General Structural Equations LISREL Models Douglas Baer Department

General Structural Equations (LISREL Models) Douglas Baer, Department of Sociology University of Victoria baer@uvic. ca Baer/ General Structural Equations / ICPSR 2005 1

What are structural equation models? Basically, sets of regression model equations Includes manifest variables (as do regular regression models) and latent variables (new) Latent variables will be familiar to those with experience with factor analysis (“factors” are latent variables) Models can be recursive or non-recursive Baer/ General Structural Equations / ICPSR 2005 2

What are structural equation models? Models subsume: factor analysis (confirmatory), regression, analysis of variance/covariance Major limitations, to be discussed in some detail in class: – Linearity assumptions (non-linear models for equations are possible) – Distributional assumptions (dummy variables still possible; issue is for any dependent variable in any equation) Baer/ General Structural Equations / ICPSR 2005 3

What are structural equation models? Models subsume: factor analysis (confirmatory), regression, analysis of variance/covariance Linear model assumptions – A lot of literature on variations (we will discuss these): distributional assumptions, linearity Major advance in treatment of measurement error Baer/ General Structural Equations / ICPSR 2005 4

Background for this course: • Should have 2 nd level regression course completed prior to attending this class (at about the level of John Fox’s text) – Transformations; dummy variables; indicator and effect coding; analysis of residuals, what is the “Hat” matrix? ; dealing with non-linearity (in general); interaction models (continuous and categorical X-variables), quadratic models – (X’X)-1 X’y Baer/ General Structural Equations / ICPSR 2005 5

Background for this course: • Should have some familiarity with matrix algebra: – matrix multiplication, addition – transpose – Singularity – Inversion Non-credit students may consider sitting in on Matrix Algebra lectures. Not recommended for credit students, whose background should be stronger. • A bit of calculus (though a quick read through Quick Calculus should suffice) Baer/ General Structural Equations / ICPSR 2005 6

Background for this course: Not required but very helpful: - Some background in or exposure to factor analysis. - (familiarity with path analysis) Baer/ General Structural Equations / ICPSR 2005 7

Complementary courses • Simultaneous Equations (very good complement) • (matrix algebra lectures: see above) • Missing data lectures (held this week) • You should not be in this course if you are taking the Regression course at the same time Baer/ General Structural Equations / ICPSR 2005 8

Credit vs. Non-credit participants • We usually expect that a small proportion of participants in this workshop will be taking the workshop as a formal university-credit course. Please identify yourself to me at the end of the class if you are in this category. • For non-credit participants, consult David Merchant if you need a letter… ICPSR will (for a small fee) provide a letter indicating attendance in particular workshops Baer/ General Structural Equations / ICPSR 2005 9

Class Exercises/Assignments • There will be 5 computer assignments/exercises over the 4 -week period. All participants (credit and non-credit) should attempt to complete at least 4 out of 5 assignments • There will be one “journal article” write up. You will be provided with SEM program output and a point-form description of variables, etc. , and asked to provide a write up of the Data, Methods and Results section of a journal paper. This is REQUIRED for credit students and RECOMMENDED for non-credit participants • There will be a 1 -hour in-class test at the end of week 2 for CREDIT participants and for those requiring a letter that indicates a “grade” for the course Baer/ General Structural Equations / ICPSR 2005 10

Class Exercises/Assignments • One take-home exam, distributed on the 2 nd last day of class and due on the last day of class for CREDIT participants and those requiring a letter with a grade. Baer/ General Structural Equations / ICPSR 2005 11

Office hours, contact information • We will try to hold office hours such that either the instructor or the TA is available evenings after class (e. g. , 5: 30 pm-6: 30 pm). Additional office hours will be scheduled for 12 noon-2 pm as needed (probably 2 -3 days/week). • Instructor office hours: 5: 30 -6: 30(or later), MONDAY, WEDNESDAY, THURSDAY (except first Thursday) • Instructor contact information: – Office: Room 213 phone: – Cell phone: 709 -0381 (Ann Arbor: ac 734) - email: baer@uvic. ca (checked frequently) Baer/ General Structural Equations / ICPSR 2005 12

Office hours, contact information • Instructor contact information: – Office: Room 216 phone: 764 -3878 – Cell phone: 709 -0381 (Ann Arbor: area code 734) (call anytime before 11 pm; pls. keep cell phone calls relatively brief – arrange follow-up meeting or phone call if necessary) - email: baer@uvic. ca (checked frequently) - Usually here on weekends (visits Newberry Sat and/or Sunday) • TA contact information: - Office: 764 -3876 Room 214 phone: - email: Baer/ General Structural Equations / ICPSR 2005 13

Availability of files: • Powerpoint files will for classes will be posted in the baer disk area on the ICPSR server • (For exclusive use of ICPSR participants) Baer/ General Structural Equations / ICPSR 2005 14

TEXTS • There is a manuscript especially prepared for this class: – An Introduction to Structural Equation Models for Latent Variables – Available from ICPSR for the cost of photocopying (TA will provide instructions on how to obtain) – For copyright reasons, this manuscript is not being made available as. pdf files – An “errata” file will be made available in the class disk area Baer/ General Structural Equations / ICPSR 2005 15

TEXTS Recommended: 1. Randall Schumacker and Richard Lomax, A Beginner’s Guide to Structural Equation Modeling. Lawrence Erlbaum, 2004 Supplementary 1. David Kaplan, Structural Equation Modeling. Sage, 2000. 2. Hoyle, Rick (ed. ) An edited volume, called Structural Equation Modeling: Concepts, Issues and Applications, edited by Rick Hoyle (Sage, 1995). 3. Ken Bollen’s Structural Equations with Latent Variables (John Wiley, 1989) , which discusses models in matrix terms. Baer/ General Structural Equations / ICPSR 2005 16

SOFTWARE Major SEM (structural equation model) software packages: Will be used in class (and in assignments and labs): 1. LISREL – the original, now in version 8. 7 (8. 7 about to be released; ICPSR has 8. 72) 2. AMOS – easy to use, not the best for complex models, distributed by SPSS, company distributing the “standalone” version has gone out of business – used mostly in first week of class 3. Will be demonstrated in class if time permits & if there is interest: 4. MPLUS – most sophisticated (lots of extensions), more difficult to use 5. EQS – less popular, now in version 6 6. A SAS procedure called CALIS Baer/ General Structural Equations / ICPSR 2005 17

Software (con’t) – Copies of software manuals have not been ordered for Ulrichs – – AMOS 4. 0 MANUAL LISREL 8 MANUAL – – – • • INTERACTIVE LISREL * supplements SIMPLIS * supplements EQS 5. 0 MPLUS 3. 0 SAS CALIS procedure (See SAS Reference guide) You will find these in the labs and in the ICPSR library We will provide handouts with information on necessary commands for each software package used in the course Baer/ General Structural Equations / ICPSR 2005 18

end (end of introduction/orientation) Baer/ General Structural Equations / ICPSR 2005 19