1R Structural Equation Modelling
William Clark, University of Michigan
8 -19 July (two week course / 35 hours)
This class will introduce students to a range of statistical tools associated with Structural Equation Models (SEM). Areas covered include measurement error, path analysis, confirmatory factor analysis, and the use of Structural Equation Models for causal inference. The relationship between Structural Equation Models and linear regression and simultaneous equations will be explored. Emphasis will be placed on the strengths and weaknesses of using SEMs for evaluating causal claims. We will explore applications of SEMs across a range of disciplines including political science, psychology, sociology, and public health. Students will learn how to estimate and interpret Structural Equation Models using MPlus..
The course aims to provide participants with the ability to design, implement, and critically evaluate statistical models of complex causal phenomenon – understood to be processes with more than one endogenous variable and where measurement of variables is understood to be problematic. Core competencies developed will include the conceptualization, estimation, and interpretation of path analytic models, confirmatory factor analysis, and models that combine the two. These competencies will be developed through the use of Mplus to analyze data sets related to applications from a variety of disciplines.
A working familiarity with multiple regression and knowledge of the fundamentals of probability theory are necessary for success in this class. In addition, some familiarity with matrix algebra might be helpful, but is not necessary.
A good place to start any discussion is:
Freedman, David, Robert Pisari, and Roger Purves. 2007. Statistics. W.W. Norton.
There are many good guides to regression analysis. But quick reviews can be found in:
Berry, William. 1993. “Understanding Regression Assumptions” Sage Quantitative Applications in the Social Sciences #92.
Edwards, Allen. 1976. An Introduction to Linear Regression and Correlation. W.H. Freeman: San Francisco.
But a more comprehensive reference tool is:
Montgomery, Douglas C., Elizabeth A. Peck, and G. Geoffrey Vining, 2006. Introduction to Linear Regression Analysis, 4th edition. Wiley.
In addition, the following paper gives some indication of where this class will be heading and so, may be useful as background reading (though students are not expected to master that material in it in advance of class):
Pearl, Judea. 2009. “Causal inference in statistics: An overview” Statistics Surveys 3:86-146.
Kline, R. B. (1998). Principles and practice of Structural Equations Modeling. New York: Guilford
Bollen, K.and Lennox, R. (1991) Conventional wisdom on measurement: A structural equation perspective. Psychological Bulletin, 110, 305-314.