通径分析及其在医学研究中的应用
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摘要
通径分析是多元回归分析的扩展。在社会学、心理学和医学研究中，
通径分析经常用来探索和分析系统内部多变量间的复杂的因果关系及其变
量间的作用程度的大小。尤其，运用隐变量通径分析方法探讨隐变量与可
测变量间的因果关系，解决社会学、心理学中一些隐变量在系统内部所起
作用大小的问题。
通径分析是在研究观察变量间的协方差矩阵和相关矩阵基础上，从定
量的角度建立模型来探索和分析系统内变量间因果关系的一种统计方法。
与传统的回归模型相比较，后者所假设的因果关系并不存在多环节的因果
结构，尽管可以包含多个自变量，各个自变量被假设处于并列的相同地位，
回归分析得到回归系数只表示在控制其他自变量的条件下每个自变量对因
变量单独的净作用。通径模型可以利用通径系数以及中间变量的传递过程
来分析变量间的间接效应，挖掘隐藏在系统内部的大量信息，分析其内部
的错综复杂的因果关系，用来指导和解决实际问题。
本文首先从理论的角度，系统地论述了通径分析的基本理论，阐明了
运用样本数据拟合通径模型的一般步骤与结果的解释方法。主要内容包括
通径分析的基本理论、通径分析的矩阵算法、基本步骤（包括模型设置、
模型识别、模型估计、模型评价、模型调试及修改）、结果解释、模型假定
的检验。运用通径图和结构方程组这两种形式对通径模型进行了合理的统
计学和专业的解释。它系统地分析了变量间的直接效应、间接效应和总效
应。
以大学生人际关系敏感的影响因素为例，结合心理学的专业知识，运
用隐变量通径分析基本理论设定了合理的通径图，运用 SAS8.0 软件的
CALIS 过程编写了相应的程序，对通径模型进行了估计、评价、检验，得到
了比较合理的统计学和专业解释。另外，系统分析了各影响因素对人际关
系敏感的直接效应、间接效应和总效应。结论分析显示，运用隐变量通径
分析方法处理和分析社会学和心理学的问题具有很大的优势及应用前景。
Path analysis is an extension of the regression model, used to research and
analyze complicate causality of variables and effects of them in the model in
social investigation, psychological investigation and medical research.
Particularly, latent variable path analysis is used to research the causality
between latent variables and manifest variables, to solve the problem that latent
variables affect the others in the social and psychological fields.
Path analysis is a useful statistical tool to analyze the causality of variables.
Conventional regression is done for each variable in the model as a dependent
on others, which indicates causes. Traditional regression model does not show
multiple causal structures. Although the regression model includes independent
variables, which are parallel, partial regression coefficients indicate net effect of
each independent variable on dependent variable controlling the others. Path
coefficients may be used to decompose correlations in the model into direct and
indirect effects. The indirect effects measure the effect of the intervening
variables. The researcher may dig a large amount of information out of the data
in order to solve the social and psychological problems.
This paper firstly focuses on the theory of path analysis including basic
theory, the matrix solutions on path analysis, data example, the step of analysis,
and the way to explain the result of the modeling. The article not only gives
rational statistical and professional interpretations of path analysis modeling by
the way of path diagram and linear structural equations, but also systematically
analyzes the direct and indirect effect of the variables.
Then using an example of factors of the sensitive to
interpersonal relationship in the college students and combining
psychological knowledge, I create a path diagram. Applying the
CALIS procedure of SAS 8.0 software, we give a rational
interpretation. We draw a conclusion that latent variable path
analysis modeling provides more objective information than the
ordinary multiple regression modeling.
通径分析经常用来探索和分析系统内部多变量间的复杂的因果关系及其变
量间的作用程度的大小。尤其，运用隐变量通径分析方法探讨隐变量与可
测变量间的因果关系，解决社会学、心理学中一些隐变量在系统内部所起
作用大小的问题。
通径分析是在研究观察变量间的协方差矩阵和相关矩阵基础上，从定
量的角度建立模型来探索和分析系统内变量间因果关系的一种统计方法。
与传统的回归模型相比较，后者所假设的因果关系并不存在多环节的因果
结构，尽管可以包含多个自变量，各个自变量被假设处于并列的相同地位，
回归分析得到回归系数只表示在控制其他自变量的条件下每个自变量对因
变量单独的净作用。通径模型可以利用通径系数以及中间变量的传递过程
来分析变量间的间接效应，挖掘隐藏在系统内部的大量信息，分析其内部
的错综复杂的因果关系，用来指导和解决实际问题。
本文首先从理论的角度，系统地论述了通径分析的基本理论，阐明了
运用样本数据拟合通径模型的一般步骤与结果的解释方法。主要内容包括
通径分析的基本理论、通径分析的矩阵算法、基本步骤（包括模型设置、
模型识别、模型估计、模型评价、模型调试及修改）、结果解释、模型假定
的检验。运用通径图和结构方程组这两种形式对通径模型进行了合理的统
计学和专业的解释。它系统地分析了变量间的直接效应、间接效应和总效
应。
以大学生人际关系敏感的影响因素为例，结合心理学的专业知识，运
用隐变量通径分析基本理论设定了合理的通径图，运用 SAS8.0 软件的
CALIS 过程编写了相应的程序，对通径模型进行了估计、评价、检验，得到
了比较合理的统计学和专业解释。另外，系统分析了各影响因素对人际关
系敏感的直接效应、间接效应和总效应。结论分析显示，运用隐变量通径
分析方法处理和分析社会学和心理学的问题具有很大的优势及应用前景。
Path analysis is an extension of the regression model, used to research and
analyze complicate causality of variables and effects of them in the model in
social investigation, psychological investigation and medical research.
Particularly, latent variable path analysis is used to research the causality
between latent variables and manifest variables, to solve the problem that latent
variables affect the others in the social and psychological fields.
Path analysis is a useful statistical tool to analyze the causality of variables.
Conventional regression is done for each variable in the model as a dependent
on others, which indicates causes. Traditional regression model does not show
multiple causal structures. Although the regression model includes independent
variables, which are parallel, partial regression coefficients indicate net effect of
each independent variable on dependent variable controlling the others. Path
coefficients may be used to decompose correlations in the model into direct and
indirect effects. The indirect effects measure the effect of the intervening
variables. The researcher may dig a large amount of information out of the data
in order to solve the social and psychological problems.
This paper firstly focuses on the theory of path analysis including basic
theory, the matrix solutions on path analysis, data example, the step of analysis,
and the way to explain the result of the modeling. The article not only gives
rational statistical and professional interpretations of path analysis modeling by
the way of path diagram and linear structural equations, but also systematically
analyzes the direct and indirect effect of the variables.
Then using an example of factors of the sensitive to
interpersonal relationship in the college students and combining
psychological knowledge, I create a path diagram. Applying the
CALIS procedure of SAS 8.0 software, we give a rational
interpretation. We draw a conclusion that latent variable path
analysis modeling provides more objective information than the
ordinary multiple regression modeling.
引文
1、 卜向东，钱宇平.通径分析及其在流行病学中的应用.流行病学进展.
北京：人民卫生出版社,1986,232～263
2、 郭志刚.社会统计分析方法—SPSS 软件应用.北京：中国人民大学出版
社,1999 年第一版,2001 年第二次印刷,145～175
3、 Path Analysis - Definition. Path analysis is a special use of multiple
regressions to help understand and parcel out the sources of variance.
www.colorado.edu/epob/epob4640mwalker/lect13.html
4、 高惠璇.SAS 系统软件使用手册 STAT.北京：中国统计出版社，76～110.
5、 马恒运.研究变量间关系的通径分析方法.经济经纬.1995, 2: 52～53.
6、 张伦俊.通径分析在税收研究中的应用.数理统计与管理.中国现场统
计研究会主办,2003,22(2):26～29
7、 孙德林.通径分析在经济统计研究中的应用
8、 孙尚拱.实用多变量统计方法与计算应用.北京：北京医科大学、协和
医科大学联合出版社，1990 年第一版，50～61
9、 孙尚拱.医学多变量统计与统计软件.北京：北京医科大学出版社
2000,163-216
10、 阮桂海, 蔡福金. SAS 统计分析实用大全.北京：清华大学出版社
2003,400～407.
11、 Charles S.Reichardt, University of Denver .The Priority of Just-Identified,
Recursive Miodels. Psychological Methods.
12、 Maruyama, Geoffrey M. (1997). Basics of structural equation modeling.
Thousand Oaks, CA: Sage Publications.pp22-61.
13、 Spirtes, Peter, Thomas Richardson, Christopher Meek, Richard Scheines,
and Clark Glymour (1998). Using path diagrams as a structural equation
modeling tool. Sociological Methods & Research, Vol. 27, No. 2 (Nov.):
182-225.
14、 Principles of Path analysis. Downloaded from the Department of
Psychology, University of Exeter at
http://www.exeter.ac.uk/~SEGLea/multvar2/pathanal.html
39
山西医科大学硕士学位论文
15、 Wright.S. (1934). The method of path coefficients. Annals of Mathematical
Statistics, Vol. 5: 161～215.
16、 崔党群.通径分析的矩阵算法.生物数学学报.1994, 9(1):71～76
17、 Path Analysis. How does path analysis portray the effects of the
independent variables in ways that ordinary multiple regression does not?
luna.cas.usf.edu/~mbrannic/files/regression/Pathan.html
18、 Retherford. Robert. D. Statistical models for causal analysis. New York:
Wiley, 1993. A Wiiley-interscience public. 93-118
19、 张家放.医用多元统计方法.武汉：华中科技大学出版社,2002,289～
308.
20、 Loehlin, J. C. Latent variable models: An introduction to factor, path and
structural analysis. Hillsdale, NJ: Lawrence Erlbaum. Second edition 1992
21、 Loehlin, J.C. 1987. Latent Variable Models. Lawrence Erlbaum Associates,
Inc. Hillsdale, NJ.
22、 Bollen, K. A. (1989). Structural equations with latent variables. NY: Wiley.
A leading readable text on structural modeling.
23、 David A. Kenny November 9, 1998 Path Analysis This page shows how to
use multiple regression to estimate the parameters of a structural model.
users.rcn.com/dakenny/pathanal.htm
24、 Department of psychology. Psy6003 Advanced statistics: Multivariate
analysis II: Manifest variables analyses. Topic 3: Path analysis.
25、 Olsson, Ulf Henning, Tron Foss, Sigurd V. Troye, and Roy D. Howell
(2000). The performance of ML, GLS, and WLS estimation in structural
equation modeling under conditions of misspecification and nonnormality.
Structural Equation Modeling 7(4): 557 -595.
26、 Everitt, B.S. and G. Dunn. 1991. Applied Multivariate Data Analysis.
Halsted Press. New York, NY. pp. 257-275.
27、 Bill Shipley, Bill (2000). Cause and correlation in Biology: A user's guide
to path analysis, structural equations and causal inference. Cambridge, UK:
Cambridge University Press.pp:100-136.
40
山西医科大学硕士学位论文
28、 Mitchell, R.J. 1993. Path analysis: pollination. In: Design and analysis of
Ecological Experiments (Scheiner, S.M and Gurevitch, J, Eds). Chapman
and hall, New York, NY. pp217-234.
29、 Roderick P. Mcdonald and Moon-Ho Ringo Ho, Uinversity of Illinois at
Urbana-Champaign. Principles and Practice in Reporting Structural
Equation Analyses Psychological Methods 2002.Vol.7.No.1.pp64-82
30、 季益宫, 于欣.德克萨斯社交行为问卷.中国心理卫生杂志.1993 年增
刊 257～259
31、 马弘.社交苦恼与回避量表.中国心理卫生杂志.1993 年增刊 209～211
32、 肖水源.社会支持评定量表.中国心理卫生杂志.1993 年增刊 42～46
33、 梁执群,王英.医学生人际关系敏感及影响因素分析.山西医学院学
报.1994, 25(1):30～32
34、 梁执群,卢莉.大学生社会支持的相关因素研究.中国公共卫生 2003,
19(4):498～499
35、 Paul E. Meehl & Niels G. Waller The Path Analysis Controversy: A New
Statistical Approach to Strong Appraisal of Verisimilitude path analysis
and structured linear equations2 psychological methods 2002.vol.7.no.3
pp283-300.
36、 Niels G. Waller &Paul E.Meehl Risky Tests, Verisimilitude and Path
Analysis. Psychological Methods.2002.vol.7no.3.pp323-337.
37、 Robert C. MacCallam, Michael W.Browne and Kristopher J.Preacher, The
Ohio State University. Commets on the Meehl-Waller (2002) Procedure for
Appraisal of Path Analysis Models. Psychological Methods. 2002. Vol. 7.
No.3.pp301-306.
38、 Stanley A Mulaik, Georgia Institute of Technology. Commentary on Meehl
and Waller’s (2002) Path Analysis and Verisimilitude. Psychological
Methods. 2002. Vol.7. No.3.pp316-322.
39、 姜乾金.医学心理学.北京：人民卫生出版社.2002,149～162
40、 张晓文,吴胜红.大学生心理健康状况与家庭收入及自我评价的相关性
研究.南京化工大学学报（哲学社会科学版）.2000,3(1): 75-78
41
山西医科大学硕士学位论文
41、 G. David Garson, Instructor Path Analysis. The Social Science Research
and Computing Lab in the College of Humanities and Social Sciences at
NC State.www2.chass.ncsu.edu/garson/pa765/path.htm
42、 林德发,范书生.独生子女大学生人格特征探析.天津师大学报 1999,
5:28～34
43、 Weiss, Gregory L. 1. Larsen, Daniel L. 2. Baker, W. Kevin 3. The
Development of Health Protective Behaviors Among College Students.
Journal of Behavioral Medicine. 19(2): 143-161, April 1996.
北京：人民卫生出版社,1986,232～263
2、 郭志刚.社会统计分析方法—SPSS 软件应用.北京：中国人民大学出版
社,1999 年第一版,2001 年第二次印刷,145～175
3、 Path Analysis - Definition. Path analysis is a special use of multiple
regressions to help understand and parcel out the sources of variance.
www.colorado.edu/epob/epob4640mwalker/lect13.html
4、 高惠璇.SAS 系统软件使用手册 STAT.北京：中国统计出版社，76～110.
5、 马恒运.研究变量间关系的通径分析方法.经济经纬.1995, 2: 52～53.
6、 张伦俊.通径分析在税收研究中的应用.数理统计与管理.中国现场统
计研究会主办,2003,22(2):26～29
7、 孙德林.通径分析在经济统计研究中的应用
8、 孙尚拱.实用多变量统计方法与计算应用.北京：北京医科大学、协和
医科大学联合出版社，1990 年第一版，50～61
9、 孙尚拱.医学多变量统计与统计软件.北京：北京医科大学出版社
2000,163-216
10、 阮桂海, 蔡福金. SAS 统计分析实用大全.北京：清华大学出版社
2003,400～407.
11、 Charles S.Reichardt, University of Denver .The Priority of Just-Identified,
Recursive Miodels. Psychological Methods.
12、 Maruyama, Geoffrey M. (1997). Basics of structural equation modeling.
Thousand Oaks, CA: Sage Publications.pp22-61.
13、 Spirtes, Peter, Thomas Richardson, Christopher Meek, Richard Scheines,
and Clark Glymour (1998). Using path diagrams as a structural equation
modeling tool. Sociological Methods & Research, Vol. 27, No. 2 (Nov.):
182-225.
14、 Principles of Path analysis. Downloaded from the Department of
Psychology, University of Exeter at
http://www.exeter.ac.uk/~SEGLea/multvar2/pathanal.html
39
山西医科大学硕士学位论文
15、 Wright.S. (1934). The method of path coefficients. Annals of Mathematical
Statistics, Vol. 5: 161～215.
16、 崔党群.通径分析的矩阵算法.生物数学学报.1994, 9(1):71～76
17、 Path Analysis. How does path analysis portray the effects of the
independent variables in ways that ordinary multiple regression does not?
luna.cas.usf.edu/~mbrannic/files/regression/Pathan.html
18、 Retherford. Robert. D. Statistical models for causal analysis. New York:
Wiley, 1993. A Wiiley-interscience public. 93-118
19、 张家放.医用多元统计方法.武汉：华中科技大学出版社,2002,289～
308.
20、 Loehlin, J. C. Latent variable models: An introduction to factor, path and
structural analysis. Hillsdale, NJ: Lawrence Erlbaum. Second edition 1992
21、 Loehlin, J.C. 1987. Latent Variable Models. Lawrence Erlbaum Associates,
Inc. Hillsdale, NJ.
22、 Bollen, K. A. (1989). Structural equations with latent variables. NY: Wiley.
A leading readable text on structural modeling.
23、 David A. Kenny November 9, 1998 Path Analysis This page shows how to
use multiple regression to estimate the parameters of a structural model.
users.rcn.com/dakenny/pathanal.htm
24、 Department of psychology. Psy6003 Advanced statistics: Multivariate
analysis II: Manifest variables analyses. Topic 3: Path analysis.
25、 Olsson, Ulf Henning, Tron Foss, Sigurd V. Troye, and Roy D. Howell
(2000). The performance of ML, GLS, and WLS estimation in structural
equation modeling under conditions of misspecification and nonnormality.
Structural Equation Modeling 7(4): 557 -595.
26、 Everitt, B.S. and G. Dunn. 1991. Applied Multivariate Data Analysis.
Halsted Press. New York, NY. pp. 257-275.
27、 Bill Shipley, Bill (2000). Cause and correlation in Biology: A user's guide
to path analysis, structural equations and causal inference. Cambridge, UK:
Cambridge University Press.pp:100-136.
40
山西医科大学硕士学位论文
28、 Mitchell, R.J. 1993. Path analysis: pollination. In: Design and analysis of
Ecological Experiments (Scheiner, S.M and Gurevitch, J, Eds). Chapman
and hall, New York, NY. pp217-234.
29、 Roderick P. Mcdonald and Moon-Ho Ringo Ho, Uinversity of Illinois at
Urbana-Champaign. Principles and Practice in Reporting Structural
Equation Analyses Psychological Methods 2002.Vol.7.No.1.pp64-82
30、 季益宫, 于欣.德克萨斯社交行为问卷.中国心理卫生杂志.1993 年增
刊 257～259
31、 马弘.社交苦恼与回避量表.中国心理卫生杂志.1993 年增刊 209～211
32、 肖水源.社会支持评定量表.中国心理卫生杂志.1993 年增刊 42～46
33、 梁执群,王英.医学生人际关系敏感及影响因素分析.山西医学院学
报.1994, 25(1):30～32
34、 梁执群,卢莉.大学生社会支持的相关因素研究.中国公共卫生 2003,
19(4):498～499
35、 Paul E. Meehl & Niels G. Waller The Path Analysis Controversy: A New
Statistical Approach to Strong Appraisal of Verisimilitude path analysis
and structured linear equations2 psychological methods 2002.vol.7.no.3
pp283-300.
36、 Niels G. Waller &Paul E.Meehl Risky Tests, Verisimilitude and Path
Analysis. Psychological Methods.2002.vol.7no.3.pp323-337.
37、 Robert C. MacCallam, Michael W.Browne and Kristopher J.Preacher, The
Ohio State University. Commets on the Meehl-Waller (2002) Procedure for
Appraisal of Path Analysis Models. Psychological Methods. 2002. Vol. 7.
No.3.pp301-306.
38、 Stanley A Mulaik, Georgia Institute of Technology. Commentary on Meehl
and Waller’s (2002) Path Analysis and Verisimilitude. Psychological
Methods. 2002. Vol.7. No.3.pp316-322.
39、 姜乾金.医学心理学.北京：人民卫生出版社.2002,149～162
40、 张晓文,吴胜红.大学生心理健康状况与家庭收入及自我评价的相关性
研究.南京化工大学学报（哲学社会科学版）.2000,3(1): 75-78
41
山西医科大学硕士学位论文
41、 G. David Garson, Instructor Path Analysis. The Social Science Research
and Computing Lab in the College of Humanities and Social Sciences at
NC State.www2.chass.ncsu.edu/garson/pa765/path.htm
42、 林德发,范书生.独生子女大学生人格特征探析.天津师大学报 1999,
5:28～34
43、 Weiss, Gregory L. 1. Larsen, Daniel L. 2. Baker, W. Kevin 3. The
Development of Health Protective Behaviors Among College Students.
Journal of Behavioral Medicine. 19(2): 143-161, April 1996.