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Last Modified on Tuesday, November 14, 2000
Welcome to Psych 431.
(Or, for that matter, anyone who visits here who has an interest in structural equation modeling.
Here is a copy of the syllabus for the course.
The first few lectures will deal with what path analysis is and what proper form for a path analysis looks like.
- A little review of Regression. When I talked with folks about regression, it seems that some of the terms and some of the visual representations of a regression were a little fuzzy. As a result, I added in this small introduction to some basics of regression. This is mostly just an introduction to terminology, such as ``score matrices" and plots. Thought it might be useful
- Basics of Path Notation . Here is an introduction to path notation. It is my hope at this point that you are able to look at a path diagram written in RAM notation and judge whether it is, in fact, proper, or if some ambiguity exists in the specification.
- Standardized Path Models . Path models are useful because they allow us to understand how variances and covariances (or, alternatively correlation coefficients) can be explained. In order to know how the parameters of a path model reproduce correlations, you'll need to learn a bit about the tracing rules for standardized path models. These tracing rules are equivalent to those you see in Loehlin's book, but you will note that I explicitly mention that the variance of the standardized variables 1 and figures (albeit transparenly) in the calculations.
- Unstandardized Path Models . Sometimes the correlation coefficient isn't the most informative statistic to use when describing a relationship between variables (even though it is a ``conceptually confortable" thing for us to work with). For that reason, I've also included a discussion of how to use the tracing rules for unstandardized path models. You'll find that this follows what was covered step by step, the handout for standardized path coefficients- it just includes terms for variances. These examples describe the tracing rules for unstandardized variables (which are all in deviation form, technically)
- Here is a summary table of the SAS programs, logs and listings which we will be discussing in the course. If I'm able, I may be able to add to these.
Example of making a covariance matrix
Example analyses based on Loehlin's Table 1-2
Regression for two Predictors
Maruyama Data Set Table 3-1
Minitheory of Love: Table 4-4
Proc Calis analyses of Loehlin's hypothetical three-factor exploratory factor model
Proc Calis of Loehlin's hypothetical data along with examples of other types of exploratory techniques
Thurstone's Box data analyzed with Calis
Growth Curve Example
Example of Tetrad model specification
Tetrad Output and SAS Log
Example of Reg with Intercept
- Generation of raw data from a known correlation/covariance matrix. Here is an example of how to generate both a predicted variance/covariance matrix from factor loadings, variances and error terms as well as code which will generate a raw data example (i.e., a data set which will have exactly the correlations specified by the model) as well as a sample from a population with known correlation. Generating an example is useful for classroom demonstrations, while generating a sample is useful in monte carlo work and in generating more ``real world" scenarios. The log and listing for this example are also available.
- Regression Example. Here is an example of how to do a regression using SAS and, just by way of introduction, what the program code would look like to do an equivalent analysis using Proc Calis.
- Matrix Algebra: An Introduction. Every statistics instructor, it seems has a short cheat sheet on matrix algebra for students to use. I've gone somewhat overboard with the possibilities of the possibilities of FrameMaker to do matrix algebra, but hope it's helpful. Here is an introduction to matrix algebra.
- Sample CALIS program for two variable regression. This example shows you how a TYPE=COV data set may be read in by means of the input statement, and then walks you through a Proc Calis and equivalent Proc Reg model. Just for fun, I also show you the code to modify the error term so that the standard errors come out the same in both Calis and Reg. You can either download this sas program and run it or, if you would like, you can access the log and list files that I got when I ran the program.
- Alternative Factor Models for Loehlin's Table 1-2 . This features a SAS program setup, the log and listing for the program.
- Regression with an Intercept: Some of you will remember from your regression coursework that it's also possible to do regression based on raw score data and a special variable which had the value ``1" for all individuals. A path model representation for that is given here.
- Maruyama Data Set Example . Here you will find the sas program, sas log, and listing for the maruyama data set described in Chapter 3 of Loehlin.
- Alternative Models for a Minitheory of Love . A short set of Calis programs designed showing different possibilities for the ``minitheory of love" Presented in Table 4-4 of Loehlin. Here is the SAS program, the log, and the listing.
- MX Sample Program Setup: I've added a short example of a program setup in AMOS to encourage you to explore playing with other software in addition to Calis.
A Simple Two-Variable Regression in CALIS and PROC REG
I've added a small example of a SAS program which creates a TYPE=COV data set and which uses PROC CALIS to analyze it. (This is the printout we went over on Wednesday, Sept. 9th). I've changed the format of the characters so you can more easily read it.
Some additional CALIS examples.
If you'd like, a zipped file with several CALIS examples is also available from SAS. Those of you who want to have copies of the data examples in Hatcher's book can find them here.
Other Structural Equation Modeling Program Resources
LISREL
For those of you who are interested in running programs in LISREL, there is a student version of the program available. It runs with a limited number of manifest variables, but is otherwise a functional copy of the program.
AMOS
For those of you who like a graphical interface, Smallwaters Corporation has AMOS available. They also have a student version you may wish to look at.
MX
Finally, for those of you who like to use matrix algebra, there is a public domain (and very flexible, I might add) program called MX.
EQS
Another program which is quite similar in input format to CALIS (and which does handle multiple groups is EQS. They also have a demo version of their software available at the EQS vendor homepage.
SEPATH
For those of you who are more familiar with Statistica, you can also use the structural equations module, SEPATH. It is, to the best of my understanding, a module in Statistica.
A good book on optimization techniques is:
Everitt, B. S. (1987). Introduction to optimization methods and their application in statistics. New York: Chapman & Hall.
As always, if you've any questions, please don't hesitate to contact me.
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