Formative constructs using PCA

Let's delve into another example using PCA that will be instructive when compared to factor analysis later on in the Exploratory factor analysis and reflective constructs section. We will return to the physical functioning dataset used earlier in this book. Here we will discuss the notions of formative and reflective constructs. See the following diagram (paying close attention to the arrow directions) for a visual representation of the differences. A formative construct is one in which a general trait is composed of a number of very specific traits as shown in the diagram. The arrows pointing towards the construct indicate that the construct is derived from the traits.

Alternately, a reflexive construct is one in which a general trait is thought to underlie and cause specific traits, as shown in the following diagram. The arrows pointing away from the construct are designed to reflect the fact that the construct drives the traits, and the specific traits are...