Path analysis and structural equation modeling are techniques to assess the direct causal contribution of one variable to another in a non experimental situation. They are therefore particularly useful in field studies, and have become increasingly popular as modern psychology draws from real problems and non-laboratory research methods. However, as I’ll show, path analysis can be very useful in laboratory experiments as well, where it can be used to determine the psychological processes ... Continue Reading

# Path Analysis Made Easy

### An Introduction to Path Analysis: Theory and Practice

## About This Course

In this introductory module I introduce the concept of mediation and differentiate it from moderation. I’ll describe and illustrate what a simple case of mediation looks like with some real world data. When you're comfortable with the idea of mediation, I'll show you some different techniques to test for significant mediated effects in your data and discuss the best one to use.=.

In the second module I'll introduce the main concepts you need to understand Path Analysis (or Causal Modeling as it is otherwise known) and show you how to do various kinds of modelling using the AMOS program, which is available online. I’ll be showing you how to construct and test some simple models using techniques you can apply to your own data.

This course is useful for research who want to model their own data. However, a second purpose of this course is to provide you with the knowledge you need to interpret descriptions of causal models that you may read about. Causal modeling is becoming increasingly popular, especially in social and clinical fields, and it is important to be able to interpret and evaluate a model you may come across in your own research or in a journal article which an editor has asked you to review.

## 2. A Quick Review of Regression

## Statistics Training: Introduction to Path Analysis

What is Simple Regression? What is Multiple Regression? In simple regression a single dependent or criterion variable is related to a single independent variable or predictor variable. Multiple regression is an extension of simple regression in which the criterion is regressed against several potential predictors. For example, a simple regression might be: can marital satisfaction be predicted from the degree of personality similarity between partners? In other words, ... Continue Reading

## 3. Moderation and Mediation Explained

## Statistics Training: Introduction to Path Analysis

Path models are built up from basic models of moderation and/or mediation. It is common in psychology for the terms moderator and mediator to be used interchangeably. However, they are conceptually different. "In general terms, a moderator is a qualitative (e.g., sex, race class) or quantitative (e.g., level of reward) variable that affects the direction and or strength of the relation between an independent or predictor variable and a dependent or criterion variable." (Baron & Kenny, ... Continue Reading

## 4. Example of the Difference between Moderation and Mediation

## Statistics Training: Introduction to Path Analysis

This example illustrates the importance of clearly specifying your theory in terms of moderators and mediators. It's taken from an advisory session with a PhD student who approached me to discuss how to test her theory. Her project was looking at the link between language deficit and self-esteem in young adults. Her hypothesis was that the effects of language deficit on self-esteem were caused by language deficit increasing shyness which in turn decreased self-esteem. Here's a path ... Continue Reading

## 5. Example of a Basic Test of Mediation

## Statistics Training: Introduction to Path Analysis

The simplest mediation analysis involves a single independent variable, a dependent variable, and a hypothesized mediator. The unmediated model is represented by the direct effect of x on y, quantified as c. However, the effect of X on Y may be mediated by a process, or mediating variable M. Complete mediation is said to occur when X no longer affects Y after M has been controlled for. In this case path c’ is zero. Partial mediation is the case in which the path from X to Y is ... Continue Reading

## 6. Mediation Analysis: Procedures and Tests

## Statistics Training: Introduction to Path Analysis

So how do we go about doing a mediation analysis? In the next four posts I'll take you through the main approaches to testing for a significant mediation effect. We'll first look at the Causal Steps approach, made famous by Baron & Kenny (1986). Then we'll look at several modern approaches for testing the significance of a mediated effect. These are the Sobel test, MacKinnon's (2002) Correction to Aroian test, MacKinnon's (2002) Distribution of Products, and finally Bootstrap ... Continue Reading

## 7. Causal Steps to Establish Mediation: Step 1

## Statistics Training: Introduction to Path Analysis

Let's start by decomposing mediation into a number of causal steps as described by Baron & Kenny (1986). We'll use our mediation model for the effects of Visual Anonymity on Group Attraction, mediated by Self-Categorization. The fist step is to show that the initial variable affects the outcome. In our model, we need to show that visual anonymity affects group attraction. Let's call this path c. In order to measure this effect (path c), we need to do a simple linear regression of ... Continue Reading

## 8. Causal Steps to Establish Mediation: Step 2

## Statistics Training: Introduction to Path Analysis

In the second step, we need to show that the initial, or predictor, variable affects the mediator. So we perform another simple linear regression using the mediator as if it were the outcome variable and regressing it on the predictor, which gives us an estimate of path a. In our example, path a describes the effect of Visual Anonymity (predictor) on Self-categorization (mediator). 9. Causal Steps to Establish Mediation: Steps 3 and 4 ... Continue Reading

## 9. Causal Steps to Establish Mediation: Steps 3 and 4

## Statistics Training: Introduction to Path Analysis

Steps 3 and 4 are conducted simultaneously using multiple regression. Step 3 consists of regressing the outcome variable y onto both the mediator, m, and the predictor, x to provide an estimate of path b. Note: it is not sufficient just to correlate the mediator with the outcome; the mediator and the outcome may be correlated because they are both caused by the initial variable X. Thus, the initial variable must be controlled in establishing the effect of the mediator on the outcome. Step ... Continue Reading

## 10. Barron and Kenny’s (1986) Criteria for Mediation

## Statistics Training: Introduction to Path Analysis

This slide summarizes Barron & Kenny's (1986) causal steps for establishing mediation, which we have just discussed. However, do all of the steps have to be met for there to be mediation? Certainly, Step 4 does not have to be met unless the expectation is for complete mediation. Moreover, Step 1 is not required, but a path from the initial variable to the outcome is implied if Steps 2 and 3 are met. However, if c' is opposite in sign to ab, then it could be the case that Step 1 is ... Continue Reading

## 11. An Example of a Mediator Acting as a Suppressor

## Statistics Training: Introduction to Path Analysis

Statistics Training: Introduction to Path Analysis ... Continue Reading

12. Testing for Significant Mediation

## Statistics Training: Introduction to Path Analysis

Statistics Training: Introduction to Path Analysis ... Continue Reading

## 13. Sobel’s Test of Significant Mediation

## Statistics Training: Introduction to Path Analysis

Statistics Training: Introduction to Path Analysis ... Continue Reading