Seat Belt Usage by Commercial Motor Vehicle Drivers (SBUCMVD) 2013 Survey. Final Report February 2014

Transcription

1 Seat Belt Usage by Commercal Motor Vehcle Drvers (SBUCMVD) 2013 Survey Fnal Report February 2014

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3 TABLE OF CONTENTS Chapter Page Executve Summary...v 1.0 Introducton Scope of the Survey Study Hghlghts Report Organzaton Sample Desgn Selecton of Prmary Samplng Unts PSU Samplng Frame Selecton of PSUs Selecton of Stes wthn PSUs Ste Samplng Frame Fnal Ste Sample Project Management and Organzaton Project Organzaton Qualty Control Montorng Confrmng Adherence to the Ste Assgnment Schedule Montorng Complance wth the Data Collecton Procedures Performance Revews of Data Collectors Managng Data Collecton Tranng QC Montors Tranng Data Collectors Tranng Data Collecton Procedures Data Collecton Procedures Overvew Observaton Procedures Data Transmsson, Data Edtng, and Imputaton Data Transmsson Data Edtng Imputaton Weghtng and Varance Estmaton...31

4 6.1 PSU Weghtng Ste Base Weghtng Weght Adjustment for Stes wth No Data Collecton CMV Weghts Estmaton of Safety Belt Use Rate Varance Estmaton Rules for Suppressng Estmates n Publcatons Lmtatons...37 Appendces Lst of Appendces A PSU and Ste Sample Selecton... A-1 B C Varance Estmaton...B-1 Tranng Agenda...C-1 Lst of Tables Tables Table 2.1: 2003 total vehcle dstance n mllons of vehcle mles...7 Table 2.2: Mleage by road type: NOPUS PSU frame...10 Table 2.3: Ratos of percent drver-hours to percent mles...11 Table 2.4: Dstrbuton of frame and ste measures by PSU, lmted access status, and separated road status...12 Table 5.1: Mssng rates of the mputed varables...30 Table 6.1: Volume count modfcaton procedure...33 Table 6.2: Estmated total number of CMVs wth 95% confdence ntervals...34 Table A.1: Dstrbutons of PSU PPS probabltes for SBUCMVD Survey and NOPUS and ther ratos... A-3

5 Table A.2: Table B.1: Dstrbutons of PSU PPS probabltes SBUCMVD Survey and NOPUS and ther ratos for the 55 NOPUS PSUs... A-4 The JKn factors...b-4 Lst of Fgures Fgure 3.1 Data Collector Evaluaton Form Exemplar Ste Assgnment Sheet Feld Gude...24

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7 Executve Summary The Seat Belt Usage by Commercal Motor Vehcle Drvers (SBUCMVD) Survey s a natonally representatve feld data collecton program that provdes estmates of safety belt use by drvers and other occupants of medum and heavy duty commercal motor vehcles (CMVs). The work s conducted on behalf of the Federal Motor Carrer Safety Admnstraton (FMCSA) under NHTSA contract DTNH22-13-D Ths survey of CMVs was conducted usng the sample desgn and feld data collecton methodologes smlar to those used n the Natonal Occupant Protecton Use Survey (NOPUS) of passenger vehcle occupants. Surveys were conducted for four consecutve years ( ) and agan n 2013 after a two-year break. The surveys are based upon a statstcally vald research desgn that ncludes medum duty, class 7, and class 8 CMVs observed from roadsdes. Data collecton stes were chosen from a randomly selected sample of Prmary Samplng Unts (PSUs, whch are a county or group of countes) across the Unted States. In 2007 the SBUCMVD survey sample contaned 22 PSUs, n 2008 the sample was ncreased to 28 PSUs, and n 2010 the sample was ncreased further to 34 PSUs. The same 34 PSUs were also used n The followng are some hghlghts of the results from the study: A total of 27,157 CMVs, 27,157 drvers, and 1,730 other occupants were observed at 1,004 stes. The overall safety belt usage rate for drvers of all medum and heavy duty trucks and buses rose from 78% n 2010 to 84% n The usage rate for CMV other occupants also ncreased from 64% n 2010 to 73% n Contnung the trend seen n prevous studes, safety belt use was observed to be hgher n states governed by prmary belt use laws (85%) than secondary belt use laws (78%). Also, as seen n prevous years, safety belt usage among drvers and other occupants n unts dentfed as part of a fleet (86%) was observed to be hgher than for ndependent owner-operators (75%). Observatons on the use of safety belts were conducted on a sample of arteral roads (ART) and lmted access hghways (LAH) by traned Data Collectors and the data collecton protocol remaned the same as n All data were collected on HTC Flyer Tablets utlzng a customzed data collecton program. Independent traffc counts were also recorded to help calbrate the estmates. Addtonal data tems were collected, ncludng: Type of CMV: e.g., straght van, artculated sngle tanker, hazmat carrer, commercal bus, etc. Locaton: urban, suburban, or rural Weather condtons: clear, lght precptaton, or lght fog Speed of observed vehcles at a gven ste: 30 mles per hour (mph) or less, mph, or over 50 mph v

8 Drvers and other occupants characterstcs: race, gender, approxmate age Drver use of cell phones and other handheld electronc devces Tme of day Precse schedules dctated that stes be vsted between 7:00 AM and 6:30 PM on weekdays and weekend days as was done n pror years. Half of the mornng weekdays were scheduled to begn at 7:00 AM and half at 8:00 AM so as to accumulate more rush-hour observatons. The target populaton of the survey can be vewed as a snapshot of all medum and heavy duty CMVs on the road at a partcular pont n tme. Ths report descrbes the overall desgn of the study, the methods used to collect the data, and the estmaton and tabulaton processes. Hghlghts from the analyses are contaned n the body of the report. Tables of the results of the study have been reported to the FMCSA under separate cover. v

9 1.0 Introducton FARS data from 2011 ndcates that approxmately 3,500 large truck and bus crashes occurred that year. One-thrd of the truck occupants who ded n those accdents that year were not wearng a seat belt. Most crashes that are fatal to CMV occupants nvolve runnng off the road and rollng over or httng a large statonary object (e.g., tree, brdge abutment, and culvert). In accordance wth Secton of the Federal Motor Carrer Safety Regulatons (FMCSR), a CMV whch has a safety belt nstalled at the drver's seat shall not be drven unless the drver has properly restraned hmself/herself wth the safety belt. In an effort to combat the low safety belt use rates among CMV drvers, former Secretary Norman Y. Mneta created the Commercal Motor Vehcle Safety Belt Partnershp. Ths partnershp ncludes professonal, safety, and government organzatons. The Federal Motor Carrer Safety Admnstraton (FMCSA) developed the Be Ready. Be Buckled. program to promote safety belt usage among commercal motor vehcle drvers and other occupants. FMCSA estmates that ncreasng safety belt use among CMV drvers to the rates of passenger vehcle usage would consderably reduce fataltes and serous njures. Surveys of safety belt use are conducted to provde FMCSA wth data to assess progress n ncreasng safety belt use and to determne how best to allocate ts resources to help reduce fataltes. In 2002, 2005, and 2006, surveys of safety belt usage among class 7 and class 8 drvers were conducted at selected truck stops. In 2007, the Seat Belt Use by Commercal Motor Vehcle Drvers Survey (SBUCMVD) was redesgned and expanded substantally n order to provde natonally representatve estmates of safety belt use among drvers and other occupants of CMVs. The orgnal sample, used n 2007, conssted of 22 Prmary Samplng Unts (PSUs, defned as countes or groups of countes). In 2008 and agan n 2010, 6 new PSUs were added to the sample, resultng n a total of 34 PSUs. Ths report provdes detals on the sample desgn, outlnes data collecton methods, and explans analyses and weghtng of the results of the 2013 survey. 1.1 Scope of the Survey The research approach for the SBUCMVD 2013 Survey used a probablty based sample to observe safety belt usage by drvers and other occupants of CMVs throughout the Unted States. Specfcally, Data Collectors observed the use of shoulder belts across the front of drvers and other occupants n medum and heavy duty trucks and buses (havng at least 6 tres). The 1,020 sample stes were located on lmted access hghways (LAH) and arteral roads (ART) n 34 PSUs across the country. Observatons were conducted on weekdays and weekend days durng daylght hours. 1

10 1.2 Study Hghlghts The SBUCMVD 2013 Survey was the ffth survey of safety belt use among drvers and other occupants of CMVs whch utlzed a natonally representatve sample. A total of 27,157 commercal vehcles were observed at 1,004 stes (note that data could not be collected at 16 stes). In addton to the 27,157 drvers, a total of 1,730 other occupants were observed. Some hghlghts are shown below wth standard errors n the parentheses. Statstcal sgnfcance s also ndcated usng 5 percent sgnfcance level. The overall safety belt usage rate for drvers of all medum and heavy duty trucks and buses rose from 78% (2%) n 2010 to 84% (2%) n 2013; the dfference s sgnfcant. Snce the ncepton of the study n 2007, overall safety belt use has steadly ncreased each year from a use rate of 64% (3%) n 2007 to the current hgh of 83% (2%)(the dfference between the 2007 and 2013 rates s sgnfcant). The usage rate for CMV other occupants also ncreased sgnfcantly from 64% (3%) n 2010 to 73% (3%) n Contnung the trend seen n prevous studes, safety belt use was observed to be hgher n states governed by prmary belt use laws (85% wth s.e. = 3%) than secondary belt use laws (78% wth s.e. = 5%); however, the dfference s not sgnfcant. Also, as seen n prevous years, safety belt usage among drvers and other occupants n unts dentfed as part of a fleet (86% wth s.e. = 2%) was observed to be sgnfcantly hgher than ndependent owner-operators (75% wth s.e. = 3%). Observed usage rate for drvers and other occupants n the West was the hghest at 91% (3%) as compared to the South (83% wth s.e. = 2%), Northeast (76% wth s.e. = 6%), and Mdwest (79% wth s.e. = 6%); however, the dfferences are not sgnfcant from each other except the dfference between the rates for the West and Northeast. Use rates are sgnfcantly hgher on expressways compared to surface streets (86% wth s.e. = 2% and 78% wth s.e. = 3%, respectvely). Use rates among drvers and occupants of vehcles carryng hazardous materals are hgher compared to vehcles not carryng hazardous materals (85% wth s.e. = 3% and 83% wth s.e. = 2%, respectvely, however ther use rate s not sgnfcantly hgher). For complete results, please refer to the tables of estmates provded under a separate cover. 1.3 Report Organzaton Chapter 2 descrbes the samplng procedures used to select SBUCMVD Survey stes. Chapter 3 dscusses Westat s approach to project management and tranng. Chapter 4 presents a summary of the procedures followed to collect the data for the SBUCMVD Survey. Chapter 5 descrbes the procedures followed n data preparaton, ncludng processng of the raw data, qualty control checks and mputatons. 2

11 Chapter 6 descrbes the weghtng and varance estmaton methodologes. It also descrbes the lmtatons of the data. Appendces nclude further detals of the samplng and estmaton as well as the complete Tranng Agenda. 3

12 2.0 Sample Desgn The SBUCMVD Survey s a natonally representatve feld data collecton program that provdes estmates of safety belt restrant use by drvers and other occupants of medum and heavy duty CMVs. The sample desgn was based on the sample desgn for the Natonal Occupant Protecton Use Survey (NOPUS, a natonally representatve survey of occupant restrant use n passenger motor vehcles), wth modfcatons to accommodate the dfferences between commercal and non-commercal motor vehcles. Ths survey desgn has been used snce The prmary purpose of the SBUCMVD Survey s to estmate safety belt use among commercal vehcle drvers and other occupants both for the populaton as a whole, and by ther characterstcs and varous commercal motor vehcle categores. The am s to generate, for the Federal Motor Carrer Safety Admnstraton, a natonally representatve database ncludng the followng nformaton: Safety belt use: belted neutral color, belted-brght color, not belted, and unknown; Drvers and other occupants characterstcs such as gender, age, and race; Use of handheld devces such as cell phones by the drver; Type of commercal motor vehcle: number of axles, body type, fleet status, HazMat status and confguraton; Presence of a prmary enforcement belt use law; Type of road: lmted access hghway and arteral; Type of area: urban, suburban, and rural; Weather: clear, lght precptaton, and lght fog; Tme of day: rush-hour and non-rush-hour traffc flow; Traffc densty: hgh, medum, and low; Day of week: weekend and weekday; and Speed of observed vehcles at a gven ste: up to 30 mles per hour (mph), mph, and over 50 mph. 4

13 The target populaton can be vewed as a snapshot of all CMVs on the road at a partcular pont n tme 1 (called the target tme pont below). Most CMV drvers are professonals, and are all on the road for workng perods each week, generally. Ths dffers sgnfcantly from noncommercal drvers, whose daly and weekly tmes on the road vary consderably across drvers (for example, some persons use ther cars to go to work, and are on the road durng rush-hour perods, whereas other persons do not work, or do not use ther car to get to work, and are not generally on the road durng these perods). Ths stablty of professonal drvers as compared to regular drvers makes certan aspects of the estmaton task easer n prncple. Suppose D s the total number of commercal drvers who are actve at the partcular tme pont, and Y d s an ndcator of seat belt usage (equal to 1 f yes, equal to 0 f no). The populaton proporton of belted drvers at that tme pont can be wrtten as: 1 D Yd D d 1 P. Usng the snapshot paradgm, ths s the total number of actve commercal drvers who are utlzng ther safety belt, dvded by the total number of actve commercal drvers at the target tme pont. Ths defnton can be naturally extended to the populaton of drvers and other occupants and any subpopulatons of nterest. 2.1 Selecton of Prmary Samplng Unts The desgn of the SBUCMVD Survey closely parallels that of the NOPUS desgn, as the two surveys have smlar objectves and are closely related. In partcular, a smlar set of roads s beng observed, wth smlar observaton technques for the two dfferng types of vehcles. For the SBUCMVD Survey desgn, as n the 2006 NOPUS, the frst stage of selecton s a set of PSUs. The number of PSUs for the 2007 study was 22; n 2008 an addtonal sx PSUs were selected to mprove the precson of estmates, brngng the total to 28. In 2010 the number of sampled PSUs was ncreased by sx agan for a total of 34. The PSU frame used for the SBUCMVD was the same frame that was used for NOPUS. The SBUCMVD PSU sample was drawn n such a way as to overlap as much as possble wth the NOPUS PSU sample usng a Keyftz procedure 2. However, the measure of sze used to sample the SBUCMVD PSUs was 1 Ths snapshot can be vewed as the result of takng photographs at one pont n tme of every ste n the U.S. road net. Ths sample desgn ncludes a full probablty sample of stes (every ste has a chance of selecton), coverng n a probablty sense every road n the U.S. The tme perod of observaton for each ste s not fxed, as conceved by the snapshot paradgm, as selected stes are allocated randomly across tme perods durng the feld perod. The target tme pont n realty s an average across many ponts of tme across the feld perod. Gven the stablty n workng patterns of CMV drvers, ths dstncton (percentage of belted CMV drvers at one sngle pont and percentage of belted CMV drvers at an average tme pont) should not be large. Bases generated by correlatons between tme and ste were avoded by carefully randomzng across sampled stes. 2 The orgnal reference for ths procedure s Keyftz, N. (1951), Samplng wth probablty proportonal to sze, adjustments for changes n probabltes, Journal of the Amercan Statstcal Assocaton, 46, It s desrable to mantan a good overlap between PSUs of the two surveys because the two surveys have smlar 5

14 dfferent than that used n NOPUS (see below), gven the dfferences n CMV and noncommercal passenger vehcle traffc. Pror to 2010, the SBUCMVD PSU sample was n fact a proper subset of the NOPUS sample 3. In other words, all CMV PSUs were also NOPUS PSUs. However, n 2010, when the addtonal sx PSUs were selected, there were some PSUs n the frame where the SBUCMVD measure of sze was larger than the NOPUS measure of sze. Ths resulted n non-nopus PSUs havng a chance of selecton nto the SBUCMVD survey. In the past, ths possblty was ntentonally elmnated rskng only a small bas. However, wth the addton of 6 PSUs, restrctons on selecton could not be permtted as the bas may not have been neglgble. As a result, one non-nopus PSU was selected nto the SBUCMVD PSU sample n spte of efforts to maxmze the overlap usng the Keyftz procedure. Detals of the formaton of the NOPUS PSU frame are gven n the 2006 NOPUS Redesgn Fnal Report. The SBUCMVD PSU frame nherted all of the exclusons of ths frame (these exclusons nclude 20 countes n Alaska, 2 n Colorado, 5 n Montana, 6 n Nebraska, 1 n Texas, and 1 n Washngton; see Table A-12 n the 2006 NOPUS Redesgn Fnal Report). These countes were excluded from the NOPUS frame because of extremely low VMT (vehcle mles traveled) PSU Samplng Frame The PSU sample was selected usng the probablty proportonal to sze (PPS) samplng method. The measure of sze for the NOPUS PSUs was proportonal (wthn each NOPUS stratum) to the total annual vehcle mles traveled (VMT) of all vehcles n the PSU. 4 For the SBUCMVD Survey, the deal measure of sze of each PSU should be proportonal to the number of CMVs whch are observed drvng n that PSU at a partcular nstant of tme. However, ths nformaton s not avalable, so the VMT was used to calculate the total CMV hours spent on the roads wthn that PSU durng the average day snce wth some smplfyng but reasonable assumptons, ths quantty s drectly proportonal to the deal measure of sze. The explct computaton of the measure of sze s gven n the followng paragraphs. Table 2.1 provdes a breakdown of VMT by non-commercal and commercal vehcles 5, and by road type. The CMV percentage of total VMT on nterstate-rural roads s close to 20%. For arteral-rural roads the CMV percentage of total VMT s slghtly less than 10%. For nterstateurban roads the CMV percentage s about 8%. For arteral-urban roads, the CMV percentage s objectves and SBUCMVD was able to use the already created NOPUS PSUs. The procedure was used to maxmze the overlap between the SBUCMVD PSUs and NOPUS PSUs. 3 The SBUCMVD PSU sample should only have had PSUs outsde of the NOPUS PSU sample f there were PSUs not sampled for NOPUS for whch the SBUCMVD measure of sze exceeded the NOPUS measure of sze (n whch case they would have to have a chance of selecton nto the SBUCMVD survey). However, pror to 2010, none of the PSUs outsde of the NOPUS PSU sample were selected, so the SBUCMVD PSU sample was n fact a proper subset of the NOPUS PSU sample. 4 The VMT NOPUS attached to NOPUS PSUs s nformaton at the county level, and t was not broken down by vehcle type. 5 The FHWA data are actually by number of axles and tres, but there s a hgh degree of overlap between commercal/noncommercal and 6-tre+/4-tres or less vehcles. Almost all 6-tre+ vehcles are commercal, and only a small percentage of 4-tre or less vehcles are drven by professonal commercal drvers. 6

15 not broken out from the local-urban roads category, so a drect estmate was not avalable for ths category. A reasonable fgure was derved usng the followng logc. The arteral-urban CMV percentage s lkely to be somewhat less than the nterstate-urban percentage of 8%, but greater than the 4.3% for arteral-urban and local-urban roads put together. Therefore, 6%, whch s roughly the mddle value, was used as an arteral-urban CMV percentage n the measure of sze calculatons. Snce these breakdowns were not avalable at the PSU level, these natonal percentages were used to calculate the measures of sze for the PSUs. The fnal step n the computaton of PSU measures of sze was then to transform CMV mles nto CMV hours for the PSU. Ths was done by dvdng VMT by average mles per hour. Informaton from natonally representatve estmates was not avalable, but we used the fact that the average mleage per hour s hgher for LAH roads than for non-lah roads. It was assumed that LAH roads have double the mles per hour as non-lah roads (e.g., 60 mph for LAH roads and 30 mph for non-lah roads). Based on ths assumpton, the LAH measure of sze computed n terms of VMT s defned to be VMT dvded by two, wth the non-lah measure of sze unchanged. Ths factor of two also plays an mportant role later when the measures of sze for road segments for ste selecton are determned. Table 2.1: 2003 total vehcle dstance n mllons of vehcle mles 6 2-Axle 4-tre or less 6-Tre or more Total Percent 6- tre+ of total vehcle mles Interstate-Rural 215,753 52, , % Arteral-Rural 373,508 40, , % Local-Rural 365,686 29, , % Interstate-Urban 395,235 34, , % Other-Urban 1,308,650 58,830 1,367, % Total 2,658, ,884 2,874, % Puttng these consderatons together, the measure of sze for each PSU was computed usng the followng algorthm. The measures of sze D for urban PSUs (contaned wthn Metropoltan Statstcal Areas) were defned as: D (0.08 / 2) A1_ VMT 0.06A2 _ VMT 0.06A3_ VMT 0.04A1_ VMT 0.06A2 _ VMT 0.06A3_ VMT A1_VMT s the total annual VMT on A10-A18 (LAH) roads n the PSU; A2_VMT s the total annual VMT on A20-A28 (arteral) roads n the PSU; A3_VMT s the total annual VMT on A30- A38 (collector) roads n the PSU. 6 The data from ths table s from the FHWA webste, and s gven on the Mcrosoft Excel spreadsheet 7

16 The measures of sze D for rural PSUs (outsde of Metropoltan Statstcal Areas) were defned as: Selecton of PSUs D (0.2 / 2) A1_ VMT 0.1A2 _ VMT 0.1A3_ VMT 0.1A1_ VMT 0.1A2 _ VMT 0.1A3_ VMT The basc method of PSU samplng was PPS samplng usng the measure of sze defned n the prevous secton. In order to maxmze the overlap between the NOPUS and SBUCMVD samples, the Keyftz procedure was used. The current sample of 34 PSUs s the result of augmentaton of the orgnal sample of 22 PSUs selected n The frst augmentaton was occurred n 2008, when 6 more PSUs were added. The augmented sample of 28 PSUs was supplemented agan by addng another 6 PSUs n Each tme, the Keyftz procedure was used for augmentaton, whle maxmzng the overlap between the NOPUS and SBUCMVD samples. The procedure provded new probabltes that are approprate for the augmented sample, and those new probabltes were used n weghtng. Detals of PSU sample selecton are descrbed n Appendx A, whereas the weghtng procedure s explaned n Chapter Selecton of Stes wthn PSUs The next stage, after PSU selecton, was ste selecton. The same 840 stes that were sampled for the 2008 study and used n 2009, were retaned for the 2010 study. From the sx new PSUs selected n 2010, 30 stes were selected wthn each PSU usng PPS systematc samplng (where sze s a modfed length of the road segment n mles), n the same way stes were sampled for the 2007 study (see the SBUCMVD 2007 Fnal Report for a descrpton). Altogether 1,020 stes were used n 2010, and the same stes were used agan n An mportant desgn choce that lmts the generalzablty of the seat belt use estmates s the excluson of some road types. Only LAHs and arteral roads are part of the SBUCMVD Survey. CMV travel s much more concentrated on these knds of roads as compared to passenger vehcles, but there s stll some CMV travel on the local roads. The Large Truck Methodology Study 7, however, found that CMV observaton rates were very low for local roads. It would requre a very large sample of local road segments to acheve the necessary number of CMVs for observaton to produce a relable estmate for ths road type, as there are so very few CMVs per gven hour on these road segments. Furthermore, the bas caused by non-coverage of the excluded road types s consdered neglgble. For LAH roads, segments (stes) conssted of portons of roadways between ext ramps. For ART roads, segments conssted of the portons of roadways between ntersectons. The segments n each selected PSU were sorted by road type pror to samplng. A measure of sze 7 Large Truck Methodology Study Fnal Report, prepared for the Natonal Hghway Traffc Safety Admnstraton and the Federal Motor Carrer Safety Admnstraton under Contract DTNH22-05-D by Westat, September

17 based on the length n meters was assgned to each segment. Ths measure of sze s dscussed n Secton Segments were sampled by the PPS method wthn each PSU. The next step was to select an observaton pont. Segments from separated hghways (A15-A18, A25-A28, and A35-A38) were undrectonal on the frame. In other words, the segment s desgnated as northbound or southbound, or eastbound or westbound. Segments from nonseparated hghways desgnated on the frame as bdrectonal were selected as such, and a drecton was randomly chosen from the two drectons determned by the road segment (except for one-way streets). For separated segments, ths step was skpped, as the segment already has ts drecton defned for t. The frst ntersecton occurrng n the chosen drecton on the roadway on whch the road segment les was chosen as the data collecton ste. CMV traffc was observed n the drecton approachng the ntersecton. The desgn for LAH segments was smlar, but n ths case the observaton pont was an overpass n the segment, or the closest overpass to the segment. A fnal part of the desgn was to select the tme at whch stes were to be vsted. It s mportant to note that no observatons are to be made at nght. It s very dffcult to conduct observatons at nght because a certan amount of lghtng s requred, whch exsts only for a small percentage of roads. Thus, the use rate P (as gven n the last paragraph of Secton 2.0) wll refer only to daylght mles for the CMV drvers. If there s a dfference n safety belt use behavor at nght, then ths fact wll reman unrevealed by ths study. Excludng nghts, the observatons were spread across the days of the week and across the hours of the day, so that each day of the week and each hour of the day had the same percentage of observatons. A randomzed scheme was establshed so that the ste vstatons for each PSU were randomly allocated across the possble tme slots for the PSU. Ths was vewed to be a less mportant aspect of the SBUCMVD Survey desgn than t s for the NOPUS desgn, gven the greater stablty of work-hours for commercal drvers as opposed to non-commercal drvers Ste Samplng Frame Segments of road were sampled drectly from a master lst developed usng TeleAtlas Dynamap Dsplay software of A10-A18 (LAHs), A20-A28 (arteral roads), A30-A38 (connector) roads 8 n each PSU. Segments from separated roads (FCC codes: A15-A18, A25-A28, A35-A38) were represented on the frame drectonally: there are northbound and southbound segments or eastbound and westbound segments for each dscrete locaton of road. When these segments were selected, the drectonalty of the segment was respected: for example, f the northbound segment was selected, then traffc n the northbound drecton was observed. Thus, durng the snapshot only one-half of the traffc flow s beng represented for ths segment. Ths s accounted for n the samplng process by dvdng the L j measure of sze by a factor of 2 for these segments, where L j s the length of the segment. Segments from nonseparated roads (FCC codes: A11-A14, A20-A24, A30-A34) were not represented drectonally: the segments represented traffc flow n both drectons. Therefore, the measures of sze for these segments was not dvded by 2. 8 Roads on mltary bases were excluded regardless of ther FCC code. 9

18 Table 2.2 below presents mles of road by road type from the NOPUS PSU frame (a total of 3,100 countes). Of the elgble road mles, 7.4% are LAH roads and 92.6% are ART roads. Table 2.2: Mleage by road type: NOPUS PSU frame Road type NOPUS PSU frame mles Percent of total mles Percent of elgble mles A10-A18 - LAH 58, A20-A28 & A30-A38 - Arteral 725, A40+ - Local 5,263, Total 6,047, From Table 2.1, the CMV traffc on the LAHs n 2003 was about 86,700 mllon VMT, out of a total of about 215,900 mllon VMT over all road types: 40% of the VMT for CMVs was on LAHs so that the VMT rato between LAH and non-lah s 2:3. It s assumed that CMV drvers spend half as much tme drvng on lmted access hghways for each mle they drve as they do for each mle on arteral roads. Therefore, when we convert the VMT nformaton nto drver hours, we take the rato between LAH and non-lah to be 1:3, that s, 25% of CMV drver hours are spent on LAHs. Table 2.3 presents the rato of the percentage of mles to the percentage of drver-hours for LAH and non-lah stes. Ths rato was appled to the ste mleage estmate to convert t to a CMV drver-hours measure for each ste, as drver hours represent our populaton measure (we want the populaton percentage of drvng hours that CMV drvers utlze ther seat belts: see the dscusson n Secton 2). 10

19 Table 2.3: Ratos of percent drver-hours to percent mles Road type Percent of elgble mles (%) Percent of CMV drver-hours (%) Rato drverhours/mles LAH ART All stes (subscrpted as j for PSU and ste j) were selected wth probablty proportonal to road length L j, multpled by an extra factor (3.4 or 0.8) whch dffered dependng on whether the ste was an LAH ste or an ART ste and another factor (0.5 or 1) dependng on whether the ste s separated or not. The purpose of the frst extra factor was to oversample LAH stes (LAH stes were oversampled at a rate of 3.4/0.8 = 4.25 relatve to non-lah stes). Ths measure of sze can be wrtten as U j a j b j L j, where aj 0.5 f ste j s separated, = 1 f t s not, and bj 3.4 f ste j s an LAH, = 0.8 f t s non-lah. The probablty of selecton assgned to each ste j n a gven PSU was determned proportonally to ths measure of sze ( U j ). A detaled calculaton of ths ste selecton probablty s gven n Appendx A. Thrty stes were systematcally selected for each PSU. The sort order for the systematc sample was frst by LAH status (LAH or non-lah), followed by road name wthn LAH status. The stes correspondng to each road name were sorted by the north-south or east-west sequence. A total of 1,020 stes selected from the 34 PSUs were used for the 2013 SBUCMVD Survey, of whch 840 stes were carred over from the 2009 survey and 180 addtonal ones from the 2010 survey Fnal Ste Sample Table 2.4 presents the dstrbuton of the fnal ste sample across the PSUs and accordng to three subgroups: non-lah non-separated roads; non-lah separated roads, and LAHs. The fourth possble category of LAH non-separated hghways was neglgbly small and s left out for smplcty s sake (the few stes n ths category dd have a chance of selecton but none were selected). The percentages of the mleages of these three categores on the ste frame wthn each PSU (note that the mleage for the separated roads n the table s the mleage dvded by 2 to represent a sngle drecton), are compared to the percentages of the ste measures of sze of the three categores wthn the PSU. The sample percentages should be close to the ste measure of sze percentages (not the orgnal mleages), and ths s n fact the case. Note that the ste sze measures and sample percentages for the non-lah stes are consderably less than ther mleage percentages, as was planned (the oversamplng rate for LAH segments s 3.4/0.8 or 4.25). 11

20 Table 2.4: Dstrbuton of frame and ste measures by PSU, lmted access status, and separated road status Separated road or not Ste frame dstance n mles Percent of ste frame dstance (%) Percent of ste measure of sze (%) Number of stes n sample Percent of ste sample (%) LAH PSU or not

21 Separated road or not Ste frame dstance n mles Percent of ste frame dstance (%) Percent of ste measure of sze (%) Number of stes n sample Percent of ste sample (%) LAH PSU or not , ,

22 Separated road or not Ste frame dstance n mles Percent of ste frame dstance (%) Percent of ste measure of sze (%) Number of stes n sample Percent of ste sample (%) LAH PSU or not Total Total Total

23 3.0 Project Management and Organzaton 3.1 Project Organzaton The SBUCMVD Survey was conducted by over 20 Westat project staff and over 80 Westat feld staff. Feld staff comprsed those people n the PSUs collectng data or supervsng the collecton of data. Project staff encompassed those n the home offce such as the Project Drector, Project Manager, Feld Drector, statstcans, programmers, Geographc Informaton System (GIS) Montors, and techncal support. The organzatonal chart shown below depcts the project s lne of command. Project Drector Project Manager Feld Drector GIS Montors Tablet Tech. Support Statstcans QC Montors Programmers Data Collectors Gven that all Data Collectors and Qualty Control (QC) Montors were n the feld, communcaton was crtcal to the overall management of the project. Consequently, part of the project organzaton ncluded a herarchy for contactng supervsors when questons or problems arose. Data Collectors were advsed to frst contact ther QC Montor when they had a queston or problem. QC Montors carred cell phones and ther numbers were provded on the back of each Data Collector s ID badge. If Data Collectors were unable to contact ther QC Montor, they were nstructed to contact ther GIS Montor or the Feld Drector. Indvdual Google voce numbers were set up to reach the Feld Drector and GIS Montors. The Google voce numbers forwarded calls to correspondng offce phones and cell phones so project staff could resolve problems and provde gudance durng busness hours and outsde of them. If the QC Montors needed addtonal drecton, they also contacted ther GIS Montor or the Feld Drector as approprate. 15

24 Three tablet techncans were avalable to ad Data Collectors and QC Montors wth techncal problems. Google voce numbers were establshed for these ndvduals as well and calls were accepted from 8 a.m. to 10 p.m. every day. 3.2 Qualty Control Montorng The QC Montors, n concert wth the Feld Drector and GIS Montors, were responsble for mplementng qualty assurance procedures durng data collecton. Specfc qualty assurance dutes performed by the QC Montors are provded below Confrmng Adherence to the Ste Assgnment Schedule The QC Montors conducted surprse vsts to check on the Data Collectors. Ths was possble snce QC Montors were provded wth Ste Assgnment Sheets showng scheduled days and tmes of data collecton as well as computer-generated maps detalng the locaton of each ste. Addtonally, each QC Montor was suppled wth a tablet that was pre-loaded wth CMV stes n Google Navgaton, thereby provdng turn-by-turn drectons to the stes. Data Collectors were unaware of when and where the QC Montor would vst them. All teams were at ther assgned stes at the assgned tme durng QC vsts. In the event observatons at a ste needed to be rescheduled, the QC Montor helped the Data Collectors select a tme that was smlar to the orgnally assgned tme. For example, QC Montors confrmed that weekday rush-hour stes were rescheduled to occur on a weekday durng rush-hour traffc flow. In addton to the qualty assurance dutes lsted above, the QC Montors were also vtal n montorng the overall progress of the feld work. Each nght, the QC Montors called a member of each of ther teams to determne whch stes they observed and detaled the results of each ste vst. QC Montors recorded the progress of the teams on a paper form and faxed them to the GIS Montors each nght. The nformaton was entered nto an MS Access database and referenced durng the qualty control checks the next day Montorng Complance wth the Data Collecton Procedures Durng ther vst to a PSU, QC Montors accompaned ther teams on each type of observaton ste (arteral and LAH) to verfy that all data collecton procedures were followed. The QC Montors ensured that the Data Collectors understood and properly used the tablets. After workng closely wth ther teams durng tranng and conversng wth them through daly phone calls, the QC Montors often knew whch teams were strugglng wth the protocol and arranged to spend more tme wth them. See Fgure 3.1 for further nformaton on the types of evaluatons that QC Montors conducted durng ther vsts. 16

25 Fgure 3.1: Data Collector Evaluaton Form 17

26 In the event Data Collectors were not complyng wth data collecton procedures and errors were detected, QC Montors provded feedback on how to correct the errors. If protocol problems were dentfed durng the QC vst or durng the GIS Montor revew of submtted data, the QC Montor resolved the problems through nstructon or extra ste vsts Performance Revews of Data Collectors At the end of the data collecton perod the QC Montors completed a performance revew for each member of ther data collecton teams. The Feld Drector then dscussed each revew wth the QC Montor and called only those Data Collectors wth problems. All Data Collectors receved a copy of ther revew n the mal. Data Collectors were expected to perform the followng dutes and were evaluated on ther ablty to perform these tasks: Attended and successfully completed tranng; Took care of ther data collecton equpment and returned t at the end of the study; Made travel arrangements for data collecton wth Westat s travel offce; Submtted correct tmesheets and trp expense reports; Properly used the Ste Assgnment Sheets to determne where and when to collect data; Collected data at the correct tme or worked wth ther QC Montors to determne an alternate tme to complete a ste (f necessary); Precsely followed study protocols to complete data collecton; Used maps and navgaton software to locate stes: - If unable to locate a ste, selected an alternate ste accordng to the protocols n the manual; - If unable to locate an alternate ste, contacted ther QC Montor or GIS Montor for assstance; Reported ther day s work to the QC Montors durng nghtly calls; and Cooperated wth ther QC Montors durng surprse vsts. 18

27 3.3 Managng Data Collecton Crtcal to the management of the SBUCMVD Survey are the schedules used to determne the exact day and tme at whch each data collecton team should vst each ste. These schedules determne the day-to-day actvtes of the Data Collectors, allow for QC Montor surprse vsts, and provde a bass for montorng the progress of the entre survey. The schedules were prnted n a format known as the Ste Assgnment Sheet (see Fgure 3.2). The Ste Assgnment Sheet dentfed each ste, the day and tme of data collecton, the type of study to be conducted, the flow (drecton) of traffc, the Overpass for a lmted access hghway ste, the Intersectng Road for an arteral ste, the cty n whch the ste was located as well as the Observed Road tself. Every Data Collector receved a Ste Assgnment Sheet and all QC Montors receved Ste Assgnment Sheets for the teams they supervsed. Fgure 3.2: Exemplar Ste Assgnment Sheet Although Westat made every effort to create a realstc yet effcent tme schedule, the need for data collecton to be rescheduled at some stes naturally occurred. The most common reasons for reschedulng were bad weather, road constructon, and techncal problems wth the tablet. In the event that Data Collectors needed to reschedule, they were nstructed to talk to ther QC Montor 19

28 or GIS Montor and to choose the same type of day of week and same tme of day as was orgnally desgnated for a partcular ste. In addton to the Ste Assgnment Sheet, all feld staff receved computer-generated maps that corresponded to ther data collecton schedules and navgaton software for the tablet. Ths effort was made to help Data Collectors navgate n unfamlar terrtory, locate the carefully assgned stes and conduct data collecton at the desgnated tmes. Data Collectors receved custom maps for ther specfc PSU whle QC Montors receved a complete set of maps for all of the PSUs n ther purvew. Wth respect to navgaton software, all CMV stes were pre-loaded nto the tablet for a Data Collector s assgned PSU and the QC Montors receved the stes n all of the PSUs they supervsed. Thus, t was relatvely smple for Data Collectors and QC Montors to obtan turn-by-turn drectons to any assgned ste. Westat also dstrbuted commercal maps of each PSU and authorzed Data Collectors to obtan supplemental maps from local departments of transportaton, county or cty offces, stores, etc., as needed. 3.4 Tranng All recruted feld staff were requred to attend tranng n Baltmore, Maryland. The tranng faclty was selected because t was moderately prced, had suffcent sleepng and meetng rooms, and provded a complmentary shuttle to and from BWI Arport. The QC Montors receved one day of specalzed tranng on August 7 th, Data Collectors, along wth QC Montors, receved two days of tranng August 8 th and August 9 th, QC Montors Tranng The QC Montor one-day tranng focused on dutes specfc to QC Montors. The topcs ncluded QC vst protocols, answerng questons on locatng stes, resolvng data nconsstences dscovered by Westat staff, and conductng performance revews of the Data Collectors. QC Montors were also traned to operate the navgaton software and collect data usng the tablet as well as dentfy the types of CMVs ncluded n the survey. Subsequently, QC Montors attended the two days of tranng targeted to Data Collectors durng whch they contnued to famlarze themselves wth data collecton equpment and protocols. QC Montor dutes durng Data Collector tranng ncluded assstng the nstructors n the classroom and gvng specal attenton to Data Collectors n need of help. They also receved ther own teachng tme wth ther teams to go over questons and phone call protocols Data Collectors Tranng The Data Collectors tranng course was based on nstructon provded n prevous years and on the tablet data collecton program. The 82 tranees (10 QC Montors, 68 Data Collectors, and 4 back-ups) were dvded nto three subgroups to mnmze the student/teacher rato. Each class had three nstructors and 3-4 QC Montors. 20

29 The tranng revewed both the techncal and admnstratve protocols that were requred to successfully complete the data collecton actvtes (see Appendx C for a copy of the tranng agenda). All Data Collectors and QC Montors receved copes of the tranng manual (prevously delvered under a separate cover). The followng topcs were covered n the tranng sessons and manual: SBUCMVD Survey Overvew Data Collecton Protocols and Feld Technques Schedules and Maps Tablets Admnstratve Procedures In addton to classroom lectures, several hands-on actvtes were also conducted. Frst, Data Collectors were gven the opportunty to practce classfyng CMV characterstcs from photos of CMVs. Data Collectors were presented wth photos of CMVs and asked to dentfy and record ther characterstcs. Ther observatons were then compared to correct responses. Ths exercse gave Data Collectors much needed practce n properly dscernng CMV characterstcs. Approxmately 70 dfferent CMVs wth dfferent confguratons and body types were presented. Specal attenton was gven to classfyng non-standard CMVs and classroom dscusson ensured that all of the Data Collectors understood the ratonale for each decson. Second, vdeo smulaton of traffc was used to allow Data Collectors to practce observng and categorzng CMVs and ther occupants and also to famlarze themselves wth the tablet and SBUCMVD Survey procedures. The vdeos featured vehcles from the perspectve of the Data Collector so the tranees could smulate data collecton. They were asked to work wth ther partners and use ther tablets to set-up a ste and record ther observatons of the CMVs n the vdeo. Instructors stopped the vdeo whenever necessary to answer questons. Fnally, on the second day of tranng, feld smulaton of data collecton was conducted. Data Collectors worked wth ther assgned partners under the supervson of ther QC Montors. Westat staff were also avalable to answer questons. Two stes near the hotel, one LAH ste and one arteral ste, were used for the feld exercse n whch teams were gven the opportunty to apply what they had learned n the classroom sessons. In order to mnmze the number of Data Collectors utlzng the practce stes at one tme, Data Collectors rotated between feld practce, meetng wth ther QC Montors, revewng tablet procedures wth a tech, and a class on admnstratve procedures. 21

30 4.0 Data Collecton Procedures 4.1 Data Collecton Procedures Overvew Data collecton for the SBUCMVD 2013 Survey was conducted from August 11 th August 17 th, Data were collected at 1004 of the 1020 sampled stes. Observatons were made on weekdays and weekends begnnng at 7:00 AM or 8:00 AM and endng before dark. As prevously mentoned, observatons were conducted on lmted access hghways and arteral roads. For the LAH stes the observatons were conducted from overpasses. For arteral stes, Data Collectors conducted ther observatons at the assgned ntersecton. Each ste vst ncluded an observaton perod of 40 mnutes followed by a 15-mnute traffc count. Usng the Ste Assgnment Sheet, the Data Collectors navgated to each ste at the scheduled tme. In some cases t was not possble to collect data at a selected ste. Stes were deemed napproprate for data collecton due to constructon and not havng a safe locaton for Data Collectors to stand to conduct observatons. Procedures for selectng an alternate ste and reschedulng stes were provded to staff. 4.2 Observaton Procedures Data collecton was conducted by teams of two personnel: a Spotter and a Recorder. The Spotter conducted observatons wth the help of bnoculars and nformed the Recorder of the response category for each of the survey varables. The Recorder entered the nformaton called out by the Spotter nto the tablet. Data collectors were traned to observe as many CMVs as possble, whle stll collectng accurate data on each of the CMV varables (.e., qualty over quantty). If there were too many CMVs to observe, Data Collectors were traned to observer the frst vehcle to cross an magnary lne whch was to cross all lanes of traffc (ths was done to nsure that Data Collectors were randomly observng CMVs, rather than focusng on one partcular lane or CMVs whch were smpler to observe). The tablet program recorded data through a seres of screens. When preparng for data collecton, the Recorder frst entered requested ste level nformaton such as ste ID, weather, area type, and alternate ste nformaton. The program also compared the date aganst the scheduled day from the Ste Assgnment Sheet. If data collecton was beng ntated on a day that dffered from the schedule, the program warned the Recorder to conduct observatons at the scheduled tme. Once the ste setup nformaton was entered, the program contnued to the observaton stage. Screens stepped the Recorder through enterng nformaton on the CMV and drver and other occupant characterstcs (see Fgure 4.1 for a complete lstng of the characterstcs captured). The tablet automatcally lmted response optons based on prevous entres. For example, f the Recorder selected Bus for the CMV confguraton, the tablet prompted the Recorder to ndcate 22

31 the type of Bus : Commercal, School, or Passenger Van (15). An oops button was provded n case the Recorder made an error nputtng data. Addtonally, screens dd not advance unless a response was entered for each varable. After data entry was completed for a gven vehcle, the program looped back through the CMV, drver and other occupant screens as the Spotter contnued to observe and call out characterstcs and the Recorder entered them nto the tablet. The tablet tmed the observaton perod and ended data collecton after the allotted 40 mnutes elapsed. After the observatons were complete, the Recorder mmedately performed the traffc count. The Recorder smply pressed a button on the tablet for each CMV that passed. Agan, the tablet tmed the traffc count and automatcally stopped after 15 mnutes. The Feld Gude, presented n Fgure 4.1, provdes a concse summary of the data collecton procedures. Whle t s presented n table form here, t was actually made nto a small lamnated booklet for Data Collectors and was easly carred n a pocket. Used by the Spotter, ths booklet presented the requred data collecton nformaton n the same sequence and the same optons as found n the tablet. Ths allowed the Spotter to call out the nformaton to the Recorder n a logcal and approprate manner. The legend for the Westat Maps was also ncluded here n order to make more space avalable on the maps for data collecton stes. Lastly, the nstructons for transferrng data from the tablet to Westat were ncorporated so data collectors would have an easy reference to look over when transmttng data. For complete detals of the data collecton procedures see the tranng manual whch was prevously delvered. 23

32 Fgure 4.1: Feld Gude 24

33 Fgure 4.1: Feld Gude (contnued) 25

34 Fgure 4.1: Feld Gude (contnued) 26

35 Fgure 4.1: Feld Gude (contnued) 27

36 5.0 Data Transmsson, Data Edtng, and Imputaton 5.1 Data Transmsson The SBUCMVD Survey data captured on the tablets were uploaded each nght to Westat servers. Occasonally, Data Collectors experenced problems connectng to Westat severs due to equpment falure or nablty to connect to the cell network or a W-F network. In these rare nstances, tablet techncal support was contacted and alternate arrangements were made. The data arrved from the tablet as text fles that were mported each mornng to a customzed MS Access database. One copy of the database was used to accumulate the daly raw data and a second copy was made for Westat staff to conduct qualty control checks. 5.2 Data Edtng The data edtng conssted of two elements: 1) performng checks of the data uploaded from the feld and 2) creatng a varable for vehcle class (medum duty, class 7, or class 8) utlzng the vehcle varables. The ntal qualty control checks made wthn 24 hours ncluded: A revew to ensure that stes were beng completed as scheduled. If assgned stes were not completed, Data Collectors were contacted and stes were rescheduled. A check that all of the fles from the tablet were n the database as expected. GIS Montors verfed that both the observatonal and traffc count data for each assgned ste were n the database. A GPS verfcaton that data collecton occurred at the assgned locaton. Usng longtude and lattude, queres flagged any stes that were completed more than 0.05 mles from the assgned locaton. A check that the percentage of restrant use was wthn expected ranges. For example, stes wth 100% raw restrant use or 0% raw restrant use were flagged and Data Collectors were contacted. A check of the number of errors (number of tmes the oops button was used by a Data Collector). A query flagged the team s wth excessve errors and they were contacted. Once the ntal qualty control checks were completed, the resultng database was mported to SAS. SAS was then used for further data preparaton. The duraton of tme spent observng restrant use and countng traffc volume were calculated from the tablets tmers. Also, the number of vehcles observed at each ste was calculated along wth the estmate of average traffc speed n meters. Addtonally, CMVs were classfed nto medum duty, class 7, and class 8 categores accordng to the body type, confguraton, and number of axles as follows: 28

37 All two-axle, sx-tre vehcles were classfed as medum duty vehcles except two-axle tanker trucks and ntermodal contaner trucks whch were classfed as class 7. All three-axle CMVs were classfed as class 7 except for commercal buses, school buses, and dump trucks whch were classfed as class 8. All four or more axle CMVs and bobtals were classfed as class Imputaton Usng Westat mputaton software, AutoImpute, mssng values for 15 varables at the CMV level were mputed. For each varable wth mssng values, the software package frst developed a regresson model wth the varable to be mputed as the dependent varable and all other varables as the predctors. Any varable that was helpful for mputaton was used as a predctor. Ths regresson modelng helps to mantan the correlaton structure n the data. The predcted values of the regresson model were then used to create seven mputaton cells, where hot-deck mputaton was carred out. Regresson modelng and creaton of mputaton cells are done automatcally by the software package. Hot-deck mputaton s a technque where a recpent (unt needng mputaton) wthn the cell s randomly matched wth a donor (unt havng the data present) wthn the cell, and the recpent receves the donor s value. The mputaton cells were based on ftted regresson models of each varable on all other varables. For example, HazMat status was found to be hghly correlated to body type, so mputaton cells for mssng HazMat status were set up based on body type. The regresson model usually had more than one predctor, and the predcted values were grouped to create mputaton cells. In the ntal cycle, these regresson models were generated after fllng n all mssng values usng crude hot-deck mputaton, 1 and then new mputatons were generated usng regresson-based mputaton cells. Ths process was terated untl convergence resulted. 2 Only cases wth at least some vald data had ther mssng data mputed. Cases where all the varables were mssng were classfed as total nonresponse and ther mssng values were not mputed. Table 5.1 provdes the varables mputed along wth ther mssng rates. Note that the amount of mssng data decreased from the 2010 survey. The total number of mssng values that were mputed n 2013 was 335 compared to 686 n 2010, although the total number of CMVs n 2013 was slghtly ncreased, by 1 percent, over The mssng rates for the other occupant varables were calculated out of the number of other occupant records (1,730) except for the other occupant status, whose rate was calculated out of 27,157 (total number of CMVs). There 1 To mpute, we need a regresson model. However, to develop the regresson model, we need the mssng values to be mputed but the regresson model s not yet avalable. So, mssng values are ntally mputed by the hot-deck method wthout the regresson model to create mputaton cells but usng the whole sample as a sngle mputaton cell. Therefore, the ntal mputatons are not as good as they can be, and n ths sense they are crude. 2 The convergence crteron s set by the statstc of the regresson model. It s expected that the statstc s lower at the ntal cycle than those at later cycles as mssng values are crudely mputed at the ntal cycle but wll ncrease and converge to a certan lmt as the teraton goes on. The convergence s checked by comparng the ncrease n the statstc and the crteron specfed by the user. When the ncrease s less than equal to the crteron specfed, t s sad that the convergence s acheved. We used the default value of

38 were 1,730 observed other occupants and 24 wth mssng other occupant status, of whch none was mputed to be an other occupant. Table 5.1: Mssng rates of the mputed varables Varable Total number of cases Number of mssng cases Mssng rate (%) Fleet 27, Confguraton 27, Body Type 27, Number of Axles 27, HazMat Status 27, Electronc Devce 27, Drver s Age 27, Drver s Sex 27, Drver s Race 27, Drver s Belt Use 27, Other Occupant Status 27, Other Occupant s Age 1, Other Occupant s Sex 1, Other Occupant s Race 1, Other Occupant s Belt Use 1,

39 6.0 Weghtng and Varance Estmaton As explaned n Secton 2.0, the sample desgn for the 2013 SBUCMVD Survey s a three-stage desgn consstng of: A frst stage of 34 prmary samplng unts (PSUs); A second stage of 30 stes wthn each PSU; and A fnal stage of ndvdual CMVs selected durng a randomly selected tme-wndow at each ste. The fnal weght to be used to analyze the SBUCMVD data was the product of weghts developed for the three stages of sample selecton. 6.1 PSU Weghtng The PSU weght s smply the nverse of the PSU selecton probablty. If t s denoted by, 1 then the PSU weght for PSU s gven by w, 1,2,..., Ste Base Weghtng The second stage of selecton was at the ste level. From each selected PSU, 30 stes were selected as explaned n Secton If the selecton probablty of ste j from PSU s denoted 1 by p j, then the ste base weght s defned by the nverse of the probablty, p j. The overall ste base weght s then the product of the PSU weght and the wthn-psu ste base weght, 1 namely w w p. j j 6.3 Weght Adjustment for Stes wth No Data Collecton Westat used a detaled procedure for locatng a sutable and safe vantage pont for observaton. If none was avalable wthn the ste, as s descrbed n Fgure 4.1, the Data Collector looked for an alternate. In all of these cases, the Data Collector dd not go outsde the selected PSU, or outsde the selected road (e.g., US Route 15). When ths process s exhausted, wthout fndng a sutable observaton pont, the ste s coded as uncollectble. Uncollectble stes are elgble, as there s certanly traffc through the ste, but are treated lke nonresponse as no data were collected. In 2013, there were no uncollectble stes. If there had been some such stes, the nonresponse weghtng adjustment would have been performed as done before and descrbed below: A weghtng-cell nonresponse adjustment s made for the elgble uncollectble stes usng a factor, whch s calculated as the rato of the total base weght of all stes n the weghtng cell 31

40 dvded by the total base weght of the collectble stes. The weghtng cells are defned by cross-classfcatons of PSU and LAH status (LAH or non-lah). For a gven cell, f the adjustment factor s g j for ste j, the adjusted weght denoted by w j s gven by: gw j j f ste js collectable w j 0 f ste j s uncollectable Note that uncollectble stes receve a 0 weght. The adjustment factor s one for all stes that are n the weghtng cells wthout any uncollectble ste. Sxteen stes were found to be nelgble because they were drt or gravel roads (sometmes through a farm or natonal forest) or on prvate property. Those nelgble stes are gven the same weght as elgble stes so that they represent nelgble stes n the total ste populaton. However, they are not used n analyss. 6.4 CMV Weghts The last stage of selecton s the assgnment of a random tme perod to the ste, and then a samplng of k j CMVs from the K j CMVs whch pass through the ste durng the selected tmewndow 3. The condtonal probablty of selecton of each sampled CMV n ths process s k j /K j (gven ste selecton). The true condtonal probablty of selecton of the CMV ncludes a passthrough-rate factor t j = v j /L j where v j s the average speed through the segment n terms of the length of the tme-wndow and L j s the length of the segment (t j s an estmate of the number of tmes a CMV could pass through the ste durng the tme-wndow). For example, suppose the tme-wndow s 30 mnutes, the average speed s 60 mph and the ste length L j s 10 mles long. Then v j s 30 (30 mles per the tme-wndow length of 30 mnutes), and t j would be 3. A CMV gong 60 mles per hour could pass through 3 of these ten-mle long stes durng the 30-mnute tme nterval. Based on the snapshot approach of the study by selectng a random tme and a random road segment for observaton, we can nterpret ths as the CMV n the example has 3 tmes more chance of beng selected than a CMV travellng n a road segment wth the same length (10 mles) but wth the average speed of 20 mles per hour. Another meanngful nterpretaton s that the samplng procedure enables us to estmate the seat belt usage rate n terms of percent of drver hours. Incorporatng the pass-through-rate factor, the condtonal probablty of selecton of each observed CMV s then gven by: q j k K j j t j 1 Then the wthn-ste CMV weght s gven by q K j j kj t. j 3 As an approxmaton, ths process s consdered as a smple random sample, though the actual process s closer to systematc samplng by observng one CMV after the other as they are avalable and possble to observe. 32

41 The tme perod for observng CMV volume at each locaton was 15 mnutes, but the tme perod for observng safety belt use was much longer, 40 mnutes. Therefore, the 15 mnute volume count s adjusted by the rato R = (tme-length for observng belt use) / (tme-length for the volume count) = 40/15. Ths adjusted volume count s stll denoted as K j. Ideally, K j should be obtaned durng the same observaton tme wndow but t s not possble to count all CMVs passng by whle observng seat belt use of all of those CMVs. Therefore, CMV volume s counted n a separate tme perod of 15 mnutes mmedately after seat belt observatons. However, ths procedure causes other problems: Traffc often moves n waves; the adjusted volume count does not well represent the true CMV volume count for the seat belt observaton tme wndow. It s often observed to be less than the observed number of CMVs (k j ), even zero whle k j > 0. The rato (weghtng factor) of the adjusted volume count (K j ) to the observed number of CMVs (k j ), that s K j / k j, can be unrealstcally large, especally when the volume count s low. The stuaton that K j = 0, even though k j > 0, arses when k j s small. For those cases, t s safe to assume that all CMVs passng through the ste durng the observaton tme wndow can be observed, so volume count s not necessary n ths sense, and we can set K j = k j. For low volume stes (k j < 30), the ratos, K j / k j, are often less than one, whch s nonsenscal because conceptually K j k j. (In 2008 about 94% of such cases had k j < 30.) Therefore, t s very reasonable to assume that for k j < 30, K j = k j. Consequently, for the small number of remanng stes wth K j < k j, we also set K j = k j. Table 6.1: Volume count modfcaton procedure Condton Set volume count Rato (weghtng factor) (K j ) (K j / k j ) k j < 30 K j = k j 1 k j > 29 and K j < k j. K j = k j 1 All others As s As s The threshold 30 was selected by consderng the smallest number of CMVs that t was possble for a Data Collector observe whle not mssng any passng CMVs. Analyzng the 52 stes wth large volume counts (>200) n 2008, t was found that the mnmum number of CMVs observed was 56, maxmum was 156, and the average was 108. Ths means that when there are enough CMVs to observe, on average 108 CMVs can be observed durng the 40 mnutes observaton perod but at least 56 CMVs and as many as 156. Therefore, the threshold of 30 s rather a conservatve value. The fnal CMV weghts were then computed usng the modfed K j n the weghtng formula below that ncludes the overall ste level adjusted weght, w j. Every CMV observed at the same ste receved the same weght, and each drver and other occupant n an observed CMV receved 33

42 the same CMV weght. Puttng altogether, the fnal weght for a CMV n ste j n PSU s gven by: where K W w q g p q g p tk j j j j j j j j j j j 1 s the PSU weght (that s, the nverse of the PSU probablty of selecton); g s the adjustment factor for elgble stes where no data collecton was done; j 1 p j s the ste base weght; t s the pass through rate factor; j K s the modfed CMV volume count (K j ). j The summaton of the weghts W j over all of the observed CMVs provdes an unbased estmator of the number of CMVs on the road n the U.S. at the observed ponts n tme (n a sense the estmator s the number of CMVs durng a mean observed tme, where the observaton tmes are spread over weekdays and weekends of the observaton perod n August). Table 6.2 below presents these estmates for SBUCMVD snce Table 6.2: Estmated total number of CMVs wth 95% confdence ntervals Lower bound 95% confdence nterval Upper bound 95% confdence nterval Year Total of CMV weghts Standard error ,000 97, , , ,000 75, , , ,161 69, , , ,916 65, , , ,477 67, , ,736 The replcate weghts were used to generate a standard error for ths estmator, and a confdence nterval was generated usng the t-dstrbuton (wth 18, 24, 24, and 30 degrees of freedom, respectvely for the 2007, 2008, 2009, and 2010/2013 survey year). These are all provded n the above table. 34

43 6.5 Estmaton of Safety Belt Use Rate Let P be a populaton safety belt use rate as defned n Secton 2.0, whch we want to estmate from the survey data. Its estmate ˆP s obtaned from the followng formula usng the weght developed n the prevous secton: Pˆ 34 m kj 1 j1 k1 34 m k j 1 j1 k1 WI j jk jk WI j y jk where I jk s an ndcator varable to denote whether the subject k observed n ste j n PSU belongs to the populaton of nterest or not (= 1 f yes, and 0 f not), y jk s the belt use status (0 or 1) of subject jk, and m s the number of stes from whch data were collected n PSU. If Ijk 1 for all jk, then the numerator s an estmate of the total number of drvers wearng a safety belt durng the observaton perod, and the denomnator s an estmate of the total number of drvers durng the same observaton perod. So ths rato gves a natonal estmated proporton of drvers usng a safety belt durng the observaton perod. 4 The estmator defned above s called the rato estmator. The seat belt use rate can be estmated for any subpopulaton by confnng the summatons n the above formula over the subpopulaton by approprately defnng I jk. The seat belt use rate for other occupants can be estmated by the same formula by replacng y jk for other occupant s seat belt use status and defnng Ijk 1 f subject jk s other occupant, and Ijk 0 f subject jk s a drver. However, f we want to estmate the seat belt use rate for both drvers and other occupants, we need to expand the summaton n both denomnator and numerator of the formula to nclude both of them. 6.6 Varance Estmaton Varance estmaton provdes the precson of safety belt use estmate. As was done n NOPUS, the jackknfe replcaton method was used for varance estmaton. Ths method was chosen to be able to use the n-house analyss system called Wesvar to analyze the SBUCMVD survey data. 5 SBUCMVD uses mplct stratfcaton by sortng the PSU samplng frame before selectng a systematc sample of PSUs. Ths mplct stratfcaton was reflected by usng the JKn method of Wesvar. 4 The estmate can also be consdered as an estmate of the natonal proporton of drver hours of drvers usng a safety belt durng the observaton perod. 5 The method, as a resamplng method of varance estmaton, also has an advantage of beng able to reflect varous weghng adjustments more easly n varance estmaton than the Taylor method, whch s also often used to estmate the varance of survey estmates. 35

44 To apply the method, four varance strata were frst created as follows: Varance Stratum 1 (s=1): the frst eght PSUs accordng to the NOPUS order of selecton (PSUs =1 through =8) Varance Stratum 2 (s=2): the next nne PSUs accordng to the NOPUS order of selecton (PSUs =9 through =17); Varance Stratum 3 (s=3): the next nne PSUs accordng to the NOPUS order of selecton (PSUs =18 through =26); Varance Stratum 4 (s=4): the next eght PSUs accordng to the NOPUS frame orderng (PSUs =27 through =34); From each varance stratum, one replcate s created by droppng one PSU at a tme wthn the stratum (or assgnng a zero weght to all CMVs n the PSU). Therefore, there s one replcate correspondng to each PSU, and the four strata have 8, 9, 9, and 8 replcates, respectvely, totalng 34. A varance estmate for ˆP, defned n Secton 6.5, s calculated by usng the replcates created above as follows. Frst, the replcate estmate P ˆsa s calculated for each replcate a wthn varance stratum s usng the same form as ˆP but usng the replcate weghts. Then the varance of ˆP s estmated by: ˆ n 1 vp ( ) Pˆ Pˆ 4 n s s 2 sa s1 ns a1 where n s s the number of PSUs (or replcates) n stratum s. Detaled dscusson of ths varance estmator wth theoretcal justfcaton s presented n Appendx B. 6.7 Rules for Suppressng Estmates n Publcatons Three consderatons are used n SBUCMVD Survey s cell suppresson protocol: 1) the number of observatons contrbutng to the numerator of the rato estmator correspondng to the statstc n queston, 2) the number of observatons contrbutng to the denomnator of the rato estmator, and 3) the confdence that the estmate n queston s nonzero. For example, for belt use statstcs, consderaton 1 (the numerator sample sze) would be the number of belted drvers and other occupants observed n the specfed drver and other occupant group, and the consderaton 2 (the denomnator sample sze) would be the number of drvers and other occupants observed n the group. The SBUCMVD Survey suppresses cell estmates n publcatons f the numerator sample sze s less than 5, the denomnator sample sze s less than 30, or the confdence s less than 90%. 36

45 6.8 Lmtatons It s mportant to understand that the SBUCMVD 2013 Survey estmates do have lmtatons. The estmated belt use rates only apply to CMVs wth 6 or more tres (medum duty, class 7 and class 8). Furthermore, they do not nclude CMVs travelng on local roads or at nght. It s also mportant to note that safety belt use was defned as observng a shoulder belt across the front of the CMV drvers or other occupants (see Fgure 4.1). CMV drvers and other occupants only wearng a lap belt would have been categorzed as not belted n ths survey because utlzng the road-sde observatonal methodology makes observng lap belts mpossble. 37

46

47 Appendx A PSU and Ste Sample Selecton A-1

48 Selecton of PSUs The current sample of 34 PSUs was selected n three stages at three dfferent tme ponts. Frst, 22 PSUs were selected n 2007 usng probablty proportonal to sze (PPS) samplng. The desred uncondtonal probablty of selecton (2007) for each PSU on the 2006 NOPUS frame was defned by: D, 1, 2,,22, D (2007) 22 FNOPUS where D was the measure of sze for PSU n the NOPUS frame (denoted as F NOPUS ) as defned n Secton and the constant 22 was the SBUCMVD PSU sample sze n These were the target uncondtonal probabltes of selecton passng through both samplng processes: NOPUS PSU samplng followed by SBUCMVD subsamplng from ths NOPUS PSU sample (see Secton 2.1). However, we wanted to maxmze the sample overlap between two surveys usng the Keyftz method. 1 Let NOPUS PSU sample be denoted as S NOPUS. If a partcular PSU was not n S NOPUS, then ts condtonal probablty was assgned to 0 (t had no chance of enterng the SBUCMVD sample). 2 (2007) If a partcular PSU was n S NOPUS, the condtonal probablty p for selecton nto the (2007) NOPUS SBUCMVD sample was set to be proportonal to as follows: p (2007) (2007) NOPUS 22 for S 55 (2007) NOPUS 1 0 for S NOPUS NOPUS NOPUS where s the probablty of selecton for PSU n NOPUS. Then the overall NOPUS (2007) uncondtonal probablty, whch s equal to p, s proportonal to (2007) or D as desred for S. These probabltes were used to select 22 PSUs n NOPUS In 2008, 6 PSUs were added to the 22 PSUs selected n The desred uncondtonal PSU probabltes of selecton were equal to: (2008) 1 Keyftz, N. (1951). Samplng wth probabltes proportonal to sze: adjustment for changes n the probabltes. Journal of Amercan Statstcal Assocaton, 46, Ths procedure could ntroduce bas by forcng p (2007) 0 for SNOPUS assumed ths bas was neglgble., whch s explaned later. It was A-2

49 28D 28, 1, 2,,28. (2008) (2007) D 22 FNOPUS Tables A.1 and A.2 n the SBUCMVD 2009 Fnal Report present the dstrbuton of (2008), NOPUS, and the ratos between these probabltes over the orgnal NOPUS frame and sample respectvely. In 2010, another 6 PSUs were added to the 28 PSUs selected prevously, as explaned below. The desred uncondtonal PSU probabltes of selecton were equal to: (2010) 34D 34, 1, 2,,34. (2010) (2008) D 28 FNOPUS Tables A.1 and A.2 present the dstrbuton of (2010) NOPUS,, and the ratos between these probabltes over the orgnal 2006 NOPUS frame and sample respectvely. Table A.1: Dstrbutons of PSU PPS probabltes for SBUCMVD Survey and NOPUS and ther ratos Varable (2010) NOPUS (2010) NOPUS N Mnmum Maxmum Mean Sum st Percentle th Percentle th Percentle th Percentle th Percentle th Percentle th Percentle th Percentle th Percentle A-3

50 Table A.2: Dstrbutons of PSU PPS probabltes SBUCMVD Survey and NOPUS and ther ratos for the 55 NOPUS PSUs Varable (2010) NOPUS (2010) NOPUS N Mnmum Maxmum Mean Sum st Percentle th Percentle th Percentle th Percentle th Percentle th Percentle th Percentle th Percentle th Percentle The condtonal probablty of selecton was calculated for each PSU on the NOPUS frame, condtonng on whether the PSU s on the NOPUS sample or not as follows: If (2010) NOPUS, then p (2010) NOPUS (2010) for SNOPUS 0 for SNOPUS But f (2010) NOPUS, then p (2010) (2010) NOPUS NOPUS 1 1 for S for S NOPUS NOPUS Thrty four PSUs were selected from the NOPUS frame usng p (2010) as measure of sze usng the Keyftz method. As the SBUCMVD PSU sample sze was ncreased by sx n 2010, the uncondtonal probablty (2010) became larger than NOPUS for more than 10% of PSUs n the NOPUS PSU frame, as shown n Table A.1. Ths became too much to gnore (as was done n the past by settng the condtonal probablty equal to zero for PSUs not n the NOPUS PSU sample) because the rsk of bas was too great. Therefore, the past practce was not followed. Instead, selecton of PSUs that were not part of the 55 NOPUS sample PSUs (such PSUs wll be referred to as non-nopus PSUs) was allowed. The SBUCMVD 2009 Fnal Report shows that n 2008 a (2008) NOPUS much smaller number of PSUs (< 5%) were n ths stuaton, where, whch was A-4

51 gnored, rskng a small bas. Among the 34 PSUs that were selected, only one non-nopus PSU was selected wth the remanng 33 beng selected from the NOPUS sample. In order to maxmze the correlaton between the 2010 and 2009 SBUCMVD samples, t was also necessary to maxmze the overlap wth the 2008 PSU sample because the same sample was used n Ths correlaton reduces the varance of dfference estmates across years. To maxmze the overlap, the Keyftz procedure was agan used. The overlap between the realzed NOPUS PSU sample and the 28 PSUs sampled for the 2008 survey was maxmzed by computng condtonal probabltes, and by selectng a sample based on those condtonal probabltes. The desred condtonal probablty of selecton for each PSU on the NOPUS frame n 2010, f the 33 PSUs had been selected at once, was: p (2010) (2008) NOPUS 33 for S 55 (2008) NOPUS 1 0 for S Applyng the Keyftz method to select a sample of 33 PSUs for 2010 from the NOPUS PSUs, the (2010) probabltes p (gven the 2008 sample of 28 PSUs) were assgned to be one for 28 PSUs (2010) selected n 2008, and smaller than p for PSUs not selected n 2008, as follows: NOPUS NOPUS 1 for 2008 SBUCMVD sample (2010) (2010) (2008) p p p for 2008 SBUCMVD sample (2008) 1 p (2010) Snce p was equal to 1 for the 28 PSUs selected n 2008, these PSUs were all selected n the 2010 sample. For the 27 NOPUS PSUs not selected n 2008, p (2010) was equal to a number between 0 and 1. Then the overall condtonal selecton probablty of a remanng PSU from the NOPUS sample nto the SBUCMVD sample of 34 PSUs became equal to (2010). Although t dd not occur, f (2008) had exceeded (2010) for any PSUs on the NOPUS PSU (2010) sample but not n the 2008 SBUCMVD sample, then p would have been set to 1 for these PSUs: these would have been condtonal certanty PSUs. (2010) p The SBUCMVD PSU sample was drawn systematcally wth a random start, usng the, (as measures of sze), and usng the orgnal NOPUS frame orderng (to preserve to the extent possble the NOPUS stratfcaton structure). (2010) The fnal uncondtonal probabltes of selecton are, as proved below. A-5

52 Snce SNOPUS and SNOPUS (2010) Pr SCMV probablty where are mutually exclusve and exhaustve events, the uncondtonal can be parttoned as follows: Pr SCMV (2010) SCMV SNOPUS SNOPUS (2010) SCMV SNOPUS SNOPUS (2010) (2010) Pr Pr Pr Pr (2010) S CMV s the 2010 SBUCMVD PSU sample. For the cases wth For the second cases wth Pr S 0 (1 ) : (2010) NOPUS (2010) (2010) NOPUS NOPUS (2010) CMV NOPUS : (2010) NOPUS ( ) Pr S 1 (1 ) (2010) NOPUS (2010) NOPUS NOPUS (2010) CMV NOPUS (1 ) Therefore, the uncondtonal probabltes for all cases are (2010) as desred. As mentoned earler, the same PSU sample used n 2010 was also used n Selecton of Stes wthn PSUs All stes (subscrpted as j for PSU and ste j) were selected wth probablty proportonal to road length L j or L j /2 (dependng on whether the road s separated or not) multpled by an extra factor whch dffered dependng on whether the ste was an LAH ste or an arteral ste. Ths extra factor was to oversample LAH stes. Therefore, the measure of sze depended on L j, whether t s separated or not, and whether t s an LAH or not as defned below: U a b L j j j j where aj 1 f t s not separated, 0.5 f t s separated, bj 3.4 f t s an LAH, 0.8 f t s an arteral. Based on ths measure of sze, the probablty proportonal to sze of selecton assgned to each ste j was defned as: p m U j j M j1 U j wth m and M were the ste sample sze and the total number of stes, respectvely, for PSU. A-6

53 Thrty stes were selected systematcally wth j p from each PSU. The sort order for the systematc sample was frst by LAH status (LAH or non-lah), followed by road name wthn LAH status. The ste correspondng to each road name was sorted by the north-south or eastwest sequence. A-7

54

55 Appendx B Varance Estmaton B-1

56 Varance Estmaton From the vewpont of weghtng and varance estmaton, the desgn can be vewed as an ultmate clusters desgn (see Kalton 1979), 1 as the samplng fractons at the frst stage are very small (fnte populaton correctons are neglgbly close to 1). As was done n NOPUS, we used the jackknfe varance estmator for varance estmaton of the belt use rate ˆP defned n Secton 6.5, under ths ultmate clusters desgn approach. The jackknfe method nvolves the creaton of replcates and calculaton of replcate estmates. The varance estmate s gven n terms of varablty of replcate estmates of ˆP. There was mplct stratfcaton of PSUs as the PSU sample was selected systematcally, observng NOPUS sortng order. To capture some of the effects of ths mplct stratfcaton on the varance, four varance strata were defned based on ths sort orderng 2 : Varance Stratum 1 (s=1): the frst eght PSUs accordng to the NOPUS order of selecton (PSUs =1 through =8) Varance Stratum 2 (s=2): the next nne PSUs accordng to the NOPUS order of selecton (PSUs =9 through =17); Varance Stratum 3 (s=3): the next nne PSUs accordng to the NOPUS order of selecton (PSUs =18 through =26); Varance Stratum 4 (s=4): the next eght PSUs accordng to the NOPUS frame orderng (PSUs =27 through =34); Usng the strata above, replcates were created by droppng one PSU at a tme wthn a varance stratum or equvalently assgnng a zero weght to all CMVs n the PSU. Therefore, there s one replcate correspondng to each PSU, and the four varance strata have 8, 9, 9, and 8 replcates, respectvely, totalng 34. When a replcate s created wthn each (varance) stratum, by droppng one PSU at a tme, the CMVs n remanng PSUs n the stratum are weghted up by a factor n s n s 1, where n s s the number of PSUs n the stratum (see for example Wolter 2007, Secton and 4.5) 3. To defne the replcate weght, let s frst defne the replcate weght factor defned for each PSU. For PSU a n varance stratum s when PSU a s dropped from varance stratum s for 1 Kalton, G. (1979). Ultmate cluster samplng. Journal of the Royal Statstcal Socety, Ser. A, 142, Ths s a tradeoff between capturng the mprovement n varance from the mplct stratfcaton, and mantanng a suffcent number of degrees of freedom for the varance estmator. If we use no strata, then we have 33 degrees of freedom, n whch no mplct stratfcaton s reflected n varance estmaton. Under the proposed approach of usng 4 strata, we have (8-1)+(9-1)+(9-1)+(8-1) =30 degrees of freedom. If we use the maxmum number of strata (17) by parng adjacent PSUs n the sort order, then we gan the maxmum effect from the mplct stratfcaton, but have only 17 degrees of freedom (17 pars). Four strata wth 30 degrees of freedom seems to be a good tradeoff for these conflctng goals. 3 Wolter, K. (2007). Introducton to Varance Estmaton, 2 nd edton. New York: Sprnger. B-2

57 s and s 1, 2, 3, 4, a1, 2,, n and s a 1, 2,, ns, the replcate weght factor s defned as follows: r ( R) sa 1 f s s ns f s s and a a ns 1 0 f s s and a a where R s the seral replcate number assgned to the replcate created by droppng PSU sa. The values of 1 through 8 are assgned to the 8 PSUs n varance stratum 1, 9 through 17 to those n varance stratum 2, 18 through 26 to those n varance stratum 3, and 27 through to 34 to those PSUs n varance stratum 4. Then the R -th replcate weght for all CMVs n ste k n PSU sa s gven by: W r W ( R) ( R) sak sa sak where Ws ak s the full sample fnal weght as defned n Secton 6.4. As can be seen n the above formula, the replcate weght s defned for all sample CMVs. The replcate weght for the replcate correspondng to the dropped PSU sa s equal to the (full sample) fnal weght for the CMVs not n varance stratum s, the fnal weght nflated by the factor of n s n s 1 for CMVs n the PSUs other than the dropped one n the varance stratum s, and zero for CMVs n the dropped PSU. Note that droppng of the PSU s affected by assgnng a weght of zero. The replcate estmate of the belt use rate for occupants n subpopulaton U of nterest, s then defned by: Pˆ 4 ns ksa ( R) s1 a1 k1 jk sa 4 ns ksa s1 a1 k1 jk W I y ( R) sakj sakj sakj W I ( R) sakj sakj where I s akj s an ndcator varable to denote whether occupant j observed n ste k n PSU sa belongs to subpopulaton U of nterest or not (= 1 f yes, and 0 f not), ys akj s the belt use status (0 or 1) of occupant sakj, and m s the number of stes from whch data were collected n PSU. Note that ths replcate estmate s exactly n the same form as ˆP defned n Secton 6.5 except ndexng s dfferent and the fnal weghts are replaced by the replcate weghts. Note also that there are 34 replcate estmates, each correspondng to each replcate number, R 1,2,...,34. B-3

58 A varance estmate for ˆP s then gven by: 34 2 ( R) ( R) vp ( ˆ) J Pˆ Pˆ R1 ( R) where J ( ns 1) ns f replcate R s created from varance stratum s. Ths factor called the JKn factor s presented n Table B.1, and t s the same wthn the varance stratum. 4 Ths varance estmator s known to be consstent (.e., gve a correct estmate when the sample sze s large). For an example, see Theorem 2.1 n Shao and Tu, If the samplng fracton was not neglgble, the fnte populaton correcton factor n the above formula should have been appled, but because the samplng fracton was neglgble, t was assumed that the fnte populaton correcton was equal to one. Ths assumpton makes the varance estmator slghtly upward based. Table B.1: The JKn factors Varance stratum Replcate Number JKn factor Westat (2002). WesVar4.2 User s Manual. Rockvlle, MD.: Westat 5 Shao, J., and Tu, D. (1995). The Jackknfe and Bootstrap. New York: Sprnger. B-4

59 Appendx C Tranng Agenda C-1

60 C-2

61 C-3

62 C-4