Title page
Contents
Acronyms 4
1. Introduction 6
Example 1: Variance Estimation of Linear Composite Estimator 7
2. Approximation by Substitution 9
Example 2: Use the Variance Estimate of the All-CRSS-Crash Estimate 10
Example 3: Use the Variance Estimate of the CRSS Non-Fatal Crash Estimate 11
3. Approximation by GVF 12
Example 4: Use CRSS GVF 13
4. The Proposed Method 16
Example 5: Use the Proposed Method to Make Simple Estimates 19
Example 6: Use the Proposed Method in Logistic Regression Analysis 26
Example 7: Use the Proposed Method for Multiple Year Comparison 28
5. Summary 33
6. References 34
Appendix A: Example Programs in SAS and SUDAAN 35
Example A-1: Variance Estimation of Linear Composite Estimator 35
Example A-2: Use the Variance Estimate of the CRSS Estimate 36
Example A-3: Use the Variance Estimate of the Non-Fatal CRSS Estimate 37
Example A-4: Use CRSS GVF 38
Example A-5: Use the Proposed Method for Simple Estimates 39
Example A-6: Use the Proposed Method in Logistic Regression Analysis 42
Example A-7: Use the Proposed Method for Multiple Year Comparison 44
Appendix B: Example Programs and Output in R 46
Example B-1: Variance Estimation of Linear Composite Estimator 47
Example B-2: Use the Variance Estimate of the CRSS Crash Estimate 48
Example B-3: Use the Variance Estimate of the Non-Fatal CRSS Estimate 49
Example B-4: Use CRSS GVF 50
Example B-5: Use the Proposed Method for Simple Estimates 52
Example B-6: Use the Proposed Method in Logistic Regression Analysis 54
Example B-7: Use the Proposed Method for Multiple Year Comparison 56
Table 1. SAS output for Example 1 7
Table 2. SAS Outputs for Example 2 10
Table 3. SAS Output for Example 3 11
Table 4. SAS Output for the Example 4 14
Table 5. Use the Proposed Method for Example 1 - SUDAAN Output 22
Table 6. Use the Proposed Method for Example 2 - SUDAAN Output 23
Table 7. Use the Proposed Method for Example 1 - SAS Output 24
Table 8. Use the Proposed Method for Example 2 - SAS Output 24
Table 9. Statistics Produced by the Same Model Using Different Data Sets 28
Table 10. 2018 and 2019 Total and Percentage Injury or Fatal Crash Estimates 30
Table 11. 2018 and 2019 Total Injury or Fatal Crash Comparison 31
Table 12. 2018 and 2019 Percentage of Injury or Fatal Crash Comparison 32