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36 Standardized Procedures for Personal Travel Surveys Household income: categories corresponding to those in Table 7 in Section 2.5.4; Race: categories of white, black/African American, American Indian/Alaska native, Asian, Native Hawaiian/Pacific Islander, other single race, and two or more races; Age: categories of 05, 610, 1114, 1517, 1864, 6574, 75 and over; Gender: male and female. 4. Total error should be measured using the Percentage RMSE statistic defined in Equation 1. 2 1 ni 1 rij - sij n ji Percent RMSE = n rij 100 (1) ni i ji j where ni = number of variables i; nji = number of categories j in variable i; rij = reference value of variable i in category j; and sij = sample value of variable i in category j. 2.6.2 A-2: Weighting and Expansion of Data Weighting is the process of assigning weights to observations in a sample so that the weighted sample accurately represents the population. Expansion is the multiplication applied to each observation in a sample so that the expanded sample is an estimate of the population. Weight- ing is determined by comparing values of variables within the sample with values of correspond- ing variables from a reliable external source such as the census. Expansion factors are the inverse of the sampling rate. Weighting and expansion are often combined into a single factor or weight, which reflects both the relative representativeness of each observation in the sample and the number of simi- lar cases each observation in the sample represents in the population. Separate weights are usu- ally assigned to households, persons, and trips. These weights sum to the number of households, persons, and trips in the population, respectively. The reader is referred to Section 9.2 of the Technical Appendix for further elaboration. It is recommended that the following standardized procedures be adopted: 1. Each travel survey should conduct a weighting and expansion exercise to include the weights in the data set and to include a description of the weighting process in the metadata; 2. The weights should include expansion factors so that the sum of the weights match popu- lation estimates; and 3. The two-stage procedure, described in the technical appendix, Section 9.2.2, should be adopted as the standard method of calculating weights. 2.6.3 A-3: Missing Data Imputation As discussed in Section 9.3 of the Technical Appendix, imputation is the substitution of val- ues for missing data items or for values of data items that are known to be faulty. Data values are known to be faulty if they are infeasible (e.g., a 5-year old with a driver's license) or are incon- sistent with other information known of an individual or their household. There are two mech- anisms for substituting values for missing or faulty data items--deductive imputation (or infer- ence) and regular imputation. Inference involves deriving the value of a missing or faulty data item from the information known of a respondent or their household, when such a derivation can be made with relative certainty. For example, the gender of a person can often be inferred from their first name, and a person 16 years of age or older who reports making multiple trips alone by car probably has a driver's license. Imputation, on the other hand, is the generation of