An Introduction to Path Analysis: Theory and Practice

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

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

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 ... Continue Reading

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

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

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

Let's start by decomposing mediation into a number of causal steps as described by Baron & Byrne (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

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

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

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

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

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