TY - JOUR

T1 - The Meaning of Higher-Order Factors in Reflective-Measurement Models

AU - Eid, Michael

AU - Koch, Tobias

PY - 2014/8/22

Y1 - 2014/8/22

N2 - Higher-order factor analysis is a widely used approach for analyzing the structure of a multi-dimensional test. Whenever first-order factors are correlated researchers are tempted to apply ahigher-order factor model. But is this reasonable? What do the higher-order factors measure?What is their meaning? Willoughby, Holochwost, Blanton, and Blair (this issue) discuss thisimportant issue for the measurement of executive functions. They came to the conclusion that for-mative measurement structure might be more appropriate than a reflective measurement structurewith higher-order factors. Willoughby et al. refer to 4 decision rules for selecting a measurementmodel presented by Jarvis, MacKenzie and Podsakoff (2003). Whereas the rules of Jarvis et al.are based on plausibility arguments, we would like to go a step further and show that stochasticmeasurement theory offers a clear and well-defined theoretical basis for defining a measurementmodel. In our comment we will discuss how stochastic measurement theory can be used to iden-tify conditions under which it is possible to define higher-order factors as random variables ina well-defined random experiment. In particular, we will show that for defining second-orderfactors it is necessary to have a multilevel sampling process with respect to executive functions.We will argue that this random experiment has not been realized for the measurement of exec-utive functions and that the assumption of second-order or even higher-order factors would notbe reasonable for theoretical reasons. Finally, we will discuss the implications of this reasoningfor the measurement of executive functions and other areas of measurement. We will start withthe definition of first-order factors, and then we will discuss the necessary conditions for definingsecond-order factors.

AB - Higher-order factor analysis is a widely used approach for analyzing the structure of a multi-dimensional test. Whenever first-order factors are correlated researchers are tempted to apply ahigher-order factor model. But is this reasonable? What do the higher-order factors measure?What is their meaning? Willoughby, Holochwost, Blanton, and Blair (this issue) discuss thisimportant issue for the measurement of executive functions. They came to the conclusion that for-mative measurement structure might be more appropriate than a reflective measurement structurewith higher-order factors. Willoughby et al. refer to 4 decision rules for selecting a measurementmodel presented by Jarvis, MacKenzie and Podsakoff (2003). Whereas the rules of Jarvis et al.are based on plausibility arguments, we would like to go a step further and show that stochasticmeasurement theory offers a clear and well-defined theoretical basis for defining a measurementmodel. In our comment we will discuss how stochastic measurement theory can be used to iden-tify conditions under which it is possible to define higher-order factors as random variables ina well-defined random experiment. In particular, we will show that for defining second-orderfactors it is necessary to have a multilevel sampling process with respect to executive functions.We will argue that this random experiment has not been realized for the measurement of exec-utive functions and that the assumption of second-order or even higher-order factors would notbe reasonable for theoretical reasons. Finally, we will discuss the implications of this reasoningfor the measurement of executive functions and other areas of measurement. We will start withthe definition of first-order factors, and then we will discuss the necessary conditions for definingsecond-order factors.

KW - Sociology

UR - http://www.scopus.com/inward/record.url?scp=84906542270&partnerID=8YFLogxK

U2 - 10.1080/15366367.2014.943591

DO - 10.1080/15366367.2014.943591

M3 - Journal articles

AN - SCOPUS:84906542270

VL - 12

SP - 96

EP - 101

JO - Measurement

JF - Measurement

SN - 1536-6367

IS - 3

ER -