Please wait a minute...
Advances in Psychological Science    2018, Vol. 26 Issue (12) : 2272-2280     DOI: 10.3724/SP.J.1042.2018.02272
Research Method |
Regression mixture modeling: Advances in method and its implementation
Meng-Cheng WANG1,2,3(),Xiangyang BI4()
1. Department of Psychology, Guangzhou University
2. The Center for Psychometric 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
Download: PDF(816 KB)   HTML
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks     Supporting Info
Guide   
Abstract  

The person-centered methods, including latent class analysis (LCA) and latent profile analysis (LPA), are increasingly popular in recent years. Researchers often add covariate variables (i.e., predictor and distal variables) into LCA and LPA models. This kind of models are also called regression mixture models. In this paper, we introduce several new methods. Those methods include (1) the LTB method proposed by Lanza, Tan and Bray (2013) to model categorical outcome variables; and (2) the BCH method proposed by Bolck, Croon and Hagenaars (2004) to deal with continuous distal variables. Using an empirical example, we demonstrate the process of analyses in Mplus. The future directions of those new methods were also discussed.

Keywords person-centered method      mixture modeling      latent class analysis      latent variable modeling      Mplus     
ZTFLH:  B841  
Corresponding Authors: Meng-Cheng WANG,Xiangyang BI     E-mail: wmcheng2006@126.com;necessity@126.com
Issue Date: 30 October 2018
Service
E-mail this article
E-mail Alert
RSS
Articles by authors
Meng-Cheng WANG
Xiangyang BI
Cite this article:   
Meng-Cheng WANG,Xiangyang BI. Regression mixture modeling: Advances in method and its implementation[J]. Advances in Psychological Science, 2018, 26(12): 2272-2280.
URL:  
http://journal.psych.ac.cn/xlkxjz/EN/10.3724/SP.J.1042.2018.02272     OR     http://journal.psych.ac.cn/xlkxjz/EN/Y2018/V26/I12/2272
  
  
  
  
  
  
适用情况 方法 Mplus语句:
Auxiliary=()
评价
结果变量 分类
变量
单步法 无单独语句 直接将类别结果变量作为LCA的测量指标; 这种做法显然会影响测量模型; 纳入不同的结果变量会造成测量模型结果的差异, 因此不推荐使用。
LTB DCAT 是处理类别结果变量最好的方法之一, 推荐使用。
连续
变量
单步法 无单独语句 非正态时表现不佳。
BCH BCH 是处理连续结果变量最好的方法之一, 在 DU3STEP不报告结果时使用。
稳健三步法:类别方差不等 DU3STEP 在结果变量类别内正态分布, 方差不等时表现佳。但会出现类别顺序变化的不足。
稳健三步法:类别方差相等 DE3STEP 在结果变量类别内正态分布, 方差相等时表现佳。
LTB DCON 对假设前提比较敏感, 当假设违反时会扭曲估计结果, 不推荐使用
PC method E 精确性较差, 不推荐实际使用
预测变量 PC method R 结果有偏, 不推荐使用。
单步法 无单独语句 表现良好, 当变量较多时使用不便。
稳健三步法 R3STEP 表现良好, 操作方便, 推荐使用。
  
Title: Lantent Class Analysis
Data: File is older_survey.dat ;
Variable: Names = C2A C2B C2C C2D C2E C2F C2G C2H C2I C2J C2K C2L C2M C2N C2P C2Q ifold age gds agesq11(11 年龄平方项(/100));
USEVARIABLES = C2A-C2Q;
MISSING are all (-9999) ;
CATEGORICAL = C2A-C2Q;
CLASSES = C (2);
Analysis:
TYPE = MIXTURE;
Starts = 50 3;
PROCESSORS = 4; !根据电脑情况指定
PLOT:
TYPE = PLOT3;
SERIES = C2A-C2Q (*);
Savedata:
file is older_survey.txt ;
save is cprob;
output: tech11 tech14;
  
  
Title: Regression Mixture Modeling with Predictive Variable
Data: File is older_survey.dat ;
Variable: Names = C2A C2B C2C C2D C2E C2F C2G C2H C2I C2J C2K C2L C2M C2N C2P C2Q ifold age gdsagesq;
USEVARIABLES = C2A-C2Q;
MISSING are all (-9999) ;
CATEGORICAL = C2A-C2Q;
CLASSES = C (2);
AUXILIARY = age (R3STEP);!选择稳健三步法
Analysis:
TYPE = MIXTURE;
PROCESSORS = 4;
PLOT:TYPE = PLOT3;
SERIES = C2A-C2Q (*);
Savedata: file is older_survey.txt ;
save is cprob;
output: tech11 tech14;
  
TESTS OF CATEGORICAL LATENT VARIABLE MULTINOMIAL LOGISTIC REGRESSIONS USING
THE 3-STEP PROCEDURE
Two-Tailed
Estimate S.E. Est./S.E. P-Value
C#1 ON
AGE 0.153 0.014 11.219 0.000
Intercepts
C#1 -12.935 1.031 -12.541 0.000
  
Title: Regression Mixture Modeling with categorical outcome variable
Data: File is older_survey.dat ;
Variable: Names = C2A C2B C2C C2D C2E C2F C2G C2H C2I C2J C2K C2L C2M C2N C2P C2Q ifold age gdsagesq;
USEVARIABLES = C2A-C2Q;
MISSING are all (-9999) ;
CATEGORICAL = C2A-C2Q;
CLASSES = C (2);
AUXILIARY = ifold (DCAT);!选择DCAT法
Analysis:
TYPE = MIXTURE;
PROCESSORS = 4;
LRTSTARTS = 2 1 80 16;
PLOT:
TYPE = PLOT3;
SERIES = C2A-C2Q (*);
Savedata:
file is older_survey.txt ;
save is cprob;
output: tech11 tech14;
  
EQUALITY TESTS OF MEANS/PROBABILITIES ACROSS CLASSES
IFOLD
Prob S.E. Odds Ratio S.E. 2.5% C.I. 97.5% C.I.
Class 1
Category 1 0.265 0.033 1.000 0.000 1.000 1.000
Category 2 0.735 0.0337 2.133 0.389 1.492 3.049
Class 2
Category 1 0.435 0.016 1.000 0.000 1.000 1.000
Category 2 0.565 0.016 1.000 0.000 1.000 1.000
  
Title: Regression Mixture Modeling with continuous outcome variable
Data: File is older_survey.dat ;
Variable: Names = C2A C2B C2C C2D C2E C2F C2G C2H C2I C2J C2K C2L C2M C2N C2P C2Q ifold age gdsagesq;
USEVARIABLES = C2A-C2Q;
MISSING are all (-9999);
CATEGORICAL = C2A-C2Q;
CLASSES = C (2);
AUXILIARY = gds (BCH);!选择BCH法
Analysis:
TYPE = MIXTURE;
PROCESSORS = 4;
LRTSTARTS = 2 1 80 16; !配合tech14
PLOT: TYPE = PLOT3;
SERIES = C2A-C2Q (*);
Savedata: file is older_survey.txt ;
save is cprob;
output: tech11 tech14;
  
EQUALITY TESTS OF MEANS ACROSS CLASSES USING THE BCH PROCEDURE
WITH 1 DEGREE (S) OF FREEDOM FOR THE OVERALL TEST
GDS
Mean S.E.
Class 1 4.540 0.211
Class 2 2.903 0.075
Chi-Square P-Value
Overall test 52.233 0.000
  
1 邱皓政 . ( 2008). 潜在类别模型的原理与技术. 北京: 教育科学出版社.
url: http://61.136.169.171:8081/opac/book/012004149697?globalSearchWay=title
2 张洁婷, 焦璨, 张敏强 . ( 2010). 潜在类别分析技术在心理学研究中的应用. 心理科学进展, 18( 12), 1991-1998.
url: http://d.wanfangdata.com.cn/Periodical/xlxdt201012019
3 Asparouhov, T., &MuthÉn, B. ( 2014). Auxiliary variables in mixture modeling: Three-step approaches using M plus. Structural Equation Modeling, 21( 3), 329-341.
url: http://psycnet.apa.org/psycinfo/2014-29172-001
4 Asparouhov, T., &MuthÉn, B(2015 ).Auxiliary Variables in Mixture Modeling: Using the BCH Method in Mplus to Estimate a Distal Outcome Model and an Arbitrary Secondary Model.Mplus Web Notes: No.21. Retrieved from
url: http://www.statmodel.com
5 Bakk Z., Oberski D. L., &Vermunt J. K . ( 2016). Relating latent class membership to continuous distal outcomes: Improving the LTB approach and a modified three-step implementation. Structural Equation Modeling, 23( 2), 278-289.
url: http://www.tandfonline.com/doi/abs/10.1080/10705511.2015.1049698
6 Bakk Z., Tekle F. B., &Vermunt J. K . ( 2013). Estimating the association between latent class membership and external variables using bias-adjusted three-step approaches. Sociological methodology.43( 1), 272-311.
7 Bakk, Z., &Vermunt, J.K. ( 2016). Robustness of stepwise latent class modeling with continuous distal outcomes. Structural Equation Modeling, 23( 1), 20-31.
url: http://psycnet.apa.org/record/2015-59198-002
8 Bauer, D.J., &Curran, P.J . ( 2003). Distributional assumptions of growth mixture models: Implications for overextraction of latent trajectory classes. Psychological Methods, 8( 3), 338-363.
pmid: 14596495 url: http://www.ncbi.nlm.nih.gov/pubmed/14596495
9 Bolck A., Croon M., &Hagenaars J . ( 2004). Estimating latent structure models with categorical variables: One-step versus three-step estimators. Political Analysis, 12( 1), 3-27.
url: http://pan.oxfordjournals.org/content/12/1/3
10 Clark, S.L., &MuthÉn, B . ( 2009). Relating latent class analysis results to variables not included in the analysis. Retrieved from
url: http://statmodel2.com/download/relatinglca.pdf
11 Collins, L.M., &Lanza, S.T . ( 2010). Latent class and latent transition analysis: With applications in the social, behavioral, and health sciences . New York: Wiley.
12 Lanza S. T., Tan X., & Bray B. C . ( 2013). Latent class analysis with distal outcomes: A flexible model-based approach. Structural Equation Modeling, 20( 1), 1-26.
pmid: 4240499 url: http://www.ncbi.nlm.nih.gov/pubmed/25419096
13 Morin A. J. S., Morizot J., Boudrias J-S., &Madore I . ( 2011). A multifoci person-centered perspective on workplace affective commitment: A latent profile/factor mixture analysis. Organizational Research Methods,14( 1), 58-90.
url: http://psycnet.apa.org/record/2010-25667-006
14 Sterba, S.K. ( 2013). Understanding linkages among mixture models. Multivariate Behavioral Research, 48( 6), 775-815.
pmid: 26745595 url: http://www.ncbi.nlm.nih.gov/pubmed/26745595
15 Vermunt, J.K. ( 2010). Latent class modeling with covariates: Two improved three-step approaches. Political Analysis, 18, 450-469.
url: http://www.jstor.org/stable/25792024
16 Wang C-P., Brown C. H., &Bandeen-Roche K . ( 2005). Residual diagnostics for growth mixture models: Examining the impact of a preventive intervention on multiple trajectories of aggressive behavior. Journal of the American Statistical Association, 100( 471), 1054-1076.
url: http://www.jstor.org/stable/27590635
[1] WANG Meng-Cheng, DENG Qiaowen, BI Xiangyang.  Latent variable modeling using Bayesian methods[J]. Advances in Psychological Science, 2017, 25(10): 1682-1695.
[2] CHEN Yushuai; WEN Zhonglin; GU Honglei. Factor Mixture Model: An Integration of Latent Class Analysis and Factor Analysis[J]. Advances in Psychological Science, 2015, 23(3): 529-538.
[3] WANG Xia;TAN Guohua;WANG Xu;ZHANG Minqiang;LUO Cong. The Mixture Item Response Theory Models and Its Application Traces[J]. Advances in Psychological Science, 2014, 22(3): 540-548.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
Copyright © Advances in Psychological Science
Support by Beijing Magtech