Imputing Missing Ferry Boarding 

Counts for Estimating National Totals

2022 FCSM Research & Policy Conference

Session C-6: Lifting the Fog: Editing and Imputation

2022-10-25

Young-Jun Kweon

Bureau of Transportation Statistics
This study was performed under the sponsorship of the Department of Transportation in 

the interest of information exchange. The U.S. Government assumes no liability for its 

contents or use thereof.

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Disclaimer
• INTRODUCTION

NCFO / Imputation Study

• DATA

Questionnaire / Released Tables

• METHODS 

Prep ADS / MI Models / Comparison Metrics / Model Estimation

• RESULTS

• CONCLUSIONS

Outline

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INTRODUCTION

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National Census of Ferry Operators

• The Safe, Accountable, Flexible Efficient, Transportation Equity Act–A Legacy for 

Users (SAFETEA-LU) of 2005 (P.L. 114-94) requires BTS to maintain a national ferry 

database. 

• BTS conducts a biennial census of all ferry operators in the U.S. and its territories. 

• Who should be included?

• Ferry operators providing itinerant, fixed route, common carrier passenger/vehicle rollon, roll-off (RoRo) ferry service, and railroad car float operations

• Who should NOT be included?

• Non-itinerant operations (e.g., cruise-to-nowhere services)

• Excursion (e.g., whale watches, casino boats, dinner cruises, etc.)

• Passenger only water taxi services not operating on a fixed route

• LoLo (Lift-on/Lift-off) freight/auto carrier services

• Long distance passenger only cruise ship services

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INTRODUCTION
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• Background:

 About 5% are missing in passenger and vehicle boarding counts.

 With the missing data, trend analysis is challenging. 

• Purpose:

 To impute missing annual boarding counts

• 2018 NCFO

 238 operators invited (frame)

 181 operators participated

2018 NCFO Imputation Study

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INTRODUCTION
DATA

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• 5 Sections: (1) Operator Info, (2) Vessel Info, (3) Terminal Info, 

(4) Segment Info, and (5) Funding Info. 

2018 NCFO Questionnaire

DATA

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2018 NCFO Data Release

5 Tables Operator Operator-Segment Segment Terminal Vessel

155 Variables 47 48 7 19 34

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DATA
METHODS

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Prep Analysis Data Set

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METHODS

• 5 NCFO tables + State Population SEQID OPERATOR_ID SEGMENT_ID

  PASSENGERSVEHICLESSEGMENT LENGTHANNUAL TRIPS  SEGMENT TYPESERVING NPS  TICKET REVENUETRIP PURPOSE  PARKINGTRANSIT CONNECTION  PASSENGER CAPACITY  STATE POPULATION

IDs Segment-Operation Characteristics

Segment Characteristics

Operator Characteristics

Terminal Characteristics

Vessel Characteristics
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MI Models

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METHODS

• 6 Combinations of Methods/Restrictions & 8 Variable Sets:

A total of 48 Model Specifications

111 112 121 122 123 124

211 212 221 222 223 224

311 312 321 322 323 324

411 412 421 422 423 424

511 512 521 522 523 524

611 612 621 622 623 624

711 712 721 722 723 724

811 812 821 822 823 824

MCMC FCS

Variable Set 1

Variable Set 8







Variable Set 2

Model 322

• FCS method with Variable Set 3 (12 

variables)

• Box-Cox transformation for all continuous 

variables

• No min/max/round imposed on 

categorical variables

Variable Set 3

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Comparison Metrics & Simulated Data

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METHODS

• Root Mean Squared Error (RMSE) =

∑ AAAAAAAAAAAA−IIIIII IIII 2

NN

942  # #  # # #

943  #   #  #

:  : : : : : : Obs No. PASSENGERS

            

1 # # # #  # #

2 # # # # # # #

3 # #  # # # #

4 #  # # #  #

5 # # # # # # #

6 # #   # # #

7 # # # # # # #

: : : : : : : :

939 # # # #  # #

940 # # # # # # #

941 #  # # # # 

Obs No.PASSENGERS            

1 # # # #  # #

2 # # # # # # #

3 # #  # # # #

4 #  # # #  #

5 # # # # # # #

6 # #   # # #

7 # # # # # # #

: : : : : : : :

939 # # # #  # #

940 # # # # # # #

941 #  # # # # 

Obs No.PASSENGERS            

1 # # # #  # #

2 # # # # # # #

3 # #  # # # #

4 #  # # #  #

5 # # # # # # #

6 # #   # # #

7 # # # # # # #

: : : : : : : :

939 # # # #  # #

940 # # # # # # #

941 #  # # # # 

Obs No.PASSENGERS            

1 # # # #  # #

2 # # # # # # #

3 # #  # # # #

4 #  # # #  #

5 # # # # # # #

6 # #   # # #

7 # # # # # # #

: : : : : : : :

939 # # # #  # #

940 # # # # # # #

941 #  # # # # 

Data 1 Data 2 Data 3 Data 30

  

forced missing cases in each data
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Model Estimation

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METHODS

• Among 48 models, 21 models were estimated and included for 

model comparison

111 112 121 122 123 124

211 212 221 222 223 224

311 312 321 322 323 324

411 412 421 422 423 424

511 512 521 522 523 524

611 612 621 622 623 624

711 712 721 722 723 724

811 812 821 822 823 824

### : Failed producing imputed values in at least 

one of 30 data sets

### : Produced same results 
RESULTS

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2020 NCFO

Data Collection Year

2022 NCFO

Data Year
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• RMSE(Passenger) = ∑ PP PPPPAAAAAAAAAAAA−PP PPPPIIIIII IIII

2

4444×3333

Results: All 30 Data Sets 

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RESULTS

Average of Passengers in 2018 NCFO:

131,204 persons per segment

Rank Model RMSE

1 121 294,912

2 111 297,203

3 712 299,134

4 812 305,134

5 623 310,022

6 512 312,194

7 622 314,309

8 624 314,309

9 522 315,487

10 524 315,487

Top 10 Models: All 30 Data Sets
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• RMSE(Passenger) = ∑ PP PPPPAAAAAAAAAAAA−PP PPPPIIIIII IIII

2

4444

Results: By Data Set

RESULTS

Rank Model RMSE

1 812 116,687

2 712 120,990

3 322 124,631

4 324 124,631

5 622 125,002

Data 1

  

Top 5 Models by Data Set

Rank Model RMSE

1 712 133,719

2 121 134,371

3 812 135,959

4 622 138,663

5 624 138,663

Data 2

Rank Model RMSE

1 111 336,627

2 712 342,691

3 121 351,350

4 812 356,842

5 622 359,865

Data 3

Rank Model RMSE

1 111 470,599

2 121 487,447

3 812 505,332

4 412 516,106

5 712 516,111

Data 4

Data 5

Rank Model RMSE

1 712 210,778

2 111 212,953

3 622 215,804

4 624 215,804

5 121 219,367

Data 6 Data 30

Rank Model RMSE

1 111 239,243

2 323 246,124

3 522 248,447

4 524 248,447

5 412 251,256 17

Rank Model RMSE

1 121 424,625

2 623 443,567

3 522 451,134

4 524 451,134

5 512 451,662
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Comparison: Quasi-Nat’s Total

RESULTS

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 Quasi-Nat’l Obs. Total = ∑AA CC CC CC PPPPPPPPAAAAAAAAAAAA

 Quasi-Nat’l Est. Total = ∑NNoooo−MMMM MM MM PPPPPPPPAAAAAAAAAAAA + ∑FF FF MMMM MM MM PPPPPPPPIIIIII IIII Obs No. PASSENGERS

            

1 # # # #  # #

2 # # # # # # #

3 # #  # # # #

4 #  # # #  #

5 # # # # # # #

6 # #   # # #

7 # # # # # # #

: : : : : : : :

939 # # # #  # #

940 # # # # # # #

941 #  # # # # 

Data 1 Obs No. 

PASSENGERS            

1 # # # #  # #

2 # # # # # # #

3 # #  # # # #

4 #  # # #  #

5 # # # # # # #

6 # #   # # #

7 # # # # # # #

: : : : : : : :

939 # # # #  # #

940 # # # # # # #

941 #  # # # # 

Before forced missing After forced missing

 
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Results: Quasi-Nat’l Total

RESULTS

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 Observed Total vs.  Estimated Total

 Observed Total

 Each box plot includes 

30 estimated totals, 

one for each data set. 

National Total (Passenger Boarding)
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Results: % Error in Nat’l Total

RESULTS

Percent Error % = 

EE . TT −OOOO . TT

OOOO . TT

× 100%

Obs. Total = Est. Total

Percent Error (Passenger Total)

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CONCLUSIONS

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• MI models developed are not acceptable for boarding count imputation 

at an individual segment level.

• They may be acceptable for estimating national total boarding count.

 An individual model would be not appropriate. Instead, several MI models and 

averaging should be used for estimating national total. 

Conclusions

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CONCLUSIONS
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• Analyzing 2020 & 2018 NCFO together

• Applying logical imputation on cases where statistical imputation is not 

likely to work

• Employing ML methods (e.g., random forest and Ensemble)

• Estimating boarding counts of operators nonresponding to both 2020 

and 2018 censuses

Moving Forward

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CONCLUSIONS
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• Aubrey Nguyen, IT Auditor, U.S. Government Accountability Office (GAO)

ORISE Fellow, USDOT (Formerly)

• Clara Reschovsky, NCFO Program Manager/Survey Statistician, USDOT

Acknowledgement

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Contact

Young-Jun Kweon

young-jun.kweon@dot.gov

NCFO

ferry@dot.gov
Questions?

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