Chapter 1

# Introduction to Structural Equation Modeling

### Learning Outcomes

By the end of this chapter, students will be able to:

• Identify the definitions of the chapter vocabulary.
• Summarize an overview of structural equation modeling.
• Draw, label, and explain a two variable path diagram based on a story problem.

We are writing this book to graduate students everywhere who have no (or little) experience with statistics. We will address the reader as "you." We are writing to you.

Our purpose in this book is to change the way you think about statistics. If you are like many new graduate students, you have been dreading this class. And, given the way that most statistics classes teach the subject, we don't blame you. Somehow those classes make statistics seem impossible. It is not impossible. It is not voodoo or abstract nonsense.

Statistics describe relationships. It tries to predict how one thing affects another thing.

Structural equation modeling (SEM) is a branch of statistics that uses diagrams and numbers to describe how one thing predicts something else. Users of SEM search for truth in a way that is organized and quantifiable. (That means that it can be measured with numbers.) Throughout this book, you will learn how to gather, organize, and analyze data that will inform and transform the world. You will come to understand and enjoy statistics and the stories it tells through numbers.

Let's say that you want to know the heart rate of people from Mars. (Heart rate is an example of a variable.We will italicize the variables in this chapter to help you identify them.) Because you are looking for an answer to a question, you are a researcher. The answer that you are looking for is a number.

You ask a nurse to measure the heart rate of people from Mars. (All the people from Mars is called the population.) But you can't test everyone in the population, because that is thousands of people. That would take a lot of time. Instead, you can test a group of people from Mars. (This is called a sample.) If you choose a good sample group, their information represents all of the people from Mars.

So you get a group of people from Mars and the nurse measures the heart rate of each person in the sample group. The heart rate for an individual is a number. You now have a set of numbers that tells you the heart rate of the individuals in this group. (This is called a data set.)

That is nice information. But now you want to know more. You want to know how gender predicts heart rate. Then you want to know how gender and age predict heart rate. And then you want to know how gender and age and ethnicity predict heart rate.

All of these predictive relationships between variables can be described using structural equation modeling (SEM). You take your data, organize it, and then analyze it to figure out the story the numbers tell. When done correctly, the data shows what is really happening. You will know how gender, age, and ethnicity predict the heart rate of a person from Mars.

This module explains and shows examples.

MODULE

Let’s review and practice what you have learned so far.

### Learning Outcomes Check

I can identify the definitions of the chapter vocabulary.

I can summarize an overview of structural equation modeling.

I can draw, label, and explain a two variable path diagram based on a story problem.