This online week is concerned with introducing certain fundamental concepts of path analysis and latent variable structural equation modeling. Path analysis can be understood within the context of regression (e.g., PROCESS) and in a broader more general sense that takes us beyond standard regression procedures. Indeed, path analysis and latent variable structural equation modeling are specific analytic techniques often categorized together under the larger umbrella of structural equation modeling. This online week will take us beyond standard applications of regression and into more complex model building procedures. This includes path analysis where we have greater flexibility in the testing of influences on an outcome variable so that several predictor variables can now be depicted in ways that allow for multiple tests of mediation and moderation among variables “on the way”, so to speak, to tests of ultimate influences on one or more outcome variables. Now we have the potential to move beyond asking “does this variable effect this other variable?” to asking and testing questions about the mechanisms (mediation) and conditions (moderation) of effects. And to do all of these tests within one model (“whole analysis” approach), controlling for the full set of predictor variables simultaneously, rather than “chopping up” the tests and control of variables into separate arbitrarily defined models that are later stitched back together for interpretation purposes. This chopping up and stitching exercise is an old and sloppy analytic approach associated with incorrect models and misunderstandings of phenomena. When reading Chapter 12 in Keith, it is important to distinguish your reading between the presentation of concepts of path analysis (e.g., jargon and notation, recursive and nonrecursive models, model identification) and the “chop and stitch” path analysis approach described in the chapter (indicated by discussions of simultaneous and sequential multiple regressions, conducted in SPSS). The concepts sections of the chapter are helpful (you are specifically guided to read the concepts sections), the path analysis approach part of the chapter is not helpful except as an example of what not to do (see the Course Syllabus for guidance on reading Chapter 12). The correct approach to path analysis is the “whole analysis” approach found in statistical software dedicated to path analysis and latent variable structural equation modeling (e.g., PROCESS, Mplus). Keith knows this as in Chapter 14 he basically makes that point (you will read Chapter 14 in a later online week). Latent variable structural equation modeling takes us to even higher levels of sophistication in the testing of proposed effects among variables in that all of this can be done with virtually all measurement error being removed from the tests, allowing the power and accuracy of our statistical tests to often be substantially improved. But before we dive into path analysis and latent variable structural equation modeling there are certain fundamental concepts that need to be addressed, which will be the focus of this online week.
Playlist:
Readings, attached:
Meyers et al., Chapter 6A (Section 6A.6 to the top of page 223); Chapter 11A (page 493 to the top of page 500, Section 11A.4.3 to the middle of page 507)
Keith, Chapter 12 (beginning on page 264, the following sections: Jargon and Notation, Recursive and Nonrecursive Models, Identification, Exogenous and Endogenous Variables, Measured and Unmeasured Variables, Figure 12.17 on page 277); Chapter 13 (all)
YouTube Playlist: “Director’s Cut: Moderation and Mediation (Inquiries into Complexity),” on the YouTube Channel The Essence of Regression. View in their entirety each of the videos on the Playlist.
Your reading for this online week is from Meyers et al. as well as Keith, there is also an assigned YouTube Playlist (see Course Syllabus for details).
Submit a response, stated in your own words, to each of the following ten questions:
When writing please just write 1. Then answer, no need to add question in paper.
1) From the reading in Meyers et al., what are some of the differences between exploratory and confirmatory factor analysis?
2) What is a measured variable? What is a latent variable?
3) What are the clear differences between latent and measured variables? What are the fuzzy differences? How does Meyers et al. resolve the differences between latent and measured variables?
4) What do we mean when we say that confirmatory factor analysis is theory based? How is this distinct from exploratory factor analysis?
5) Dissertations are confirmatory in nature, not exploratory. Based on what you have learned from your Meyers et al. reading, what is meant by that statement?
6) From the reading in Keith, why do we like overidentified models?
7) Describe exogenous and endogenous variables in a model. How might you illustrate these variables in a path diagram?
8) According to Keith, what are the two primary dangers of path analysis and how can they be “dealt with.”
9) According to the videos on the assigned Playlist, what are some of the essential differences between moderation and mediation? Do they share anything in common, or do they represent fundamentally different concerns? How do they introduce complexity into the understanding of effects? Be specific and support your answers.
