# Learning about Quality: How the Quality of Military Personnel Is Revealed over Time

By James R. Hosek; Michael G. Mattock | Go to book overview

Chapter Four
MODEL IMPLEMENTATION
In this chapter we first give an informal, intuitive explanation of how the model is implemented and then present a more precise mathematical characterization. Readers mainly interested in the policy implications of the work may safely skip the mathematical exposition.
HOW THE MODEL WORKS: BASIC INTUITION
The model works in two steps:
 Step 1: Estimate a statistical relationship between AFQT, unobserved quality, and promotion speed to E-4 and E-5 for a group of enlistees. Step 2: Use estimates from Step 1 and individual AFQT and promotion speed to E-4 and E-5 to estimate individual quality.

In the first step, we use the population in a particular service, cohort, and occupation to estimate a model relating promotion to quality for the population. Then we use the model to calculate the probability of particular promotion outcomes for an individual, given the individual's AFQT and quality factor, to calculate the expected value of the individual's quality index. (We think of it as using the estimated relationship to “handicap” individuals for their observable characteristics; when we see how people perform relative to their handicap we get information about the unobserved component of quality.)

Details of Step 1

The quality index is composed of directly observable components, like AFQT and education, and an indirectly observable component, the individual quality of job match, or “quality factor.” Figure 4.1 shows how these components fit into the overall quality index.

As Figure 4.1 indicates, the overall quality index, q, in turn affects the speed of promotion to E-4 and to E-5. So quality is “indicated” by promotion speed to E-4 and E-5, and is “caused” by AFQT and an unobservable quality factor. (This is why this kind of model is referred to as a “Multiple-Indicator Multiple-Cause” (or “MIMIC”) model.)

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Learning about Quality: How the Quality of Military Personnel Is Revealed over Time

• Title Page *
• Preface iii
• Contents v
• Figures vii
• Tables ix
• Summary xi
• Acknowledgments xv
• Abbreviations xvii
• Chapter One - Introduction 1
• Chapter Two - Previous Studies and Personnel Quality Indicators 5
• Chapter Three - A Bayesian Model of Service Member Quality 17
• Chapter Four - Model Implementation 27
• Chapter Five - Data and Empirical Results 39
• Chapter Six - Conclusions 55
• Appendix A - Standardization and Comparison Between Groups 61
• Appendix B - Analysis Tables 69
• Appendix C - Parameter Estimates 85
• Bibliography 107
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