1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 APPLICATION OF SEASONAL ADJUSTMENT FACTORS TO SUBSEQUENT YEAR DATA Corresponding Author Harshad Desai, PE, MSCE Red Hills Engineering LLC 669 Eagle View Circle Tallahassee, FL 32311 Phone: 850-597-0551 harshadamita@hotmail.com Wiley Cunagin, PE, PhD Atkins 3700 Capital Circle SE Apt. 415 Tallahassee, FL 32311 Phone: 850-212-6309 wcunagin@gmail.com Kevin Cunagin Pavement Analytics LLC PO Box 670 Tallahassee, FL 32302 Phone: 979-574-7841 kcunagin@pavementanalytics.com Denise Hoyt, MSCE Pavement Analytics LLC PO Box 670 Tallahassee, FL 32302 Phone: 979-492-3390 dhoyt@pavementanalytics.com Richard L. Reel, Jr., PE Florida Department of Transportation Traffic Data Section Transportation Statistics Office 605 Suwannee Street, MS 27 Tallahassee, FL 32399-0450 Richard.Reel@dot.state.fl.us Steven Bentz Florida Department of Transportation Traffic Data Section Transportation Statistics Office 605 Suwannee Street, MS 27 Tallahassee, FL 32399-0450 Steven.Bentz@dot.state.fl.us Text 2,752 Tables and Figures 1,000 Total 3,752
53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 ABSTRACT Seasonal adjustment factors are used by state highway agencies to convert short term traffic counts into estimates of Annual Average Daily Traffic (AADT). These factors are typically calculated from continuous traffic counter data. The protocol for the process is set out in the Federal Highway Administration s (FHWA s) Traffic Monitoring Guide (TMG). This protocol specifies that temporary counts collected during a year should be adjusted by seasonal factors computed from continuous data collected during the same calendar year. It had been suggested that, if the prior year seasonal factors could be used, AADT estimates would be available soon after temporary counts were conducted. This study investigated whether the seasonal factors from sequential years could be applied without loss of statistical accuracy. It was shown that there is no significant loss of accuracy in estimating AADT when prior year seasonal adjustment factors are applied to current year short term traffic volume counts. There is likewise no significant loss of accuracy when vehicle miles of travel are computed using prior year seasonal adjustment factors. INTRODUCTION The Florida Department of Transportation (FDOT) has established a traffic data collection program in compliance with guidelines published by the Federal Highway Administration (FHWA). The traffic volume element of this program includes both continuous automatic traffic recorder (ATR) volume counts and short term volume counts. Current practice uses seasonal (monthly) adjustment factors to convert the short term traffic counts into estimates of Annual Average Daily Traffic (AADT) based on data acquired in the same calendar year at ATR sites. This protocol results in a delay in the availability of AADT estimates until at least two months after the end of the calendar year. It has been suggested that using seasonal factors computed from previous year ATR data would make AADT estimates available during the calendar year in which the volume counts are collected. This paper presents the results of a study that evaluated the feasibility of this change in protocol. BACKGROUND The following guidance is provided in the FHWA s Traffic Monitoring Guide (TMG) (1). Adjustments to Short Duration Volume Counts Short duration volume counts usually require a number of adjustments in order to convert a daily traffic volume "raw" count into an estimate of AADT. The specific set of adjustments needed is a function of the equipment used to collect the count and the duration of the count itself. Almost all short duration counts require adjustments to reduce the effects of temporal bias, if those short
94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 duration counts will be used to estimate AADT. In general, a 24-hour, axle count, is converted to AADT with the following formula: AADT hi = VOL hi * M h * D h * A i * G h (3-1) Where AADT hi = the annual average daily travel at location i of factor group h VOl hi = the 24-hour axle volume at location i of factor group h M h = the applicable seasonal (monthly) factor for factor group h D h = the applicable day-of-week factor for factor group h (if needed) A i = the applicable axle-correction factor for location i (if needed) G h = the applicable growth factor for factor group h (if needed). This formula is then modified as necessary to account for the traffic count's specific characteristics. For example, if the short duration count is taken with an inductance loop detector instead of a conventional pneumatic axle sensor, the axle correction factor (A i ) is removed from the formula. Similarly, if the count is taken for seven consecutive days, the seven daily volumes can be averaged, substituted for the term VOl hi, and the day-of-week factor (D h ) removed from the equation. Lastly, growth factors are only needed if the count was taken in a year other than the year for which AADT is being estimated. Seasonal (Monthly) Factors Monthly (or weekly) factors are used to correct for seasonal bias in short duration counts. Directions on how to create and apply monthly factors are provided in the previous chapter on Continuous Counts, and in the general discussion of factoring in Chapter 4 of Section 2. Those procedures are recommended for the HPMS reporting. States may choose to select alternative seasonal adjustment procedures if they have performed the analytical work necessary to document the applicability of their chosen procedure. STUDY APPROACH The focus of this research was to investigate the statistical accuracy of using prior year seasonal adjustment factors for application to current year short term traffic counts to compute estimates of Annual Average Daily Traffic (AADT). The work performed in this study focused on analysis of historical traffic volume data acquired by FDOT s ATR equipment. Specifically, seasonal (i.e., monthly) adjustment factors were taken from the Traffic Characteristics database for analysis. These data included the years 2008 through 2011. Both individual sites and Seasonal Factor groups were downloaded. Seasonal
135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 Factor groups are the counters within each county that are combined to compute the seasonal factors for each county. The data processing capabilities of the SAS software were applied to prepare the downloaded data for analysis. The statistical tools used included the SAS procedures FREQ, Univariate, GLM, and TTest. ANALYSIS Statistically, there are two applicable questions that can be addressed in determining whether an acceptable level of statistical accuracy can be attained when using prior year seasonal factors to adjust current year data: 1. Do the distributions (patterns) of factors throughout each year differ from year to year by site, seasonal factor group, or statewide? 2. Do the individual monthly factors differ from year to year by site, seasonal factor group, or statewide? The statistical procedures that best address these questions are the Pearson Chi Square Test for distributions and the Paired T Test for individual factors Pearson Chi Square Test Pearson s chi squared test evaluates a null hypothesis that the frequency distribution of specified events is consistent with a reference distribution. Although the comparison is usually versus a particular theoretical distribution (e.g., Normal), it is also applicable to nonparametric (i.e. random) distributions. Parson s chi square test can be used to perform two types of comparison: 1. Goodness of fit 2. Independence Goodness of Fit A goodness of fit test evaluates whether an observed frequency distribution is different from a reference distribution. A test of independence determines whether paired observations on two variables, presented in a contingency (i.e., frequency) table are independent of each other. Computationally, the Pearson procedure first calculates from the data a chi squared statistic, X 2, which is a normalized sum of squared differences between the observed and reference
176 177 178 179 180 181 frequencies. Next, the degrees of freedom are calculated for the statistic. Last, X 2 is compared to a critical value taken from the theoretical distribution that demarcates no significance difference between the distributions. The Pearson cumulative test statistic is 182 183 184 185 186 Where: = Pearson's cumulative test statistic, which asymptotically approaches a distribution. = an observed frequency; 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 = an expected (reference) frequency, asserted by the null hypothesis; = the number of cells in the table. The chi square statistic is used to compute a p value for statistical significance. Test of Independence Independence is assessed by computing the value of p and observing whether it is that is less than or equal to 0.05. This threshold means that the null hypothesis that the row variable (the current year seasonal factor) is independent of the column variable (the prior year seasonal factor) in the contingency table can be rejected. The alternative hypothesis is that the row and column variables have an association or relationship. Paired T Test The Paired T Test evaluates the hypothesis that tests the difference between population means that is assumed to be normally distributed is zero. The test statistic is computed as: 206 207 208 209 210 where d bar is the mean difference s 2 is the sample variance
211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 n is the sample size t is the Student t quantile with n-1 degrees of freedom. The statistical tools produce a mean difference and variance that establishes the confidence interval for the difference. If the confidence interval includes the value zero, it can be concluded that there is no statistical difference between the values that are being compared. If the confidence limits do not include zero, then a statistically significant difference exists and further consideration should be given before the factors are used. Analysis of Impact on VMT In addition to determining whether the seasonal factors are significantly different from year to year, the impact on statewide vehicle miles of travel (VMT) was also evaluated. This was accomplished by applying the seasonal factor group adjustment factors for each to the section VMT unadjusted VMT values and summing the values for comparison. RESULTS As previously stated, the seasonal (monthly) traffic adjustment factors are computed for each ATR site. The data include one seasonal traffic adjustment factor (taf) for each month for each ATR site. Each temporary count site is assigned according to its county and highway system to a county-specific Seasonal Factor Category (SFCAT) that is based on the ATR factors. The SFCAT may combine data from more than one ATR. Comparison of Distributions The distributions were analyzed using SAS procedures FREQ and UNIVARIATE. Figure 1 (taken from the SAS output) shows the results for the comparison of all paired seasonal adjustment factors statewide. The horizontal axis shows the range of observed values for 2011 while the vertical axis shows the range of values for 2010. Each value is entered into the cell in the table corresponding to its 2011 and 2010 values. The ideal comparison result would be a table with entries only on the diagonal. Statistical analysis using the Chi Square procedure for Figure 1 produced a p (probability) value less than 0.001 which is a very significant result. This indicates that a strong statistical relationship exists between the 2010 and 2011 values. The Chi Square results were also produced for 339 individual ATR sites. Of these, 39 had nonsignificant probability (p) levels. In these cases, it cannot be assumed that there is a strong relationship between the 2010 and 2011 values.
252 253 254 255 Figure 1. Contingency Table of TAF 2011 versus TAF 2010 Using ATR Sites 256 257 258 259 260 261 262
263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 However, these cases may be due to the fact that the Chi Square procedure assumes that each cell has at least five observations. This was not true in this analysis. Therefore, the conclusion that a relationship exists must be supported by additional information. The same Chi Square analysis was performed for pairs of years 2010/2009, 2009/2008, and 2008/2007 as well as an aggregation of all permutations of those years. The results were consistent with the 2011/2010 pairing. While the Chi Square analysis for individual sites is informative, in practice FDOT applies the seasonal adjustment factors using county-specific Seasonal Factor Categories (SFCATs). Consequently, the Chi Square analysis was applied to those categories. The results for all of the SFCAT groups taken together are shown in Figure 2. As with the individual site analysis, the Chi Square procedure a p (probability) value less than 0.001 which is a very significant result. This means that there is a strong relationship for the SFCAT groups from one year to then next. The results for each category were also produced. Regression Another way of looking at the relationship between consecutive year seasonal adjustment factors is to compute regression coefficients for the second year based on the first year. This calculation was done for the 2011 factors regressed on the 2010 factors. In this case, the initial value was set to be zero since the change from year to year is desired. Averaging the linear regression coefficients over all groups yielded an average change of 0.0000. That is, overall the factors for 2010 will give the same values as the 2011 factors except for local variation.
291 292 293 Figure 2. Contingency Table of TAF 2011 versus TAF 2010 Using Seasonal Factor Categories 294 295 296
297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 Paired T Test As previously stated, the Chi Square results are informative but not conclusive since the underlying assumption of 5 observations per cell in the contingency table was not met. It was therefore determined that the Paired T Test would be performed. The Paired T Test looks at the distribution of differences between two paired values and then determines whether the mean difference in the values is statistically different from zero. This is done by computing both the mean of the differences and the variance of the differences and constructing confidence limits. If the value zero lies within the confidence limits, it is concluded that there is no statistically significant difference between the values. When performing the Paired T test, t is a value dependent on the variance of the sample distribution, the degrees of freedom are related to sample size, and Pr> t is the probability that the differences are significantly different. Application of the Paired T test to the data found that, in nearly every case, there was no statistically significant difference between the pairs of factors. At the 95% confidence level, the difference between the 2010 and 2011 paired seasonal adjustment factors for the individual sites was between -0.0113 and +0.0131. That is, 95% of the stations had factor differences less than those limits. The corresponding values for the SFCAT group factors found that, at the 95% confidence level, the difference between the 2010 and 2011 paired factors for the group factors was between - 0.0075 and +0.0086. That is, 95% of the groups had factor differences less than those limits. VMT ANALYSIS The impacts of using different factors for computing vehicle miles of travel (VMT) were also addressed. Data were downloaded from the Traffic Characteristics data base that included the total volume counts for each short term site, the length of the section, and the seasonal factor group that is assigned to the section. These data were applied to the 2007 through 2011 SFCAT seasonal adjustment factors to compute VMT. The Paired T Test was performed to determine whether there were statistically significant differences between the VMT produced in successive years. The results are shown in Figure 3.
337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 Compare Year To Year Difference t Value DF Pr > t 2011 2010 vmt2011 - vmt2010 3.54 32915 0.0004 2010 2009 vmt2010 - vmt2009-4.62 32915 <.0001 2009 2008 vmt2009 - vmt2008-4.05 32915 <.0001 2008 2007 vmt2008 - vmt2007 3.19 32915 0.0014 Figure 3. Paired T Test Results VMT by Successive Years. Figure 3 shows that there were no statistically significant differences in statewide VMT between successive years. Total VMT comparisons are shown in Figure 4. The total VMT ranged from a minimum of 1,051,151,338 in 2010 to a maximum of 1,053,933,652 in 2008. This is a range of 0.26 percent of the mean VMT. 353 354 355 356 Figure 4. Comparison of Total VMT by Year.
357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 CONCLUSION This research has shown that there is no significant loss of accuracy in estimating AADT when prior year seasonal adjustment factors are applied to current year short term traffic volume counts. There is likewise no significant loss of accuracy when vehicle miles of travel are computed using prior year seasonal adjustment factors. Since it is desirable to use the most recent traffic volume data, it is suggested that preliminary AADT estimates be computed as short term traffic counts are obtained and passed through the editing process. For those locations where multiple counts are taken during the year, these preliminary values may need to be revised as additional data become available. In addition, since the data for this study are specific to Florida, other states may wish to verify them using their own data. The advantages of this capability are significant. The latest available estimates of AADT can be computed from temporary counts much sooner than if end of year processing is required. The many users of these data will then have their information available as much as a year prior to current practice. This practice could thereby accelerate the performance of any planning or engineering analysis that needs the most recent traffic data.