Structural Equation Modeling (SEM)

Plain English: SEM lets you know if you are really looking at what you think you are looking at.

A Little More Detail: SEM help you identify a "thing" that cannot be grouped or classified easily or with common ways to measure it. Think of something like "love" and how you would see if someone loved someone or something else.

You would need to think about what defines "love" it ways you can observe directly. Do you want to say it is what kind things you say, what nice things you do, how much time you think about who/what you love? SEM would help you identify if the things you picked out are reliable ways of measuring "love." If you picked the right things, when you collected you information, you would be able to see if someone loved someone or something else with some measure of confidence.

Adding Some Complexity: Keeping with the idea of "love," there are different kinds of love. Also the way "love" is demonstrated may change over time (think about the difference between newlyweds and a couple that has been together for 50 years). In these situations you would look at either look at "model fit" or "latent growth" telling you if there is a difference between tow observations, or an evolution over time.