실질적으로 어떻게 적용해야 할지에 대하여 논의하였다.
- keywords
- Latent growth model, Quadratic latent growth model, Sample size, Simulation, 잠재성장모형, 2차 함수 잠재성장모형, 표본크기, 몬테카를로 시뮬레이션
Abstract
Recently, latent growth models (LGMs) have been widely used in education or psychology for analyzing behavioral change over time. Although there have been a plethora of methodological research for the last couple of decades, required sample sizes for the model under various conditions still remains unclear for most substantive researchers. The present study carried out a series of Monte Carlo simulations with three mostly used types of LGM and tried to provide general guidelines for minimum required sample sizes for accurate estimation. According to the results, larger sample sizes were required when the number of measurement occasions were small, when missing responses were present, and when a binary outcome variable was included in the model. In particular, when the complex conditions were combined, very large sample sizes were required showing interactions between those conditions. Additionally, we discovered that quadratic growth models required remarkably larger sample sizes compared to linear or lambda-estimated growth models with minimal number of time points. Finally, we discussed how to apply the simulation results to determining appropriate sample sizes in practical situations.
- keywords
- Latent growth model, Quadratic latent growth model, Sample size, Simulation, 잠재성장모형, 2차 함수 잠재성장모형, 표본크기, 몬테카를로 시뮬레이션
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