Sociology 952

Mathematical and Statistical Applications in Sociology

Topic:  Path Analysis and Structural Equation Models

Semester 2, 2007-2008

Robert M. Hauser

Department of Sociology

University of Wisconsin-Madison

The seminar will focus on sociological applications of path analysis and structural equation models.  Following a review of basic ideas of structure, interpretation, estimation, and inference in recursive models, the seminar will work through problems of specification, identification, and model selection in simple recursive and latent-variable models, using published examples where possible.  The LISREL model will be introduced, and its use in the specification of a variety of models will be reviewed:  Factor models, MIMIC models, recursive and nonrecursive models with and without unobservables, multiple group models, simple models of nested data, models of repeated measurements, models for ordinal categorical data, and models for missing data. If time permits, we may look into the specification of latent growth curve models.  Most estimation will be carried out using LISREL (version 8.8), but students are free to use other software packages.

Note that several of the course meetings have (tentatively) been scheduled for Friday, rather than Monday at a room to be announced later. This is necessary because no classes can be held on the first Monday of the term and because the instructor has other scheduled commitments. Those special dates are indicated in bold on the schedule.

The last weeks of the course will be devoted to oral presentations and critiques of student research papers.  The research paper and final exercise are due by 9:00 am on Friday, May 9, 2008.  No late papers will be accepted.  

EXPECTATIONS

Seminar participants are expected to be comfortable with multiple regression analysis, with standard methods of statistical inference, and with standard methods of data analysis. The seminar is primarily about linear causal relationships (except insofar as it treats cross-population comparison). Also, it is not about making causal inferences, except in a very limited way. It is primarily about assessing the consequences of well-specified prior assumptions about causality. Seminar participants should be familiar with standard methods of data analysis, regression diagnostics, and variable transformations. For a helpful review of these matters, see, for example, Frederick Mosteller and John W. Tukey (1977) Data Analysis and Regression: A Second Course in Statistics. Reading, Massachusetts: Addison-Wesley, esp. Chs. 4-6.

ASSIGNMENTS AND EVALUATIONS

Weekly exercises will be assigned, and each student is expected to prepare an original research paper and present it to the seminar.  Grades will be based on completion of the exercises and on the quality of the research paper and presentation. There will be no final examination.  All work must be completed and turned in on time. No incompletes will be given. Students who expect and desire to gain facility in the specification and interpretation of structural equation models must complete the exercises. “Just sitting in” on the course will prove to be a waste of time after the first few weeks.

FINAL EXERCISE:  The final exercise will count more toward the final grade than earlier weekly exercises.  In that exercise, students will be expected to use the ideas and methods of the course to carry out and report findings from their analysis of a set of data that will be supplied by the instructor.  The report should be lucid, orderly, self-contained, and brief (no more than 10 pages typewritten, double-spaced); printed output from the analysis should be turned in with the report. The final exercise is due no later than 3:30 pm on Friday, 9 May, 2008.

SEMINAR PAPER:  The seminar paper should be a modest, self-contained research report.  It need be no longer than the final exercise, excepting the need to introduce the topic and data to the reader.  It may be an original analysis of data or a reanalysis of previously published data.  Single equation models of observable variables are not acceptable.  Ideally, the paper might become the basis for a thesis or research article. Students should plan to begin work on this paper early in the course according to the following schedule:

Week 5 (25 February)  Written plan (1-2 pages)  

Week 6 (3 March)  Meet with instructor to discuss and approve plan  

Week 11 (7 April)  First draft due (by 9:00 am)  

Week 14 (9 May)  Final paper due (by 9:00 am)

Students who plan to use original or potentially identifiable data for human subjects, including data from public use archives that contain geographic identifiers or have not been approved by the Behavioral and Social Science Institutional Review Board (IRB), should consult with the instructor about IRB approval early in the semester.

COMPUTING

Students who do not already have accounts in the Social Science Computing Cluster may open instructional accounts and use shared (common SSC) resources and those of the Department of Sociology (see http://www.ssc.wisc.edu/).  LISREL 8.5 and PRELIS 2.5 are available on Linux servers. LISREL 8.8 is available on Winstat (Terminal Servers). The PC versions of LISREL 8.80 and AMOS 7 are available in the Social Science MicroComputing Labs (Rms. 3218 Sewell Building, 4218 Sewell Building). Graduate students may request after-hours access for the 4218 lab.

Some students may prefer to use other software that is also available in the SSC: e.g., CALIS (a SAS module). Mplus 4.21is available on Winstat (Terminal Servers), and it may soon be updated to Mplus 5.0. SmartDraw 2007, which is an excellent tool for drawing path diagrams, is available on Winstat (Terminal Servers).

Many useful resources and links, including demonstration editions of SEM programs, are available on the World Wide Web.

A free, student version of LISREL 8.80 may be downloaded without charge from

http://www.ssicentral.com/lisrel/student.html. Also, see the SSI homepage, http://www.ssicentral.com/. There is a lot of useful information on this website.

A free, reduced demonstration version of MPlus 5.0 is available at http://www.statmodel.com/demo.shtml. Also, see the MPlus home page at http://www.statmodel.com/. There is a lot of useful information on this website.

Another standard program, EQS (http://www.mvsoft.com/), is not presently supported by the SSC or SSML.

Useful advice can sometimes be obtained from SEMNET, the Structural Equation Modeling Discussion Group (http://aime.ua.edu/cgi-bin/wa?A0=SEMNET). Use SEMNET at your own risk.

SmartDraw (http://www.smartdraw.com ) is an excellent program for drawing path diagrams (and many other kinds of drawings). Stay tuned for information about a special price for students in this seminar, if there is sufficient demand.

Instruction in the use of SSC facilities will be announced.  Instructional accounts in the SSC will be terminated at the end of the course, and students should plan to back up or delete their files before the end of May 2008.

It is possible to use vast amounts of machine time with nothing to show for it unless great care is exercised in preparation for maximum-likelihood estimation using LISREL or other similar computer programs.  Members of the seminar who have other resources for computing may feel free to use them, but the instructor will take no responsibility for the use of LISREL on other systems, e.g., on personal computers, or for the use of other software.

ADVICE

On any aspect of the course, see R.M. Hauser, 4430 Sewell Building, from 2:00 to 4:30 pm on Tuesday, or by appointment.  For replies to brief questions, send MAIL to hauser@ssc.wisc.edu, and, if appropriate, include code or data sufficient to help with your question. For appointments, call or send mail to Mark Schmidt (mschmidt@ssc.wisc.edu) at the Center for Demography of Health and Aging, Room 4418 (262-4715) with a “cc” to hauser@ssc.wisc.edu. Again, bring your data and/or code as appropriate on a thumb-drive or other portable media.

For advice on the use of SSC computing facilities, see an SSC Consultant in the 4th floor corridor of the north wing of the Sewell Building (262-9917), or send email to consultant@ssc.wisc.edu.  The SSC Consultant will provide advice about system access issues and standard statistical programs (STATA, SAS, SPSS), but not about LISREL, AMOS, or MPlus syntax, error messages, model specification, etc.  See the instructor for advice about model specification.