ISSN 0439-755X
CN 11-1911/B

中国科学院心理研究所

• •

### 分类精确性指数Entropy在潜剖面分析中的 表现：一项蒙特卡罗模拟研究

王孟成1,2,3;邓俏文1,2;毕向阳4;叶浩生1,2,3;杨文登1,3

1.  (1广州大学心理系; 2广州大学心理测量与潜变量建模研究中心; 3广东省未成年人心理健康与教育认知神经科学实验室, 广州 510006) (4中国政法大学社会学院, 北京 102249)
• 收稿日期:2016-06-03 出版日期:2017-11-26 发布日期:2017-09-25
• 通讯作者: 王孟成, E-mail: wmcheng2006@126.com; 杨文登, E-mail: yangwendeng@163.com E-mail:E-mail: wmcheng2006@126.com; E-mail: yangwendeng@163.com
• 基金资助:
国家自然科学基金(31400904); 广州大学“创新强校工程”青年创新人才类项目(2014WQNCX069); 广州大学青年拔尖人才培养项目(BJ201715)。

### Performance of the entropy as an index of classification accuracy in latent profile analysis: A Monte Carlo simulation study

WANG Meng-Cheng1,2,3; DENG Qiaowen1,2; BI Xiangyang4; YE Haosheng1,2,3; YANG Wendeng1,3

1.  (1 Department of Psychology, Guangzhou University; 2 The Center for Psychometrics and Latent Variable Modeling, Guangzhou University; 3 The Key Laboratory for Juveniles Mental Health and Educational Neuroscience in Guangdong Province, Guangzhou University, Guangzhou 510006, China) (4 School of Sociology, China University of Political Science and Law, Beijing 102249, China)
• Received:2016-06-03 Online:2017-11-26 Published:2017-09-25
• Contact: WANG Meng-Cheng, E-mail: wmcheng2006@126.com; YANG Wendeng, E-mail: yangwendeng@163.com E-mail:E-mail: wmcheng2006@126.com; E-mail: yangwendeng@163.com
• Supported by:

Abstract:  Latent Profile Analysis (LPA) is a latent variable modeling technique that identifies latent (unobserved) subgroups of individuals within a population based on continuous indicators. LPA has become a popular statistical method for modelling unobserved population heterogeneity in social and behavioral science. Entropy is a standardized index of model-based classification accuracy, with higher values indicating more precise assignment of individuals to latent profiles. In lots of conditions, the aim of substantial research was to assign individual to different latent subgroup. Therefore, Entropy was chosen to report as an index reflecting accuracy of class membership assignment. Unfortunately, very few methodological studies have examined the behavior of Entropy under the conditions where sample sizes, latent class separations, number of indicators, and number of classes are varying. Thus, the primary purpose of this study was to examine how Entropy will perform with different sample sizes, latent class separations, number of indicators, and number of classes. By using Monte Carlo simulation techniques, we generated artificial data to fit true models and evaluated the performance of Entropy and entropy-based indexes (CLC, ICL_BIC, sample adjusted ICL_BIC) under different modeling conditions. The simulation was repeated 100 times for each condition of the 120 combinations: sample sizes (50, 100, 500, 1000, 3000), latent class separations (0.5, 1.2, 3), number of indicators (4, 8, 12, 20), and number of latent classes (3, 5). The continuous indicators of the latent class are not allowed to correlate. Different mean levels on the observed variables are calculated by Mahalanobis distance (MD). The simulations and analyses of the sample data were conducted using the Monte Carlo facilities of Mplus7.4. For 3 latent classes, Entropy values round 0.76 and above are related to at least 90% correct assignment, and Entropy values round 0.64 and below are related to at least 20% classification error rate. When the latent classes is 5, Entropy value around 0.84 and above are related to at least 90% correct assignment. The Entropy value decreases and the classification error rate increases as sample size increases. Entropy performs well under small sample sizes (50-100) and more indicators conditions. Entropy consistently performs better when latent class separation is large (MD=3), and the result is quite consistent across the sample size and number of latent classes. The tendency of CLC, ICL_BIC, and sample adjusted ICL_BIC were similar, which increases as sample size increases, and it also increases under large class separation but the differences of Entropy caused by class separation were more noticeable. This simulation indicates that the Entropy values are strongly correlated with the correct class membership assignment, but it varies according to number of latent classes, sample sizes, latent class separation and number of indicators. Hence, it is hard to determine cutoff values for Entropy, the indicator of class assignment.