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.

 
TEXTS


Duncan, Otis Dudley, Introduction to Structural Equation Models (SEM).  New York: Academic Press, 1975 (out of print, but accessible on the password-protected seminar website).

 

Jöreskog, Karl G., and Sörbom, Dag.  LISREL 8: User’s Reference Guide (L8).  Chicago: Scientific Software International, 1997.

 

Jöreskog, Karl G., and Sörbom, Dag.  PRELIS 2: User’s Reference Guide. Chicago: Scientific Software International, 1999.

 

Loehlin, John C.  Latent Variable Models:  An Introduction to Factor, Path, and Structural Analysis (LVM).  4th ed.  Lawrence Erlbaum Associates, 2004.
 

Supplementary texts:


Bollen, Kenneth A.  Structural Equations with Latent Variables (SELV). New York:  John Wiley and Sons, 1989.

 

Bollen, Kenneth A. and Patrick J. Curran. Latent Curve Models : A Structural Equation Perspective. Hoboken, N.J.: John Wiley & Sons, 2006. 

 

Hoyle, Rick H. (ed.). Structural Equation Modeling: Concepts, Issues, and Applications (CIA).  Thousand Oaks, CA: SAGE Publications, 1995.

 

Kline, Rex B. Principles and Practice of Structural Equation Modeling. 2nd Ed. New York: Guilford Publications, 2005.

 

Morgan, Stephen L. and Christopher Winship. Counterfactuals and Causal Inference : Methods and Principles for Social Research. New York: Cambridge University Press, 2007.

 

Supplementary software manuals:

 

Byrne, Barbara M. Structural Equation Modeling with AMOS: Basic Concepts, Applications, and Programming. Mahwah, N.J.: Lawrence Erlbaum Associates, 2001.

 

Jöreskog, Karl G., and Sörbom, Dag.  LISREL 8:  Structural Equation Modeling with the SIMPLIS Command Language. Chicago: Scientific Software International, 1998.

 

Jöreskog, Karl G., Sörbom, Dag, Stephen Du Toit, and Mathilda du Toit. LISREL 8: New Statistical Features. Lincolnwood, Ill.: Scientific Software International, 2001.

 

Muthén, Linda K., and Bengt O. Muthén.  Mplus User’s Guide:  Version 3. Los Angeles, CA: Muthén & Muthén, 2004. (Also available in PDF at http://www.statmodel.com/.)

 

Copies of selected readings will be placed on reserve in the Library of the Center for Demography and Ecology, Room 4471, Sewell Building.  Selected readings are also available at the password-protected course web-site, http://www.ssc.wisc.edu/soc/class/soc952/.

 

COURSE OUTLINE AND READINGS


Note:  Copies of these materials will be placed on reserve in the Library of the Center for Demography and Ecology, Room 4457 Sewell Building. Links to the text of selected journal articles and reader chapters are provided below.  Starred items (*) are optional readings, but some of these will be strongly recommended in class.  Students should read the required material for each class meeting in advance.

 

Meeting 1 (28 January):  Organization and Purposes of the Seminar, Data Analysis, and Introduction to Path Analysis

 

Meeting 2 (4 February):  Introduction to Path Analysis, continued.

    1. Duncan, SEM, Chs. 1-2.

    2. Loehlin, LVM, Chs. 1, 7.

    3. Holland, Paul W. 1988. "Causal Inference, Path Analysis, and Recursive Structural Equations Models." Sociological Methodology 18:449-84.

    4. Goldberger, Arthur S. 1972. “Structural Equation Methods in the Social Sciences.” Econometrica 40:979-1001.

    5.* Smith, H. L. 2003. "Some Thoughts on Causation as It Relates to Demography and Population Studies." Population and Development Review 29:459-69.

    6. * Bielby, W.T., and Hauser, R.M. 1977. “Structural Equation Models,” Annual Review of Sociology 3:137-161.

    7. *Bollen, SELV, Chs. 1-3.

    8. *Hoyle, CIA, Ch. 1-2, 7, 9.

    9. * Raftery, Adrian E. 2001. “Statistics in Sociology, 1950-2000: A Selective Review.” Sociological Methodology 311-45.

 

Meeting 3 (15 February):  Recursive Models

    1. Duncan, SEM, Chs. 3-4.

    2. Duncan, O.D., “Path Analysis:  Sociological Examples,” American Journal of Sociology 72 (1966):1-16.

    3. Alwin, D.F., and Hauser, R.M., “The Decomposition of Effects in Path Analysis,” American Sociological Review 40 (1975):37-47.

    4. *Jöreskog, Karl G., and Sörbom, Dag, L8, Ch 4 (pp. 133-158).

    5. * Bollen, Kenneth A., “Total, Direct, and Indirect Effects in Structural Equation Models,” Pp. 37-69 in Clifford C. Clogg (ed.), Sociological Methodology 1987.  Washington, D.C.:  American Sociological Association, 1987.

    6. *Bollen, SELV, pp. 80-104, 123-131, 376-389.

 

Meeting 4 (18 February):  Simple Models with Unobservable Variables

    1. Duncan, SEM, Ch. 9.

    2. Loehlin, LVM, Ch. 3:87-106.

    3. Costner, H.L., “Theory, Deduction and Rules of Correspondence,” American Journal of Sociology 75 (1969):245-263. Reprinted as Ch. 16 in H.M. Blalock (ed.), Causal Models in the Social Sciences (CMISS) (Chicago:  Aldine, 1971):299-319.

    4. * Heise, D.R., “Separating Reliability and Stability in Test-Retest Correlation,” American Sociological Review 34 (1969):93-101.  Reprinted as Ch. 20 in Blalock, CMISS.

    5. * Wiley, D.E., and Wiley, J.A., “The Estimation of Measurement Error in Panel Data,” American Sociological Review 35 (1970):112-117.  Reprinted as Ch. 21 in Blalock, CMISS.

    6. *Bollen, SELV, Ch. 5, Ch. 6, Ch. 7 (pp. 226-254).

 

Meeting 5 (25 February):  The LISREL Model:  Specification and Estimation

    1. Jöreskog, Karl G., and Sörbom, Dag, L8, Chs. 1and 2.

    2. Loehlin, LVM, Ch. 2:35-60.

    3. Bielby, William T., Hauser, Robert M., and Featherman, David L., “Response Errors of Black and Nonblack Males in Models of the Intergenerational Transmission of Socioeconomic Status,” American Journal of Sociology 82 (May 1977):1242-1288.

    4. * Alwin, Duane F., and Jackson, David J., “Measurement Models for Response Errors in Surveys:  Issues and Applications,” pp. 68-119 in Karl F. Schuessler (ed.), Sociological Methodology 1980.  San Francisco:  Jossey-Bass, 1979.

    5. *Bollen, SELV, pp. 10-20, Ch. 4 (104-123), Ch. 8 (pp. 319-369).

    6. *Hoyle, CIA, Ch. 2, 3.

 

Meeting 6 (3 March):  LISREL: Testing, Nesting, and Normalizing

    1. Loehlin, LVM, Ch. 2: 61-86.

    2. Jöreskog, Karl G., and Sörbom, Dag, L8, Ch. 3.

    3. Hauser, Robert M., “Occupational Status in the Nineteenth and Twentieth Centuries,” Historical Methods 15 (Summer 1982):111-126.

    4. Long, J. Scott, “Estimation and Hypothesis Testing in Linear Models Containing Measurement Error:  A Review of Jöreskog's Model for the Analysis of Covariance Structures,” Sociological Methods and Research 5 (November 1976):157-206.

    5. * Raftery, Adrian E., “Bayesian Model Selection in Social Research,” pp. 111-195 (including commentary and replies) in Peter V. Marsden (ed), Sociological Methodology 1995.  Cambridge: Basil Blackwell, 1995.

    6. * Matsueda, Ross L., and Bielby, William T., “Statistical Power in Covariance Structure Models,” Pp. 120-158 in N.B. Tuma (ed.), Sociological Methodology 1986.  Washington, D.C.:  American Sociological Association, 1986.

    7. * Bentler, P.M., and Bonett, Douglas G., “Significance Tests and Goodness of Fit in the Analysis of Covariance Structures,” Psychological Bulletin 88 (1980):588-606.

    8. * Sobel, Michael E., and Bohrnstedt, George W., “The Use of Null Models in Evaluating the Fit of Covariance Structure Models,” Pp. 152-178 in N.B. Tuma (ed.), Sociological Methodology 1985.  San Francisco:  Jossey-Bass, 1985.

    9. *Bollen, SELV, Ch. 7 (pp. 254-305), Ch. 8 (pp. 333-350).

   10. *Hoyle, CIA, Ch. 5, 6.

 

 

Meeting 7 (10 March):  MIMIC (Multiple Indicator, Multiple  Cause) Models

    1. Hauser, Robert M., and Goldberger, Arthur S., “The Treatment of Unobservable Variables in Path Analysis,” Pp. 81-117 in H.L. Costner (ed.), Sociological Methodology, 1971.  San Francisco: Jossey-Bass, 1971.

    2. Jöreskog, Karl G., and Sörbom, Dag, L8, Ch. 5 (pp. 159-186).

    3. Hauser, Robert M., and Wong, Raymond Sin-Kwok, “Sibling Resemblance and Inter-Sibling Effects in Educational Attainment,” Sociology of Education 62 (1989):149-171.

    4. * Jöreskog, Karl G., and Goldberger, Arthur S., “Estimation of a Model with Multiple Indicators and Multiple Causes of a Single Latent Variable,” Journal of the American Statistical Association 70 (1975):631-639.

    5. * Hodge, Robert W. and Donald J. Treiman. 1968. “Social Participation and Social Status.” American Sociological Review, October, 722-40.

 

Meeting 8 (24 March):  Multiple-Group LISREL Models

    1. Sörbom, Dag, and Jöreskog, Karl G., “The Use of LISREL in Sociological Model Building,” pp. 179-199 in D.J. Jackson and E.F. Borgatta (eds), Factor Analysis and Measurement in Sociological Research:  A Multidimensional Perspective. Beverly Hills:  Sage, 1981.

    2. Jöreskog, Karl G., and Sörbom, Dag, L8, Ch. 9, *Ch. 10.

    3. Hauser, R.M., “Sample Control Cards for LISREL Models from Sörbom-Jöreskog (1981),” 2001.

    4. Loehlin, LVM, Ch. 4:129-150.

    5. * Kluegel, James R., Singleton, Royce, Jr., and Starnes, Charles E., Subjective Class Identification: A Multiple Indicator Approach,” American Sociological Review 42 (August 1977):599-611.

    6. * Hsiang-Hui Daphne, and Robert M. Hauser. “Trends in Family Effects on the Education of Black and White Brothers.” Sociology of Education 68 (April 1995): 136-60.

    7. *Kuo, Hsiang-Hui Daphne, and Robert M. Hauser. “Gender, Family Configuration, and the Effect of Family Background on Educational Attainment.” Social Biology 43 (Spring-Summer 1996): 98-131.

    8. *Bollen, SELV, Ch. 8 (pp. 350-369).

 

Meeting 9 (31 March):  Nonrecursive Models

    1. Duncan, SEM, Ch. 5-7, 10.

    2. Loehlin, LVM, Ch. 3:106-111.

    3. Duncan, Otis D., Archibald O. Haller, and Alejandro Portes, “Peer Influences on Aspirations: A Reinterpretation.” American Journal of Sociology 74,2 (1968):119-37.

    4. Jöreskog, Karl G., and Sörbom, Dag, L8, Ch. 5 (pp 175-186).

 

Meeting 10 (4 April):  Ordered Categorical Data and Models for Panel Data

    1. Duncan, Otis Dudley, “Some Linear Models for Two-Wave, Two-Variable Panel Analysis,” Psychological Bulletin 72 (1969):177-182.

    2. Loehlin, LVM, Ch. 4 (pp. 120-129).

    3. Jöreskog, Karl G., and Sörbom, Dag, L8, Ch. 6, 7.

    4. Springer, Kristen W. and Robert M. Hauser. 2006. “An Assessment of the Construct Validity of Ryff's Scales of Psychological Well-Being: Method, Mode, and Measurement Effects.” Social Science Research 35:1080-1102.

    5. Ryff, Carol R. and Burton H. Singer. 2006. “Best News Yet on the Six-Factor Model of Well-Being.” Social Science Research 35:1103-19.

    6. Springer, Kristen W., Robert M. Hauser, and Jeremy Freese. 2006. "Bad News Indeed for Ryff's Six-Factor Model of Well-Being." Social Science Research 35:1120-31.

    7.* Hauser, Robert M., Tetyana Pudrovska, and Kristen W. Springer. 2005. “Temporal Structures of Psychological Well-Being: Continuity or Change?” Presented at the 2005 Meetings of the Gerontological Society of America, Orlando, Florida.

    8.  *Jöreskog, Karl G., and Sörbom, Dag.  PRELIS 2: User’s Reference Guide. Chicago: Scientific Software International, 1996.

    9. * Duncan, O.D., “Unmeasured Variables in Linear Models for Panel Analysis,” Pp. 36-82 in Herbert L. Costner (ed.), Sociological Methodology 1972.  San Francisco:  Jossey-Bass, 1972.

    10. * Duncan, O.D., “Some Linear Models for Two-Wave, Two-Variable Panel Analysis, with One-Way Causation and Measurement Error,” Pp. 285-306 in H.M. Blalock and Others (eds), Quantitative Sociology:  International Perspectives on Mathematical and Statistical Modeling.  New York:  Academic Press, 1975.

 

Meeting 11 (7 April):  A Second-Order Factor Model

    1. Duncan, SEM, Ch. 8, 11.

    2. Hauser, Robert M., Tsai, Shu-Ling, and Sewell, William H., “A Model of the Stratification Process with Response Error in Social and Psychological Variables,” Sociology of Education 56 January 1983):20-46.

    3. * Campbell, Richard T., “Status Attainment Research: End of the Beginning or Beginning of the End?,” Sociology of Education 56 (January 1983):47-62.

 

Meeting 12 (14 April):  Models of Nested Data

    1. Hauser, Robert M., and Mossel, Peter A. “Some Structural Equation Models of Sibling Resemblance in Educational Attainment and Occupational Status,” Pp. 108-37, 298-307 in P. Cuttance and R. Ecob (eds.), Structural Modeling by Example:  Applications in Education and the Social and Behavioral Sciences. Cambridge:  Cambridge University Press, 1988.

    2. * Hauser, Robert M., “A Note on Two Models of Sibling Resemblance,” American Journal of Sociology 93 (May 1988):1401-23.

    3. * Muthén, Bengt, “Latent Variable Modeling of Longitudinal and Multilevel Data,” Pp. 453-480 in Adrian E. Raftery(ed.), Sociological Methodology 1997.  Boston 1997.

 

Meeting 13 (21 April):  Models with Missing Data or Missing Moments
    1. Allison, Paul, “Estimation of Linear Models with Incomplete Data,” Pp. 71-103 in Clifford C. Clogg (ed.), Sociological Methodology 1987. Washington, D.C.:  American Sociological Association, 1987.

    2. Allison, Paul, and Robert M. Hauser, “Reducing Bias in Estimates of Linear Models by Remeasurement of a Random Subsample,” Sociological Methods and Research 19 (May 1991):466-491.

    3. * Hauser, Robert M., and Sewell, William H., “Family Effects in Simple Models of Education, Occupational Status, and Earnings:  Findings from the Wisconsin and Kalamazoo Studies,” Journal of Labor Economics 4 (July 1986, Part 2):S83-S115.

    4. * Bielby, William T., and Hauser, Robert M., “Response Error in  Earnings Functions for Nonblack Males,” Sociological Methods and Research 6 (November 1977):241-280.

    5. *Bollen, SELV, Ch. 8 (pp. 369-376).

 

FINAL ASSIGNMENTS:    To be announced

 

Meetings 14-15 (2 May and 5 May):    Presentation of Student Papers

 

Final Assignment, Due Friday, May 9, 2008                                              Soc952-2008_syl_010508c.doc