Adjusting for Nested/Hierarchical Measures

• Activity Number: 120
• Type: Contributed
• Date/Time: Monday, August 9, 2004 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Education
• Author(s): Ralph Carlson*+ and Hilda Medrano
• Companies: University of Texas Pan American and University of Texas Pan American
• Keywords: nested/hierarchical measures ; transitive variance

Abstract

Psychological and educational measures are often organized by subtests, scales, or factors into nested/hierarchical structures. Measures are nested within a hierarchical structure if each level of one measure is within one and only one level of another measure. On the Wechsler Intelligence Scales a discrepancy of one-half or more standard deviations between the Performance Type of scale and the Verbal Type of scale would yield a Full Scale, which is the third level of hierarchy that is not interpretable due to a lack of "cohesion." When there are significant differences within a lower level of a nested hierarchical measure, all successive levels are not interpretable due to a lack of "cohesion"; therefore, there is a problem with loss of information. The study presents a model that adjusts for nested effects in nested/hierarchical measures. Thus, this model provides a solution by alleviating the loss of information due to a lack of "cohesion" across successive levels of nested/hierarchical measures. Nested variance is transitive and flows from bottom of nested/hierarchical structure to the apex; therefore, adjustment and interpretation of nested effects must be from the bottom up. The current study presents an example of the decomposition and adjustement of nested/hierarchical effects. This study presents a refinement in thinking, analysis, and interpretation of nested/hierarchical measures.