The Pennsylvania State University The Graduate School FACTORS AFFECTING AIRFIELD PAVEMENT PERFORMANCE IN THE UNITED STATES AIR FORCE ENTERPRISE WIDE A Thesis in Civil Engineering by Matthew Bennett 2019 Matthew Bennett Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science December 2019
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
The Pennsylvania State University
The Graduate School
FACTORS AFFECTING AIRFIELD PAVEMENT PERFORMANCE IN THE UNITED
STATES AIR FORCE ENTERPRISE WIDE
A Thesis in
Civil Engineering
by
Matthew Bennett
2019 Matthew Bennett
Submitted in Partial Fulfillment of the Requirements
for the Degree of
Master of Science
December 2019
The thesis of Matthew Bennett was reviewed and approved by the following:
Shelley Stoffels Professor of Civil Engineering Thesis Advisor
Sukran Ilgin Guler Assistant Professor of Civil Engineering
Shihui Shen Associate Professor of Rail Transportation
Patrick Fox John A and Harriette K Shaw Professor Head of the Department of Civil and Environmental Engineering
iii
ABSTRACT
The United States Air Force is responsible for 1.7 billion square feet of concrete and
asphalt airfield pavement which requires millions of dollars to maintain and repair each year. As
funding constraints become more stringent, Air Force engineers must ensure the proper strategic
approach is taken to manage airfield pavement maintenance and repair activities. The United
States Air Force’s strategic approach is to use pavement asset management principles to prolong
the life of the airfield pavement assets and to maintain the desirable operational mission’s level of
service. One step in pavement asset management, which is often overlooked or not routinely
performed, is to provide feedback on the effectiveness of the total pavement management system
and alignment of design methods, specifications and policies with an agency’s goals. This
research provides feedback to the United States Air Force regarding its current pavement
management policies by conducting analysis on pavement distresses. Pavement distresses are a
key variable collected to assess a pavement’s condition. To assist in providing feedback, analysis
was performed to determine which airfield pavement distresses are causing the largest cumulative
reduction in pavement conditions across the entire United States Air Force enterprise. Linear
cracking, joint seal damage, large patches, shattered slabs, joint spalling, small patches, and alkali
silica reactivity are the portland cement concrete airfield pavement distresses causing the largest
summative reduction in pavement condition. Longitudinal and transverse cracking, weathering,
block cracking, and alligator cracking are the asphalt concrete airfield pavement distresses
causing the largest cumulative reduction in pavement condition. Each distress was statistically
analyzed to determine if pavement structure or climatic variables are influencing the likelihood of
each distress occurring under current policies. The distresses were analyzed independently and
the results suggest the United States Air Force’s current design and management policies are not
fully compensating for the impacts of pavement structural and climatic factors.
iv
TABLE OF CONTENTS
LIST OF FIGURES ................................................................................................................. v
LIST OF TABLES ................................................................................................................... viii
ACKNOWLEDGEMENTS ..................................................................................................... ix
CHAPTER 1 INTRODUCTION AND BACKGROUND .................................................... 1
1.1 BACKGROUND ....................................................................................................... 1 1.2 PROBLEM STATEMENT ........................................................................................ 2 1.3 RESEARCH OBJECTIVE......................................................................................... 5
CHAPTER 2 LITERATURE REVIEW ................................................................................. 6
2.1 PAVEMENT ASSET MANAGEMENT ................................................................... 6 2.2 PAVEMENT MANAGEMENT PROCESS .............................................................. 7 2.3 FACTORS AFFECTING PAVEMENT PERFORMANCE ...................................... 26 2.4 RESEARCH ON USAF AIRFIELD PAVEMENT DISTRESSES ........................... 32
CHAPTER 3 DATA COLLECTION AND ORGANIZATION ............................................ 38
CHAPTER 4 RESEARCH METHODOLOGY ..................................................................... 44
4.1 ANALYSIS OF AGGREGATED DATA ................................................................. 44 4.2 STATISTICAL ANALYSIS ...................................................................................... 45
CHAPTER 5 RESULTS AND DISCUSSION ....................................................................... 51 5.1 AGGREGATED DATA RESULTS .......................................................................... 51 5.2 STATISTCAL RESULTS ......................................................................................... 59
APPENDIX A DETAILED STATISTICAL RESULTS ......................................................... 111
APPENDIX B USAF LOCALIZED MAINTENANCE ACTIONS ....................................... 182
APPENDIX C ACCROYNM LIST ......................................................................................... 184
v
LIST OF FIGURES
Figure 1-1 Generic Asset Management System Components .................................................. 3
Figure 2-1 Conceptual illustration of a pavement condition life cycle (Colorado State University, 2019) ............................................................................................................. 7
Figure 2-2 Standard Notation for Branch Identification (AFI 32-1041, 2017) ........................ 9
Figure 2-3 Standard Notation for Section Identification (AFI 32-1041, 2017) ....................... 9
Figure 2-6 Summary of PCN Code .......................................................................................... 13
Figure 2-7: Alligator Cracking Distress Severity Definitions (US Army Corps of Engineers, 2009) .............................................................................................................. 16
Figure 2-8: Example of Distress 41 Alligator Cracking (US Army Corps of Engineers, 2009) ................................................................................................................................ 16
Figure 2-11 Iterative Procedure to Determine Realistic Distress Deduct Values and Distress Definitions Using a Subjective Approach (Shahin, Darter, & Kohn, 1977) ...... 19
Figure 2-12 Example of a Flexible Pavement Condition Survey Data Sheet (ASTM D5340-12, 2012) .............................................................................................................. 20
Figure 2-20 Curling Stresses in a Typical PCC Slab (Pavement Interactive, 2019) ................ 29
Figure 2-21: Climate Zone Map for the US based on 2013 study (Meihaus, 2013) ................ 34
Figure 2-22: Overall Climate Zone Average Rates of Deterioration - PCC (Meihaus, 2013) ................................................................................................................................ 34
Figure 2-23: Overall Climate Zone Average Rates of Deterioration – AC (Meihaus, 2013) .. 35
Figure 2-24: AC Runway Model Based on Average Distress Behavior (Sahagun, 2014) ...... 36
Figure 2-25: PCC Runway Model Based on Average Distress Behavior (Sahagun, 2014) .... 36
Figure 5-1 ANOVA Table Example ........................................................................................ 59
Figure 5-2 Example Odds Ratios for Continuous Predictors ................................................... 60
Figure 5-3 Example Odds Ratio for Categorical Predictors .................................................... 60
Figure 5-4 Example Factorial Plot ........................................................................................... 61
Figure 5-5 Linear Cracking (US Army Corps of Engineers, 2009) ......................................... 67
Figure 5-6 Summary Statistics for Distress 63 - Linear Cracking ........................................... 69
Figure 5-7 Joint Seal Damage (US Army Corps of Engineers, 2009) ..................................... 70
Figure 5-8 Summary Statistics for Distress 67 - Joint Seal Damage ....................................... 71
Figure 5-9 Large Patch/Utility Cut (US Army Corps of Engineers, 2009) ............................. 72
Figure 5-10 Summary Statistics for Distress 67 - Large Patch/Utility Cut .............................. 73
Figure 5-11 Shattered Slab (US Army Corps of Engineers, 2009) .......................................... 74
Table 4-1 Pavement Related Factors Used in Statistical Analysis .......................................... 47
Table 4-2 Climatic Factors Used in Statistical Analysis (U.S. Department of Transportation FHWA, 2018) .......................................................................................... 48
Table 5-1: Air Force Pavement Distresses Ranked by Cumulative PCI Deduct Values ......... 53
Subgrade strength is based on the California Bearing Ratio (CBR) of the subgrade for
flexible pavements. Subgrade strength is based on the moduli of soil reaction, k, of the subgrade
for rigid pavements. The subgrade CBR and k values are then used to determine the PCN
numerical value.
As previously discussed, PCI evaluations are conducted by the USAF via visual
inspections. There are both manual and automated visual inspection methods. A manual visual
inspection is conducted by a technician physically walking on the airfield. Automated visual
inspection methods use vehicles to capture images of the pavement surface which is later
analyzed by a technician. The USAF does not currently use automated inspection methods, but
this research is applicable to automated inspection methods as well.
The USAF has a team centralized at Tyndall AFB, Florida called the Airfield Pavement
Evaluation (APE) team that performs the majority of the USAF pavement inspections. The APE
team follows the pavement inspection procedures established in ASTM D5340, which presents
the procedures to complete the PCI survey completely manually. Since the USAF uses PAVER,
part of the PCI survey is automated within the PAVER system.
14
One of the main goals of a pavement condition inspection is to determine a pavement
section’s PCI. PCI is a distress index widely used to portray a pavement’s condition (Shahin,
2005). A section’s PCI is based on distress type, distress severity, and distress quantity. The first
factor, distress type, is based on whether the pavement surface is asphalt concrete (AC) or
portland cement concrete (PCC). Table 2-1 and Table 2-2 depict the pavement distresses for both
AC and PCC pavement sections and the typical cause of such distress. Each distress has a number
associated with it, which is input into PAVER. For example, using Table 2-1, if the APE team
inspector came across an alligator crack in the AC pavement section, they would input a distress
code of 41 into PAVER.
Table 2-1: Flexible Pavement Distress Types (US Army Corps of Engineers, 2009)
Distress Name Distress Code Cause Alligator or Fatigue Cracking 41 Load Bleeding 42 Other Block Cracking 43 Climate Corrugation 44 Other Depression 45 Other Jet Blast Erosion 46 Other Joint Reflection Cracking 47 Climate Longitudinal and Transverse Cracking 48 Climate
Oil Spillage 49 Other Patching and Utility Cut Patch 50 Other Polished Aggregate 51 Other Raveling 52 Climate Rutting 53 Load Shoving 54 Other Slippage Cracking 55 Other Swell 56 Other Weathering 57 Climate
15
Table 2-2: Rigid Pavement Distress Types (US Army Corps of Engineers, 2009)
Distress Name Distress Code Cause Blowup 61 Climate Corner Break 62 Load Linear Cracks (Longitudinal, Transverse, and Diagonal)
63 Load
Durability (“D”) Cracking 64 Climate Joint Seal Damage 65 Climate Patching, Small 66 Other Patching, Large 67 Other Popouts 68 Other Pumping 69 Other Scaling 70 Other Settlement or Faulting 71 Other Shattered Slab 72 Load Shrinkage Crack 73 Other Spalling (Joint) 74 Other Spalling (Corner) 75 Other Alkali Silica Reaction 76 Other
The second factor considered in determining PCI is distress severity. Each distress for
both rigid and flexible pavement has definitions for three severity levels: low, medium, and high.
The US Army Corps of Engineers created a detailed, standardized manual and definitions for
determining a distress severity level to make the process as objective as possible. Figure 2-7
shows an example of the definitions of severity levels for the alligator cracking distress. Once the
distress severity is determined, it is also input into PAVER.
16
Figure 2-7: Alligator Cracking Distress Severity Definitions (US Army Corps of Engineers,
2009)
The final factor required to determine a pavement section PCI is distress quantity.
Depending on the distress type, the distress may be measured as length, surface area, depth, etc.
The manual created by the US Army Corps of Engineers states how to measure the quantity of
each distress. For example, alligator cracking is measured in square feet of surface area as seen in
Figure 2-8.
Figure 2-8: Example of Distress 41 Alligator Cracking (US Army Corps of Engineers, 2009)
17
After the distress quantity is collected, the distress quantity is converted to distress
density. The distress density is determined by dividing the distress quantity at each severity level
by the total area of the sample unit (Shahin, 2005). The result is then multiplied by 100 to convert
the density to a percent per sample unit for each distress type and severity (Shahin, 2005). The
distress type, distress severity, and distress density are combined to determine the PCI deduct
value required to calculate a pavement section’s PCI. Figure 2-9 provides an example of how a
PCI deduct value is determined. Each distress type has a PCI deduct curve with the three severity
levels plotted on the graph. The PCI deduct curves were created by the Army’s Construction
Engineering Research Lab from 1974 to 1976 for the Department of Defense (DoD) (Shahin,
Pavement thickness, pavement surface type, and subgrade strength are the three factors
used to represent the pavement structure. The pavement surface type and thickness data were
collected from the USAF PAVER database. The subgrade strength data were collected from the
PCN code data. Part three of the PCN code is the subgrade strength as previously discussed. This
part of the code was extracted to represent the strength of the subgrade for each section of
pavement in the Air Force inventory.
2.4 RESEARCH ON USAF AIRFIELD PAVEMENT DISTRESSES
The PCI is the heart of pavement asset management. Rarely, are pavement management
decisions made without the PCI being considered. As previously stated, a PCI is based on three
factors: distress type, distress severity, and distress quantity. It can be concluded that
understanding and evaluating pavement distresses can be considered the most important aspect of
pavement management. The focus of this research is to gain a greater understanding of pavement
distresses in the USAF airfield pavements to help the USAF decision makers make the best
pavement management decisions. A better understanding for the USAF pavement distresses will
be accomplished by analyzing the USAF pavement distress data stored in the PAVER database.
The USAF has had research performed on pavement performance in comparison to
climate in the past. There have been three predominant studies using the USAF PAVER database
33
to analyze USAF pavement assets and environmental factors affecting pavement performance.
The three studies focused on USAF pavement assets within the United States and did not consider
USAF installations in foreign countries.
The first study was performed in 2013 and generated pavement deterioration models for
every pavement family for all the bases in four distinct climate regions within in the United
States. The researchers of the study used the literature to present precipitation, temperature,
subsurface moisture, and freeze-thaw cycles as four predominant factors that have a significant
influence on pavement performance. The climate model was built using precipitation and freezing
degree-days data collected from WeatherBank Inc. “WeatherBank continuously collects data
from approximately 1,700 National Oceanic and Atmospheric Administration (NOAA), National
Weather Service (NWS), and Federal Aviation Administration (FAA) stations scattered across the
United States” (Meihaus, 2013). The four climate zones were defined as:
• No Freeze-Wet: Precipitation > 25” and FDD < 750
• No Freeze-Dry: Precipitation < 25” and FDD < 750
• Freeze-Wet: Precipitation > 25” and FDD > 750
• Freeze-Dry: Precipitation < 25” and FDD > 750
The Kriging geospatial interpolation technique was used to interpolate between locations
to develop a climate region map. Figure 2-21 depicts the climate zone region map used in the
2013 study. The study found that their climate model may have been oversimplified for the
climate regions that exist in the United States.
34
Figure 2-21: Climate Zone Map for the US based on 2013 study (Meihaus, 2013)
The climate model was used to “determine if a statistical difference in the region exists
between the regional climate regions average rate of deterioration for each family of pavements”
(Meihaus, 2013). They found that the climate region deterioration rates for both PCC and AC
were consistent with expected average deterioration rates for airfield pavements. The
deterioration rates for both AC and PCC pavements can be found in Figure 2-22 and Figure 2-23.
Figure 2-22: Overall Climate Zone Average Rates of Deterioration - PCC (Meihaus, 2013)
35
Figure 2-23: Overall Climate Zone Average Rates of Deterioration – AC (Meihaus, 2013)
In 2014, Lauren Sahagun conducted her master’s theses on modeling pavement distress
rates within USAF airfields. While Meihaus performed analysis on airfield taxiways, aprons, and
runways, Sahagun focused her analysis on USAF runways. The research set out to investigate
distress patterns within the four proposed climate regions and determine which distress types are
most prevalent in each climate zone.
Sahagun identified potential doubt in the climate regions presented by Meihuas, so
Sahagun set out to improve the model. Sahagun developed a model that included pavement type,
distress, and geographic location. Her model suggested that there are only two climate regions in
the US: western and eastern. An example of her model is presented in Figure 2-24 and Figure 2-
25. Sahagun found that some distresses were displaying a geographic pattern but could not find
correlation based solely on climate. The research could not confirm the hypothesis that climate is
the predominant contributing factor without performing additional research that considered
additional deterioration factors such as traffic, maintenance, structure, and construction history
(Sahagun, 2014).
36
Figure 2-24: AC Runway Model Based on Average Distress Behavior (Sahagun, 2014)
Figure 2-25: PCC Runway Model Based on Average Distress Behavior (Sahagun, 2014)
The third study by Parsons and Pullen also investigated the relationship between
pavement distress and climate factors. Parsons and Pullen’s hypothesis “was that certain types of
distresses would be more likely to occur, or occurs at a higher density when exposed to certain
climate factors” (Parsons & Pullen, 2016). Parsons and Pullen used Meihaus’ climate regions to
categorize the USAF pavement data and perform analysis. Installations outside of the United
States were outside the scope of the Meihaus research and were also not considered in Parsons
37
and Pullen’s research. Parsons and Pullen concluded that the following distresses were affected
by climate with significance α=0.05: alligator cracking, block cracking, joint reflection cracking,
raveling, blow-ups, D-cracking, popouts, and scaling. Six additional distresses were determined
to be affected by climate with a significance of α=0.10 to include: bleeding, rutting, swelling,
raveling, corner breaks, and ASR. They were also able to conclude that PCC pavements were
more affected by climate than AC pavements and AC pavements were more affected by moisture
than PCC.
38
CHAPTER 3
DATA COLLECTION AND ORGANIZATION
There are 3 sets of data used in this research. One of the sources of data was provided by
the Air Force Civil Engineer Center as a PAVER database E70 files. This dataset is the heart of
the research. and provides pavement inventory and distress data based on the most current
inspection for 102 USAF locations. This data was collected over the past years by the USAF
Pavement Evaluation Team in accordance with ASTM D5340-12. A PAVER database that
included current and previous inspection data was requested but was unable to be provided. The
information collected from the dataset for each location in the USAF is displayed in Table 3-1..
The User Defined Report option in PAVER was used to extract the pavement data. The
initial User Defined Report included 94 columns of data and 590,345 rows of data. After further
analyzing the data, it was evident that the data was categorized by Sample Unit instead of by
pavement SectionID. Being categorized by Sample Unit resulted in duplicate rows and after they
were removed from the User Defined Report, there were 112,059 rows of data remaining. After
further analyzing the data, additional duplicates and errors were found in the data, therefore
additional categories were removed from the User Defined Report. Such categories included
“Work Code”, “Material”, “Material Type”, and “Comments.”
39
Table 3-1: Fields Used from PAVER Database
Fields Used from PAVER Database Major Command Network Name NetworkID BranchID Branch Name Branch Use Branch Area Branch Area Units UID_SUniqueID Last Inspection Date Length Width Section Linear Units Section Rank SectionID Section True Area Section Area Units Slab Length Slab Width Slabs Years Since Major Work Years Since Inspection Surface Type - Current Thickness Thickness Units Sample Type Density Distress Code Distress Description Distress Mechanism Distress Quantity SYS_QuantityUnits Distress Quantity Units PCI Deduct Severity PCI PCI Category
40
There are two sample types in a pavement evaluation. The two sample types are Random
(R) and Additional (A) (US Army Corps of Engineers, 2015). For the purpose of this study, the
author only analyzed pavement sections that were Random sample types. This was accomplished
to ensure the pavement sections used for analysis were randomly selected to be representative of
the pavement section. When the pavement distress is collected, the distress has a severity of low,
medium or high associated with the distress quantity. To account for distress severity, the PCI
deduct values were used. Distress severity is one of the three components used to calculated PCI
deduct values. If one pavement section had two of the same distresses, but with different levels of
severity, the PCI deducts were summed to one distress per section. For example, if there is a
pavement section, A01A, with distress code 41 low severity with a PCI deduct of 5 and a distress
code 41 high severity with a PCI deduct of 10, in this research, section A01A would appear as
distress code 41 with a PCI deduct of 15. The final PAVER dataset used was left with the 37
columns displayed previously in Table 3-1 and 60,771 rows of data.
The second set of data is the climate data for each USAF location. The climate data was
manually extracted using the LTPP InfoPAVE: LTPP Climate Tool. The LTPP Climate Tool
search location bar was used to search for each USAF base analyzed and then visually verified
the location on the map after the search. These locations are very small islands that MERRA did
not have climatic data for and therefore they were removed from the research.
The date range this data was collected from is from 1980 to 2017 which was the
maximum date range at the time the data was collected. The climate data was collected for 99
The first statistical approach used was Analysis of Variance (ANOVA) using the General Linear
Model. This model allowed for One-Way and Two-Way ANOVA capabilities. In the early stages
of the analysis, it was apparent that the dependent variable, PCI Deduct, does not follow a normal
distribution and is a right skewed distribution. The data were not successfully transformed to a
normal distribution and the residuals were also not normally distributed, so a General Linear
Model ANOVA was not used.
The second statistical tool used to analyze the data was Binary Logistic Regression.
Binary Logistic Regression is typically used to describe the relationship between a set of
predictors and a binary response (Minitab, 2019). For the purposes of this research, Binary
Logistic Regression was used to assist in describing the relationship between factors that typically
affect pavement performance with a response of a distress occurring or not. Binary Logistic
Regression does not assume normality and therefore was able to be used on the non-normal data.
PCI deduct is a continuous variable, so to use binary logistic regression, the data had to
be converted to dichotomous values. To change the PCI deduct value into dichotomous values,
the author defined pavement sections that had a PCI deduct value greater than zero a categorical
variable of “1” and pavement sections with a PCI deduct value equal to zero a categorical
46
variable of “0.” For distresses, such as linear and transverse cracking in AC, where a very small
quantity has minimal effect on pavement performance, analysis was accomplished using small
values greater than zero for the dichotomous value of “0.” The analysis showed that increasing
the distress limit from no distress quantity to a small quantity does not change the results, so the
dichotomous value of “0” remained defined as sections with no distress quantity for all distresses.
If a pavement has a pavement distress, then the section is assigned a value of “1” and if it does
not have a distress it is assigned a value of “0.” Analysis is performed by examining each
individual distress independently. For example, when analysis distress code 63 is present on a
pavement section, that section is assigned to the “1” category. Similarly, for the sections that
distress code 63 does not exist, that section is assigned to the “0” category.
The factors that typically affect pavement performance are used as predictors in the
statistical analysis These factors include the pavement structure and climatic data collected for
each location analyzed. Specifically, the factors selected to be used for statistical analysis can be
found in Table 4-1 and Table 4-2.Table 4-1 defines the pavement related factors and Table 4-2
defines the climatic variable used for analysis.
47
Table 4-1 Pavement Related Factors Used in Statistical Analysis
Factors Categorical or Continuous Definition
Years Since Last Major Repair Actual Continuous
This is the number of years since the last major repair was completed to the last inspection. A major repair is assumed to reset the pavement condition to near perfect.
Feature Categorical Apron, Taxiway, or Runway
Subgrade Strength Categorical
As defined in Figure 2-2. Four variables A, B, C, D with A being the strongest subgrade and D being the weakest. Subgrade strength D was removed from the study, so only A, B, C are studied.
Thickness Continuous Thickness of pavement surface layer in inches.
Surface Type - Current (AC Pavements Only) Categorical
Asphalt Concrete (AC) Asphalt Concrete Over Asphalt Concrete (AAC) Asphalt Concrete Over Portland Cement Concrete (APC)
48
Table 4-2 Climatic Factors Used in Statistical Analysis (U.S. Department of Transportation
FHWA, 2018)
Factors Categorical or Continuous Definition
Average PRECIPITATION Continuous
The average water equivalent of total surface precipitation over year time period from 1980 to 2017 for each location in millimeters.
Average TEMP_MEAN_AVG (deg C) Continuous
An average of the annual average of the monthly mean air temperatures 2 m above the MERRA centroid from 1980 to 2017 for each location in Celsius.
Average FREEZE_INDEX Continuous
The average of the annual summation of difference between 0 degrees Celsius and mean daily air temperature, when mean daily air temperature is less than 0 degrees Celsius for each location from 1980 to 2017 in Celsius degree days.
Average FREEZE_THAW Continuous
The average of the annual number of days in the year when the maximum air temperature is greater than 0 degrees Celsius and minimum air temperature is less than 0 degrees Celsius on the same day for each location from 1980 to 2017 in number of days.
Average TEMP_MAX Continuous
The average of the annual maximum air temperature 2 m above elevation of MERRA cell centroid for each location from 1980 to 2017 in Celsius.
Average TEMP_MIN Continuous
The average of the annual minimum air temperature 2 m above elevation of MERRA cell centroid for each location from 1980 to 2017 in Celsius.
Average DAYS_ABOVE_32_C Continuous
The average of the annual number of days in the year when the maximum air temperature is greater than 32.2 degrees Celsius for each location from 1980 to 2017 in number of days.
Average DAYS_BELOW_0_C Continuous
The average of the annual number of days in the year when the minimum air temperature is less than 0 degrees Celsius for each location from 1980 to 2017 in number of days.
49
The statistical analysis was performed by considering all of the factors in Table 4-1 and
Table 4-2 at once and performing backward stepwise elimination to determine which factors are
considered significant. The purpose of this research is not to create a predictive model, instead it
is to which factors may be significant. Therefore, the first statistical result was to determine if
there is any correlation between the factors used for analysis. The correlation between factors was
determined by the Variance Inflation Factors (VIF). The “rule of thumb” of the threshold of a
VIF less than 10 was used for this research. After the first iteration of backwards elimination, if a
remaining factor had a VIF greater than 10, it was removed from the analysis and the statistics
were performed again. The iterative process of analyzing VIFs and removing factors with a VIF
greater than 10 was accomplished until all remaining factors had a VIF less than 10 to ensure no
correlation between factors.
There are three main results interpreted in the research for Binary Logistic Regression.
The first is to determine if the association between the response and the term is statistically
different. It is determined if the response and term are statistically different by comparing the p-
value at a significance level of alpha equals .05 to the null hypothesis. If the p-value is equal to or
less than .05 the association is significantly different and it can be concluded that there is a
statistically significant association between the response variable and the term (Minitab, 2019).
On the contrary, if the p-value is greater than an alpha of .05 it can be concluded that the
association is not statistically significant (Minitab, 2019). There is one distress, distress 76 Alkali
Silica Reactivity, that had a p-value of .063 that was left in the analysis, but it is recognized that
the factor is not significant with 95 percent confidence.
The second result analyzed was the effects of the predictors in terms of an odds ratio. For
continuous predictors, when the odds ratio is greater than 1, the event is more likely to occur as a
predictor increases. When the odds ratio is less than 1, the event is less likely to occur as the
predictor increases (Minitab, 2019). For example, in this research if the odds ratio is 3 for a
50
continuous climate variable, that means a specified pavement distress is 3 times more likely to
occur as that continuous climate variable increases one increment. For categorical predictors, the
odds ratio compares the odds of the event occurring at 2 different levels of the predictor: Level A
and Level B. If the odds ratio is greater than 1, the event at Level A is more likely to occur. If the
odds ratio is less than 1, the event at Level A is less likely to occur (Minitab, 2019).
Qiao, Y., Flintsch, G. W., Dawson, A. R., & Parry, T. (2013). Examining Effects of Climatic
Factors on Flexible Pavement Performance and Service Life. Journal of the
Transportation Research Board, 100-107. doi:10.3141/2349-12
Sahagun, L. (2014). Modeling Pavement Distress Rate within U.S. Air Force Airfield. University
of Nevada, Las Vegas, Las Vegas, NV.
Schwartz, C. W., Elkins, G. E., Li, R., Visintine, B. A., Forman, B., Rada, G. R., & Groeger, J. L.
(2015). Evaluation of Long-Term Pavement Performance (LTPP) Climatic Data for Use
109
in Mechanistic-Empirical Pavement Design Guide (MEPDG) Calibration and Other
Pavement Analysis. Federal Highway Administration.
Schwartz, C. W., Forman, B. A., & Leininger, C. W. (2015). Alternative Source of Climate Data
for Mechanistic-Empirical Pavement Performance Prediction. Transportation Research
Board, 2524(1), 83-91. doi:10.3141/2524-08
Shahin, M. Y. (2005). Pavement Management for Airports, Roads, and Parking Lots Second
Edition. New York: Springer Science + Business Media, Inc.
Shahin, M. Y., Darter, M. I., & Kohn, S. D. (1977). Development of a Pavement Maintenance
Management System Volume 1:Airfield Pavement Condition Rating. Champaign, IL:
Construction Engineering Research Laboratory.
Thompson, M. R., Dempsey, B. J., Hill, H., & Vogel, J. (1987). Characterizing Temperature
Effects for Pavement Analysis and Design. 66th Annual Meeting of The Transportation
Board (pp. 14-22). Washington, DC: Transportation Research Board.
Titus-Glover, L., Darter, M. I., & Von Quintus, H. (2019). Impact of Environmental Factors on
Pavement Performance in the Absence of Heavy Loads. Champaign: Applied Research
Associates, Inc.
U.S. Department of Transportation FHWA. (2018). Long-Term Pavement Performance Climate
Tool User Guide. McLean, VA: U.S. Department of Transportation Federal Highway
Administration.
UFC 3-260-03. (2001). UFC 3-260-03 Airfield Pavement Evaluation. Department Of Defense.
US Army Corps of Engineers. (1984). Engineering Manual 1110-3-138 Pavement Criteria for
Seasonal Frost Conditions. Washington, D.C.: Department of the Army Corps of
Engineers.
110
US Army Corps of Engineers. (2009). Asphalt Surfaced Airfields PAVER Distress Identification
Manual. Champaign, IL: U.S. Army Engineering Research and Development Center -
Construction Engineering Research Laboratory.
US Army Corps of Engineers. (2009). Concrete Surfaced Airfields PAVER Distress Identification
Manual. Champaign, IL: U.S. Army Engineering Research and Development Center -
Construction Engineering Research Laboratory.
US Army Corps of Engineers. (2009). PAVER Distress Identification Manual: Asphalt Surfaced
Airfields. Champaign, IL: U.S. Army Engineering Research and Development Center -
Construction Engineering Research Laboratory.
US Army Corps of Engineers. (2015). PAVER User Manual Version 7.05. Champaign, IL: U.S.
Army Corps of Engineers Engineer Research and Development Center
(ERDC)/Construction Engineering Research Laboratory (CERL).
US Department of Transportation FHWA. (1999). Asset Management Primer. U.S. Department
of Transportation Federal Highway Administration Office of Asset Management.
Vansteenburg, G. (2019, January). PAVER Level 1 Workshop.
APPENDIX A
DETAILED STATISTICAL RESULTS
Distress 63 Linear Cracking
During the first iteration Average Precipitation*Average TEMP_MEAN_AVG (deg C) had a VIF of 25.51 and was removed from the predictor list. During the second iteration, 'Average DAYS_BELOW_0_C' had a VIF of 13.53 and was removed from the predictor list. The third iteration is below.
Method
Link function Logit Categorical predictor coding
(1, 0)
Rows used 2337 Backward Elimination of Terms
Candidate terms: Years Since Major Work Actual, Thickness, Average Precipitation, Average TEMP_MEAN_AVG (deg C), Average FREEZE_INDEX, Average FREEZE_THAW, Average TEMP_MAX, Average TEMP_MIN, Average DAYS_ABOVE_32_C, Feature, Subgrade Strength, Average Precipitation*Average TEMP_MEAN_AVG (deg C), Thickness*Subgrade Strength
------Step 1------ ------Step 2------ Coef P Coef P Constant -2.34 -2.34 Years Since Major Work Actual 0.05678 0.000 0.05678 0.000 Thickness -0.1352 0.006 -0.1353 0.006 Average Precipitation -
0.000452 0.335 -
0.000460 0.010
Average TEMP_MEAN_AVG (deg C) 0.0389 0.401 0.0382 0.197 Average FREEZE_INDEX 0.001423 0.000 0.001420 0.000 Average FREEZE_THAW 0.00290 0.367 0.00289 0.366 Average TEMP_MAX 0.0698 0.024 0.0698 0.024 Average TEMP_MIN 0.0033 0.866 0.0033 0.866 Average DAYS_ABOVE_32_C -0.00598 0.083 -0.00596 0.076 Feature -0.684 0.000 -0.684 0.000 Subgrade Strength -0.755 0.305 -0.755 0.306 Average Precipitation*Average TEMP_MEAN_AVG (deg C)
-0.000001
0.985
112
Thickness*Subgrade Strength 0.0688 0.374 0.0688 0.374 Deviance R-Sq 19.49% 19.49% Deviance R-Sq(adj) 18.99% 19.03% AIC 2631.78 2629.78 AICc 2632.04 2630.01 BIC 2729.64 2721.89 ------Step 3------ ------Step 4------ Coef P Coef P Constant -2.292 -3.042 Years Since Major Work Actual 0.05681 0.000 0.05673 0.000 Thickness -0.1350 0.006 -0.0761 0.000 Average Precipitation -
0.000469 0.006 -
0.000464 0.006
Average TEMP_MEAN_AVG (deg C) 0.0404 0.127 0.0404 0.122 Average FREEZE_INDEX 0.001377 0.000 0.001365 0.000 Average FREEZE_THAW 0.00262 0.344 0.00265 0.338 Average TEMP_MAX 0.0675 0.016 0.0663 0.018 Average TEMP_MIN Average DAYS_ABOVE_32_C -0.00597 0.076 -0.00588 0.079 Feature -0.684 0.000 -0.680 0.000 Subgrade Strength -0.756 0.306 0.435 0.030 Average Precipitation*Average TEMP_MEAN_AVG (deg C)
Thickness*Subgrade Strength 0.0688 0.375 Deviance R-Sq 19.49% 19.43% Deviance R-Sq(adj) 19.06% 19.06% AIC 2627.81 2625.79 AICc 2628.02 2625.95 BIC 2714.16 2700.63 ------Step 5------ ------Step 6------ Coef P Coef P Constant -3.151 -2.873 Years Since Major Work Actual 0.05683 0.000 0.05692 0.000 Thickness -0.0774 0.000 -0.0777 0.000 Average Precipitation -
0.000456 0.007 -
0.000365 0.018
Average TEMP_MEAN_AVG (deg C) 0.0213 0.208 Average FREEZE_INDEX 0.001326 0.000 0.001148 0.000 Average FREEZE_THAW Average TEMP_MAX 0.0827 0.000 0.0798 0.000 Average TEMP_MIN Average DAYS_ABOVE_32_C -0.00716 0.020 -0.00554 0.046 Feature -0.676 0.000 -0.666 0.000 Subgrade Strength 0.440 0.030 0.468 0.014
113
Average Precipitation*Average TEMP_MEAN_AVG (deg C)
α to remove = 0.1 If a term has more than one coefficient, the largest in magnitude is shown.
Response Information
Variable Value Count Unhealthy vs Healthy
1 1256 (Event)
0 1081 Total 2337
Regression Equation
P(1) = exp(Y')/(1 + exp(Y'))
Feature Subgrade Strength
A A Y' = -2.873 + 0.05692 Years Since Major Work Actual - 0.07769 Thickness - 0.000365 Average Precipitation + 0.001148 Average FREEZE_INDEX + 0.07979 Average TEMP_MAX - 0.005542 Average DAYS_ABOVE_32_C
A B Y' = -2.692 + 0.05692 Years Since Major Work Actual
- 0.07769 Thickness - 0.000365 Average Precipitation + 0.001148 Average FREEZE_INDEX + 0.07979 Average TEMP_MAX - 0.005542 Average DAYS_ABOVE_32_C
A C Y' = -2.404 + 0.05692 Years Since Major Work Actual
- 0.07769 Thickness - 0.000365 Average Precipitation + 0.001148 Average FREEZE_INDEX + 0.07979 Average TEMP_MAX - 0.005542 Average DAYS_ABOVE_32_C
114
R A Y' = -3.539 + 0.05692 Years Since Major Work Actual - 0.07769 Thickness - 0.000365 Average Precipitation + 0.001148 Average FREEZE_INDEX + 0.07979 Average TEMP_MAX - 0.005542 Average DAYS_ABOVE_32_C
R B Y' = -3.358 + 0.05692 Years Since Major Work Actual
- 0.07769 Thickness - 0.000365 Average Precipitation + 0.001148 Average FREEZE_INDEX + 0.07979 Average TEMP_MAX - 0.005542 Average DAYS_ABOVE_32_C
R C Y' = -3.071 + 0.05692 Years Since Major Work Actual
- 0.07769 Thickness - 0.000365 Average Precipitation + 0.001148 Average FREEZE_INDEX + 0.07979 Average TEMP_MAX - 0.005542 Average DAYS_ABOVE_32_C
T A Y' = -3.101 + 0.05692 Years Since Major Work Actual
- 0.07769 Thickness - 0.000365 Average Precipitation + 0.001148 Average FREEZE_INDEX + 0.07979 Average TEMP_MAX - 0.005542 Average DAYS_ABOVE_32_C
T B Y' = -2.920 + 0.05692 Years Since Major Work Actual
- 0.07769 Thickness - 0.000365 Average Precipitation + 0.001148 Average FREEZE_INDEX + 0.07979 Average TEMP_MAX - 0.005542 Average DAYS_ABOVE_32_C
T C Y' = -2.632 + 0.05692 Years Since Major Work Actual
- 0.07769 Thickness - 0.000365 Average Precipitation + 0.001148 Average FREEZE_INDEX + 0.07979 Average TEMP_MAX - 0.005542 Average DAYS_ABOVE_32_C
Coefficients
Term Coef SE Coef VIF Constant -2.873 0.730 Years Since Major Work Actual
0.05692 0.00319 1.09
Thickness -0.0777 0.0131 1.12
115
Average Precipitation -0.000365
0.000154 1.45
Average FREEZE_INDEX 0.001148 0.000196 1.48 Average TEMP_MAX 0.0798 0.0220 4.61 Average DAYS_ABOVE_32_C
-0.00554 0.00278 4.79
Feature R -0.666 0.147 1.20 T -0.228 0.107 1.20 Subgrade Strength B 0.181 0.187 3.62 C 0.468 0.203 3.82
Odds Ratios for Continuous Predictors
Odds Ratio 95% CI Years Since Major Work Actual
1.0586 (1.0520, 1.0652)
Thickness 0.9253 (0.9017, 0.9494)
Average Precipitation 0.9996 (0.9993, 0.9999)
Average FREEZE_INDEX 1.0011 (1.0008, 1.0015)
Average TEMP_MAX 1.0831 (1.0374, 1.1307)
Average DAYS_ABOVE_32_C
0.9945 (0.9891, 0.9999)
Odds Ratios for Categorical Predictors
Level A Level B Odds Ratio 95% CI Feature R A 0.5136 (0.3850,
During the first iteration, 'Average DAYS_BELOW_0_C' had a VIF of 111.82 and was removed from the predictor list. The second iteration Average TEMP_MEAN_AVG (deg C) had a VIF of 27.04 and was removed. The third iteration had all predictors with a VIF less than 10 and are below.
Method
Link function Logit Categorical predictor coding
(1, 0)
Rows used 1064 Backward Elimination of Terms
Candidate terms: Thickness, Average Precipitation, Average FREEZE_INDEX, Average FREEZE_THAW, Average TEMP_MAX, Average TEMP_MIN, Average DAYS_ABOVE_32_C, Subgrade Strength, Surface Type - Current, Thickness*Subgrade Strength, Years Since Major Work Actual, Feature
------Step 1----- ------Step 2----- ------Step 3----- Coef P Coef P Coef P Constant 1.17 1.18 1.15 Thickness 0.0987 0.088 0.1116 0.017 0.1123 0.017 Average Precipitation -
0.000068 0.841 -
0.000066 0.847
Average FREEZE_INDEX -0.000460
0.167 -0.000473
0.154 -0.000469
0.156
Average FREEZE_THAW -0.01460 0.002 -0.01461 0.002 -0.01424 0.001 Average TEMP_MAX 0.0146 0.736 0.0127 0.768 0.0105 0.800 Average TEMP_MIN -0.0515 0.013 -0.0517 0.012 -0.0512 0.012 Average DAYS_ABOVE_32_C
-0.00217 0.710 -0.00215 0.711 -0.00163 0.751
Subgrade Strength -0.431 0.702 0.183 0.526 0.182 0.533 Surface Type - Current 0.916 0.001 0.918 0.001 0.921 0.001 Thickness*Subgrade Strength
Thickness 0.1130 0.016 0.1121 0.016 0.1088 0.018 Average Precipitation Average FREEZE_INDEX -
0.000540 0.002 -
0.000527 0.001 -
0.000520 0.002
Average FREEZE_THAW -0.01432 0.001 -0.01408 0.001 -0.01402 0.001 Average TEMP_MAX Average TEMP_MIN -0.0535 0.003 -0.0526 0.003 -0.0527 0.003 Average DAYS_ABOVE_32_C
-0.00064 0.847
Subgrade Strength 0.188 0.535 0.177 0.544 Surface Type - Current 0.925 0.001 0.921 0.001 0.923 0.001 Thickness*Subgrade Strength
α to remove = 0.1 If a term has more than one coefficient, the largest in magnitude is shown.
Response Information
Variable Value Count Unhealthy vs Healthy
1 928 (Event)
0 136 Total 1064
Regression Equation
P(1) = exp(Y')/(1 + exp(Y'))
Surface Type - Current AAC Y' = 1.910 + 0.1125 Thickness
- 0.000544 Average FREEZE_INDEX - 0.01466 Average FREEZE_THAW - 0.05337 Average TEMP_MIN - 0.03185 Years Since Major Work Actual
AC Y' = 2.810 + 0.1125 Thickness
- 0.000544 Average FREEZE_INDEX - 0.01466 Average FREEZE_THAW - 0.05337 Average TEMP_MIN - 0.03185 Years Since Major Work Actual
APC Y' = 2.392 + 0.1125 Thickness
- 0.000544 Average FREEZE_INDEX - 0.01466 Average FREEZE_THAW - 0.05337 Average TEMP_MIN - 0.03185 Years Since Major Work Actual
Coefficients
Term Coef SE Coef VIF Constant 1.910 0.338 Thickness 0.1125 0.0456 1.10 Average FREEZE_INDEX -
0.000544 0.000162 4.45
Average FREEZE_THAW -0.01466 0.00404 2.84 Average TEMP_MIN -0.0534 0.0175 5.87 Surface Type - Current AC 0.899 0.246 1.65 APC 0.482 0.298 1.65 Years Since Major Work Actual
-0.03185 0.00706 1.15
Odds Ratios for Continuous Predictors
122
Odds Ratio 95% CI Thickness 1.1191 (1.0234,
1.2237) Average FREEZE_INDEX 0.9995 (0.9991,
0.9998) Average FREEZE_THAW 0.9855 (0.9777,
0.9933) Average TEMP_MIN 0.9480 (0.9161,
0.9811) Years Since Major Work Actual
0.9687 (0.9553, 0.9821)
Odds Ratios for Categorical Predictors
Level A Level B Odds Ratio 95% CI Surface Type - Current
Wald Test Source DF Chi-Square P-Value Regression 7 67.55 0.000 Thickness 1 6.09 0.014 Average FREEZE_INDEX 1 11.28 0.001 Average FREEZE_THAW 1 13.15 0.000 Average TEMP_MIN 1 9.32 0.002 Surface Type - Current 2 13.71 0.001
123
Years Since Major Work Actual
1 20.36 0.000
124
125
Distress 65 Joint Seal Damage
During the first iteration, Thickness*Subgrade Strength had a VIF of 74.24 and was removed from the predictor list. The second iteration 'Average DAYS_BELOW_0_C' had a VIF of 11.37 and was removed. The third iteration Average TEMP_MEAN_AVG (deg C) had a VIF of 10.30 and was removed. The fourth iteration had all predictors with a VIF less than 10 and are below.
Method
Link function Logit Categorical predictor coding
(1, 0)
Rows used 2337 Backward Elimination of Terms
Candidate terms: Years Since Major Work Actual, Thickness, Average Precipitation, Average FREEZE_INDEX, Average FREEZE_THAW, Average TEMP_MAX, Average TEMP_MIN, Average DAYS_ABOVE_32_C, Subgrade Strength, Feature
------Step 1------ ------Step 2------ ------Step 3------ Coef P Coef P Coef P Constant 1.127 1.134 1.710 Years Since Major Work Actual
0.05287 0.000 0.05288 0.000 0.05284 0.000
Thickness -0.0121 0.437 -0.0121 0.437 -0.0100 0.514 Average Precipitation 0.000009 0.961 Average FREEZE_INDEX -
0.000684 0.079 -
0.000690 0.064 -
0.000787 0.020
Average FREEZE_THAW -0.01358 0.000 -0.01364 0.000 -0.01351 0.000 Average TEMP_MAX 0.0200 0.532 0.0202 0.526 Average TEMP_MIN -0.0523 0.012 -0.0524 0.011 -0.0564 0.004 Average DAYS_ABOVE_32_C
-0.00998 0.015 -0.01006 0.007 -0.00802 0.000
Subgrade Strength -0.494 0.145 -0.494 0.145 -0.475 0.166 Feature -0.549 0.000 -0.549 0.000 -0.534 0.000 Deviance R-Sq 11.98% 11.98% 11.96% Deviance R-Sq(adj) 11.45% 11.49% 11.52% AIC 2016.02 2014.02 2012.42 AICc 2016.18 2014.16 2012.54 BIC 2090.86 2083.10 2075.75 ------Step 4------ ------Step 5------ Coef P Coef P Constant 1.584 1.249 Years Since Major Work Actual
0.05299 0.000 0.05196 0.000
Thickness
126
Average Precipitation Average FREEZE_INDEX -
0.000783 0.021 -
0.000766 0.024
Average FREEZE_THAW -0.01351 0.000 -0.01357 0.000 Average TEMP_MAX Average TEMP_MIN -0.0560 0.004 -0.0576 0.003 Average DAYS_ABOVE_32_C
Wald Test Source DF Chi-Square P-Value Regression 7 195.09 0.000 Years Since Major Work Actual
1 139.68 0.000
Average FREEZE_INDEX 1 5.11 0.024 Average FREEZE_THAW 1 16.94 0.000 Average TEMP_MIN 1 8.72 0.003 Average DAYS_ABOVE_32_C
1 22.05 0.000
Feature 2 20.19 0.000
129
130
Distress 57 Weathering
During the first iteration, Average TEMP_MEAN_AVG (deg C) had a VIF of 78.51 and was removed from the predictor list. The second iteration Average 'Average DAYS_BELOW_0_C' had a VIF of 11.02 and was removed. The third iteration had all predictors with a VIF less than 10 and are below.
Method
Link function Logit Categorical predictor coding
(1, 0)
Rows used 1064 Backward Elimination of Terms
Candidate terms: Years Since Major Work Actually, Thickness, Average Precipitation, Average FREEZE_INDEX, Average FREEZE_THAW, Average TEMP_MAX, Average TEMP_MIN, Average DAYS_ABOVE_32_C, Subgrade Strength, Surface Type - Current, Feature, Thickness*Subgrade Strength
------Step 1----- ------Step 2----- ------Step 3----- Coef P Coef P Coef P Constant 1.53 1.48 1.63 Years Since Major Work Actually
-0.0053 0.628 -0.0056 0.612 -0.0056 0.612
Thickness 0.179 0.099 0.2114 0.012 0.2058 0.013 Average Precipitation -
0.001478 0.004 -
0.001467 0.004 -
0.001461 0.004
Average FREEZE_INDEX -0.000543
0.284 -0.000544
0.280 -0.000570
0.253
Average FREEZE_THAW -0.01923 0.005 -0.01909 0.005 -0.01899 0.005 Average TEMP_MAX 0.0845 0.236 0.0825 0.244 0.0765 0.270 Average TEMP_MIN -0.0561 0.076 -0.0558 0.078 -0.0561 0.076 Average DAYS_ABOVE_32_C
Wald Test Source DF Chi-Square P-Value Regression 6 29.48 0.000 Thickness 1 8.17 0.004 Average Precipitation 1 7.87 0.005 Average FREEZE_INDEX
1 21.18 0.000
Average FREEZE_THAW
1 9.26 0.002
Average TEMP_MIN 1 8.23 0.004 Average DAYS_ABOVE_32_C
1 4.96 0.026
134
135
Distress 43 Block Cracking
The first iteration had all predictors with a VIF less than 10 and are below.
Method
Link function Logit Categorical predictor coding
(1, 0)
Rows used 1064 Backward Elimination of Terms
Candidate terms: Thickness, Average Precipitation, Average TEMP_MEAN_AVG (deg C), Average FREEZE_INDEX, Average FREEZE_THAW, Average TEMP_MAX, Average TEMP_MIN, Average DAYS_ABOVE_32_C, Average DAYS_BELOW_0_C, Feature, Subgrade Strength, Surface Type - Current, Average Precipitation*Average TEMP_MEAN_AVG (deg C), Thickness*Subgrade Strength, Years Since Major Work Actual
------Step 1------ ------Step 2----- Coef P Coef P Constant -3.46 -3.06 Thickness 0.0300 0.263 0.0293 0.274 Average Precipitation 0.001158 0.207 0.000785 0.031 Average TEMP_MEAN_AVG (deg C) 0.0610 0.458 0.0381 0.556 Average FREEZE_INDEX 0.000638 0.265 0.000593 0.293 Average FREEZE_THAW 0.0126 0.357 0.0135 0.323 Average TEMP_MAX -0.0447 0.525 -0.0467 0.507 Average TEMP_MIN -0.0487 0.241 -0.0530 0.194 Average DAYS_ABOVE_32_C 0.00930 0.056 0.00973 0.044 Average DAYS_BELOW_0_C -0.0076 0.553 -0.0088 0.489 Feature -0.344 0.418 -0.337 0.433 Subgrade Strength 0.857 0.414 0.852 0.421 Surface Type - Current -0.731 0.055 -0.714 0.059 Average Precipitation*Average TEMP_MEAN_AVG (deg C)
-0.000024 0.657
Thickness*Subgrade Strength -0.270 0.229 -0.266 0.239 Years Since Major Work Actual 0.07544 0.000 0.07501 0.000 Deviance R-Sq 17.89% 17.87% Deviance R-Sq(adj) 16.23% 16.30% AIC 980.84 979.03 AICc 981.65 979.76 BIC 1080.2
4 1073.4
6 ------Step 3----- ------Step 4----- Coef P Coef P
136
Constant -3.44 -3.929 Thickness 0.0293 0.274 0.0290 0.278 Average Precipitation 0.000882 0.007 0.000870 0.007 Average TEMP_MEAN_AVG (deg C) Average FREEZE_INDEX 0.000479 0.365 0.000436 0.396 Average FREEZE_THAW 0.0095 0.420 0.00700 0.452 Average TEMP_MAX -0.0164 0.730 Average TEMP_MIN -0.0350 0.191 -0.0284 0.127 Average DAYS_ABOVE_32_C 0.00928 0.053 0.00806 0.012 Average DAYS_BELOW_0_C -0.0058 0.614 -0.00310 0.714 Feature -0.348 0.405 -0.355 0.387 Subgrade Strength 0.877 0.403 0.858 0.415 Surface Type - Current -0.710 0.061 -0.699 0.063 Average Precipitation*Average TEMP_MEAN_AVG (deg C)
Thickness*Subgrade Strength -0.273 0.220 -0.273 0.218 Years Since Major Work Actual 0.07435 0.000 0.07428 0.000 Deviance R-Sq 17.84% 17.83% Deviance R-Sq(adj) 16.36% 16.44% AIC 977.39 975.50 AICc 978.04 976.09 BIC 1066.8
4 1059.99
------Step 5----- ------Step 6----- Coef P Coef P Constant -3.976 -4.199 Thickness 0.0290 0.279 0.0269 0.312 Average Precipitation 0.000896 0.004 0.000884 0.005 Average TEMP_MEAN_AVG (deg C) Average FREEZE_INDEX 0.000262 0.187 0.000260 0.187 Average FREEZE_THAW 0.00394 0.342 0.00429 0.298 Average TEMP_MAX Average TEMP_MIN -0.0266 0.139 -0.0273 0.126 Average DAYS_ABOVE_32_C 0.00843 0.006 0.00773 0.010 Average DAYS_BELOW_0_C Feature -0.350 0.396 Subgrade Strength 0.869 0.408 0.957 0.337 Surface Type - Current -0.698 0.063 -0.703 0.062 Average Precipitation*Average TEMP_MEAN_AVG (deg C)
Thickness*Subgrade Strength -0.276 0.212 -0.293 0.173 Years Since Major Work Actual 0.07439 0.000 0.07797 0.000 Deviance R-Sq 17.82% 17.66% Deviance R-Sq(adj) 16.51% 16.52% AIC 973.64 971.50
137
AICc 974.16 971.90 BIC 1053.1
6 1041.08
------Step 7----- ------Step 8----- Coef P Coef P Constant -3.909 -3.860 Thickness 0.0275 0.301 0.0264 0.320 Average Precipitation 0.000766 0.009 0.000709 0.013 Average TEMP_MEAN_AVG (deg C) Average FREEZE_INDEX 0.000105 0.417 Average FREEZE_THAW Average TEMP_MAX Average TEMP_MIN -0.0414 0.000 -0.04750 0.000 Average DAYS_ABOVE_32_C 0.00629 0.017 0.00592 0.024 Average DAYS_BELOW_0_C Feature Subgrade Strength 0.963 0.332 0.941 0.349 Surface Type - Current -0.731 0.046 -0.798 0.018 Average Precipitation*Average TEMP_MEAN_AVG (deg C)
Thickness*Subgrade Strength -0.290 0.172 -0.287 0.172 Years Since Major Work Actual 0.07813 0.000 0.07957 0.000 Deviance R-Sq 17.56% 17.51% Deviance R-Sq(adj) 16.52% 16.55% AIC 970.58 969.23 AICc 970.92 969.53 BIC 1035.1
8 1028.87
------Step 9----- -----Step 10----- Coef P Coef P Constant -3.884 -3.874 Thickness 0.0229 0.328 0.0217 0.355 Average Precipitation 0.000720 0.011 0.000723 0.010 Average TEMP_MEAN_AVG (deg C) Average FREEZE_INDEX Average FREEZE_THAW Average TEMP_MAX Average TEMP_MIN -0.04843 0.000 -0.04869 0.000 Average DAYS_ABOVE_32_C 0.00644 0.013 0.00670 0.007 Average DAYS_BELOW_0_C Feature Subgrade Strength -0.193 0.604 Surface Type - Current -0.798 0.015 -0.810 0.011 Average Precipitation*Average TEMP_MEAN_AVG (deg C)
Thickness*Subgrade Strength
138
Years Since Major Work Actual 0.08052 0.000 0.08045 0.000 Deviance R-Sq 17.10% 17.01% Deviance R-Sq(adj) 16.32% 16.40% AIC 969.87 966.90 AICc 970.08 967.03 BIC 1019.5
7 1006.66
-----Step 11----- Coef P Constant -3.757 Thickness Average Precipitation 0.000699 0.013 Average TEMP_MEAN_AVG (deg C) Average FREEZE_INDEX Average FREEZE_THAW Average TEMP_MAX Average TEMP_MIN -0.04882 0.000 Average DAYS_ABOVE_32_C 0.00673 0.007 Average DAYS_BELOW_0_C Feature Subgrade Strength Surface Type - Current -0.818 0.011 Average Precipitation*Average TEMP_MEAN_AVG (deg C)
Thickness*Subgrade Strength Years Since Major Work Actual 0.07966 0.000 Deviance R-Sq 16.94% Deviance R-Sq(adj) 16.42% AIC 965.72 AICc 965.82 BIC 1000.50
α to remove = 0.1 If a term has more than one coefficient, the largest in magnitude is shown.
Response Information
Variable Value Count Unhealthy vs Healthy
1 244 (Event)
0 820 Total 1064
Regression Equation
P(1) = exp(Y')/(1 + exp(Y'))
139
Surface Type - Current AAC Y' = -3.757 + 0.000699 Average Precipitation
- 0.04882 Average TEMP_MIN + 0.006727 Average DAYS_ABOVE_32_C + 0.07966 Years Since Major Work Actual
AC Y' = -4.189 + 0.000699 Average Precipitation
- 0.04882 Average TEMP_MIN + 0.006727 Average DAYS_ABOVE_32_C + 0.07966 Years Since Major Work Actual
APC Y' = -4.574 + 0.000699 Average Precipitation
- 0.04882 Average TEMP_MIN + 0.006727 Average DAYS_ABOVE_32_C + 0.07966 Years Since Major Work Actual
Coefficients
Term Coef SE Coef VIF Constant -3.757 0.454 Average Precipitation 0.000699 0.000280 1.54 Average TEMP_MIN -0.04882 0.00895 1.85 Average DAYS_ABOVE_32_C
0.00673 0.00250 1.51
Surface Type - Current AC -0.433 0.212 1.58 APC -0.818 0.275 1.58 Years Since Major Work Actual
0.07966 0.00684 1.06
Odds Ratios for Continuous Predictors
Odds Ratio 95% CI Average Precipitation 1.0007 (1.0001,
1.0012) Average TEMP_MIN 0.9524 (0.9358,
0.9692) Average DAYS_ABOVE_32_C
1.0067 (1.0018, 1.0117)
Years Since Major Work Actual
1.0829 (1.0685, 1.0975)
Odds Ratios for Categorical Predictors
Level A Level B Odds Ratio 95% CI Surface Type - Current
Wald Test Source DF Chi-Square P-Value Regression 6 151.88 0.000 Average Precipitation 1 6.22 0.013 Average TEMP_MIN 1 29.75 0.000 Average DAYS_ABOVE_32_C
1 7.23 0.007
Surface Type - Current 2 8.99 0.011 Years Since Major Work Actual
1 135.55 0.000
141
142
143
Distress 67 Large Patch/Utility Cut
During the first iteration, Average Precipitation*Average TEMP_MEAN_AVG (deg C) had a VIF of 26.13 and was removed from the predictor list. The second iteration 'Average DAYS_BELOW_0_C' had a VIF of 13.24 and was removed. The third iteration had all predictors with a VIF less than 10 and are below.
Method
Link function Logit Categorical predictor coding
(1, 0)
Rows used 2337 Backward Elimination of Terms
Candidate terms: Years Since Major Work Actual, Thickness, Average Precipitation, Average TEMP_MEAN_AVG (deg C), Average FREEZE_INDEX, Average FREEZE_THAW, Average TEMP_MAX, Average TEMP_MIN, Average DAYS_ABOVE_32_C, Feature, Subgrade Strength, Thickness*Subgrade Strength
------Step 1------ ------Step 2------ ------Step 3----- Coef P Coef P Coef P Constant -2.029 -1.971 -2.092 Years Since Major Work Actual 0.04506 0.000 0.04502 0.000 0.04500 0.000 Thickness 0.0429 0.389 0.0433 0.384 0.0432 0.385 Average Precipitation -0.000066 0.698 -
0 ------Step 4----- ------Step 5----- ------Step 6----- Coef P Coef P Coef P
144
Constant -1.558 -1.557 -1.430 Years Since Major Work Actual 0.04499 0.000 0.04498 0.000 0.04515 0.000 Thickness 0.0002 0.989 Average Precipitation Average TEMP_MEAN_AVG (deg C)
α to remove = 0.1 If a term has more than one coefficient, the largest in magnitude is shown.
Response Information
Variable Value Count Unhealthy vs Healthy
1 1102 (Event)
0 1235 Total 2337
Regression Equation
P(1) = exp(Y')/(1 + exp(Y'))
Feature Subgrade Strength
A A Y' = -1.430 + 0.04515 Years Since Major Work Actual + 0.04758 Average TEMP_MEAN_AVG (deg C) + 0.000731 Average FREEZE_INDEX + 0.004798 Average FREEZE_THAW - 0.03638 Average TEMP_MAX
A B Y' = -1.137 + 0.04515 Years Since Major Work Actual
+ 0.04758 Average TEMP_MEAN_AVG (deg C) + 0.000731 Average FREEZE_INDEX
145
+ 0.004798 Average FREEZE_THAW - 0.03638 Average TEMP_MAX
A C Y' = -0.8418 + 0.04515 Years Since Major Work Actual
+ 0.04758 Average TEMP_MEAN_AVG (deg C) + 0.000731 Average FREEZE_INDEX + 0.004798 Average FREEZE_THAW - 0.03638 Average TEMP_MAX
R A Y' = -1.770 + 0.04515 Years Since Major Work Actual
+ 0.04758 Average TEMP_MEAN_AVG (deg C) + 0.000731 Average FREEZE_INDEX + 0.004798 Average FREEZE_THAW - 0.03638 Average TEMP_MAX
R B Y' = -1.477 + 0.04515 Years Since Major Work Actual
+ 0.04758 Average TEMP_MEAN_AVG (deg C) + 0.000731 Average FREEZE_INDEX + 0.004798 Average FREEZE_THAW - 0.03638 Average TEMP_MAX
R C Y' = -1.182 + 0.04515 Years Since Major Work Actual
+ 0.04758 Average TEMP_MEAN_AVG (deg C) + 0.000731 Average FREEZE_INDEX + 0.004798 Average FREEZE_THAW - 0.03638 Average TEMP_MAX
T A Y' = -1.446 + 0.04515 Years Since Major Work Actual
+ 0.04758 Average TEMP_MEAN_AVG (deg C) + 0.000731 Average FREEZE_INDEX + 0.004798 Average FREEZE_THAW - 0.03638 Average TEMP_MAX
T B Y' = -1.152 + 0.04515 Years Since Major Work Actual
+ 0.04758 Average TEMP_MEAN_AVG (deg C) + 0.000731 Average FREEZE_INDEX + 0.004798 Average FREEZE_THAW - 0.03638 Average TEMP_MAX
T C Y' = -0.8576 + 0.04515 Years Since Major Work Actual
+ 0.04758 Average TEMP_MEAN_AVG (deg C) + 0.000731 Average FREEZE_INDEX + 0.004798 Average FREEZE_THAW - 0.03638 Average TEMP_MAX
Coefficients
Term Coef SE Coef VIF Constant -1.430 0.452 Years Since Major Work Actual 0.04515 0.00275 1.09
146
Average TEMP_MEAN_AVG (deg C)
0.0476 0.0230 7.17
Average FREEZE_INDEX 0.000731 0.000206 2.37 Average FREEZE_THAW 0.00480 0.00230 3.67 Average TEMP_MAX -0.0364 0.0130 1.84 Feature R -0.340 0.141 1.19 T -0.016 0.101 1.16 Subgrade Strength B 0.293 0.186 4.00 C 0.588 0.201 4.27
Odds Ratios for Continuous Predictors
Odds Ratio 95% CI Years Since Major Work Actual 1.0462 (1.0405,
1.0518) Average TEMP_MEAN_AVG (deg C)
1.0487 (1.0025, 1.0971)
Average FREEZE_INDEX 1.0007 (1.0003, 1.0011)
Average FREEZE_THAW 1.0048 (1.0003, 1.0093)
Average TEMP_MAX 0.9643 (0.9400, 0.9891)
Odds Ratios for Categorical Predictors
Level A Level B Odds Ratio 95% CI Feature R A 0.7115 (0.5393,
Wald Test Source DF Chi-Square P-Value Regression 9 332.45 0.000 Years Since Major Work Actual
1 268.65 0.000
Average TEMP_MEAN_AVG (deg C)
1 4.27 0.039
Average FREEZE_INDEX 1 12.54 0.000 Average FREEZE_THAW 1 4.36 0.037 Average TEMP_MAX 1 7.85 0.005 Feature 2 6.32 0.042 Subgrade Strength 2 11.67 0.003
148
149
Distress 72 Shattered Slab
During the first iteration had all predictors with a VIF less than 10 and are below.
Method
Link function Logit Categorical predictor coding
(1, 0)
Rows used 2337 Backward Elimination of Terms
Candidate terms: Years Since Major Work Actual, Thickness, Average Precipitation, Average TEMP_MEAN_AVG (deg C), Average FREEZE_INDEX, Average FREEZE_THAW, Average TEMP_MAX, Average TEMP_MIN, Average DAYS_ABOVE_32_C, Average DAYS_BELOW_0_C, Feature, Subgrade Strength, Average Precipitation*Average TEMP_MEAN_AVG (deg C), Thickness*Subgrade Strength
------Step 1------ ------Step 2------ Coef P Coef P Constant -10.59 -10.81 Years Since Major Work Actual 0.05172 0.000 0.05176 0.000 Thickness -0.1381 0.146 -0.1208 0.000 Average Precipitation -
0.001443 0.071 -
0.001451 0.069
Average TEMP_MEAN_AVG (deg C) -0.0257 0.712 -0.0239 0.731 Average FREEZE_INDEX -
0.001918 0.054 -
0.001905 0.055
Average FREEZE_THAW -0.0485 0.001 -0.0483 0.001 Average TEMP_MAX 0.2860 0.000 0.2851 0.000 Average TEMP_MIN -0.0141 0.658 -0.0145 0.649 Average DAYS_ABOVE_32_C -0.02486 0.000 -0.02482 0.000 Average DAYS_BELOW_0_C 0.0419 0.002 0.0418 0.002 Feature -1.627 0.000 -1.630 0.000 Subgrade Strength 0.46 0.506 0.594 0.028 Average Precipitation*Average TEMP_MEAN_AVG (deg C)
------Step 3------ ------Step 4------ Coef P Coef P Constant -11.05 -11.85 Years Since Major Work Actual 0.05168 0.000 0.05197 0.000 Thickness -0.1213 0.000 -0.1194 0.000 Average Precipitation -
0.001335 0.074 -
0.000472 0.074
Average TEMP_MEAN_AVG (deg C) -0.0267 0.698 0.0405 0.320 Average FREEZE_INDEX -
0.001735 0.057 -
0.001353 0.110
Average FREEZE_THAW -0.0470 0.001 -0.0439 0.002 Average TEMP_MAX 0.2924 0.000 0.2870 0.000 Average TEMP_MIN Average DAYS_ABOVE_32_C -0.02477 0.000 -0.02605 0.000 Average DAYS_BELOW_0_C 0.0421 0.001 0.0395 0.002 Feature -1.626 0.000 -1.601 0.000 Subgrade Strength 0.598 0.027 0.592 0.032 Average Precipitation*Average TEMP_MEAN_AVG (deg C)
------Step 5------ ------Step 6------ Coef P Coef P Constant -11.35 -11.77 Years Since Major Work Actual 0.05149 0.000 0.05136 0.000 Thickness -0.1202 0.000 -0.1220 0.000 Average Precipitation -
0.000375 0.127
Average TEMP_MEAN_AVG (deg C) Average FREEZE_INDEX -
0.001361 0.104 -
0.001273 0.122
Average FREEZE_THAW -0.0431 0.002 -0.0426 0.002 Average TEMP_MAX 0.2928 0.000 0.2912 0.000 Average TEMP_MIN Average DAYS_ABOVE_32_C -0.02528 0.000 -0.02267 0.000 Average DAYS_BELOW_0_C 0.0362 0.003 0.0367 0.003 Feature -1.597 0.000 -1.582 0.000 Subgrade Strength 0.580 0.028 0.534 0.037
151
Average Precipitation*Average TEMP_MEAN_AVG (deg C)
------Step 7----- Coef P Constant -11.12 Years Since Major Work Actual 0.05119 0.000 Thickness -0.1204 0.000 Average Precipitation Average TEMP_MEAN_AVG (deg C) Average FREEZE_INDEX Average FREEZE_THAW -0.02260 0.000 Average TEMP_MAX 0.2713 0.000 Average TEMP_MIN Average DAYS_ABOVE_32_C -0.02129 0.000 Average DAYS_BELOW_0_C 0.01833 0.000 Feature -1.588 0.000 Subgrade Strength 0.511 0.043 Average Precipitation*Average TEMP_MEAN_AVG (deg C)
α to remove = 0.1 If a term has more than one coefficient, the largest in magnitude is shown.
Response Information
Variable Value Count Unhealthy vs Healthy
1 294 (Event)
0 2043
152
Total 2337 Regression Equation
P(1) = exp(Y')/(1 + exp(Y'))
Feature Subgrade Strength
A A Y' = -11.12 + 0.05119 Years Since Major Work Actual - 0.1204 Thickness - 0.02260 Average FREEZE_THAW + 0.2713 Average TEMP_MAX - 0.02129 Average DAYS_ABOVE_32_C + 0.01833 Average DAYS_BELOW_0_C
A B Y' = -10.97 + 0.05119 Years Since Major Work Actual
- 0.1204 Thickness - 0.02260 Average FREEZE_THAW + 0.2713 Average TEMP_MAX - 0.02129 Average DAYS_ABOVE_32_C + 0.01833 Average DAYS_BELOW_0_C
A C Y' = -10.61 + 0.05119 Years Since Major Work Actual
- 0.1204 Thickness - 0.02260 Average FREEZE_THAW + 0.2713 Average TEMP_MAX - 0.02129 Average DAYS_ABOVE_32_C + 0.01833 Average DAYS_BELOW_0_C
R A Y' = -12.70 + 0.05119 Years Since Major Work Actual
- 0.1204 Thickness - 0.02260 Average FREEZE_THAW + 0.2713 Average TEMP_MAX - 0.02129 Average DAYS_ABOVE_32_C + 0.01833 Average DAYS_BELOW_0_C
R B Y' = -12.56 + 0.05119 Years Since Major Work Actual
- 0.1204 Thickness - 0.02260 Average FREEZE_THAW + 0.2713 Average TEMP_MAX - 0.02129 Average DAYS_ABOVE_32_C + 0.01833 Average DAYS_BELOW_0_C
R C Y' = -12.19 + 0.05119 Years Since Major Work Actual
- 0.1204 Thickness - 0.02260 Average FREEZE_THAW + 0.2713 Average TEMP_MAX - 0.02129 Average DAYS_ABOVE_32_C + 0.01833 Average DAYS_BELOW_0_C
153
T A Y' = -12.08 + 0.05119 Years Since Major Work Actual - 0.1204 Thickness - 0.02260 Average FREEZE_THAW + 0.2713 Average TEMP_MAX - 0.02129 Average DAYS_ABOVE_32_C + 0.01833 Average DAYS_BELOW_0_C
T B Y' = -11.93 + 0.05119 Years Since Major Work Actual
- 0.1204 Thickness - 0.02260 Average FREEZE_THAW + 0.2713 Average TEMP_MAX - 0.02129 Average DAYS_ABOVE_32_C + 0.01833 Average DAYS_BELOW_0_C
T C Y' = -11.56 + 0.05119 Years Since Major Work Actual
- 0.1204 Thickness - 0.02260 Average FREEZE_THAW + 0.2713 Average TEMP_MAX - 0.02129 Average DAYS_ABOVE_32_C + 0.01833 Average DAYS_BELOW_0_C
Coefficients
Term Coef SE Coef VIF Constant -11.12 1.33 Years Since Major Work Actual
0.05119 0.00392 1.12
Thickness -0.1204 0.0189 1.13 Average FREEZE_THAW -
0.02260 0.00506 7.27
Average TEMP_MAX 0.2713 0.0417 7.85 Average DAYS_ABOVE_32_C
-0.02129
0.00471 7.19
Average DAYS_BELOW_0_C
0.01833 0.00331 7.20
Feature R -1.588 0.314 1.06 T -0.959 0.169 1.08 Subgrade Strength B 0.142 0.347 5.99 C 0.511 0.355 6.27
Odds Ratios for Continuous Predictors
Odds Ratio 95% CI Years Since Major Work Actual
1.0525 (1.0445, 1.0606)
Thickness 0.8866 (0.8544, 0.9200)
Average FREEZE_THAW 0.9777 (0.9680, 0.9874)
154
Average TEMP_MAX 1.3116 (1.2087, 1.4233)
Average DAYS_ABOVE_32_C
0.9789 (0.9699, 0.9880)
Average DAYS_BELOW_0_C
1.0185 (1.0119, 1.0251)
Odds Ratios for Categorical Predictors
Level A Level B Odds Ratio 95% CI Feature R A 0.2044 (0.1105,
The first iteration had all predictors with a VIF less than 10 and are below.
Method
Link function Logit Categorical predictor coding
(1, 0)
Rows used 2337 Backward Elimination of Terms
Candidate terms: Years Since Major Work Actual, Thickness, Average Precipitation, Average TEMP_MEAN_AVG (deg C), Average FREEZE_INDEX, Average FREEZE_THAW, Average TEMP_MAX, Average TEMP_MIN, Average DAYS_ABOVE_32_C, Average DAYS_BELOW_0_C, Feature, Subgrade Strength, Average Precipitation*Average TEMP_MEAN_AVG (deg C), Thickness*Subgrade Strength
------Step 1------ ------Step 2------ Coef P Coef P Constant -1.08 -1.357 Years Since Major Work Actual 0.01109 0.000 0.01107 0.000 Thickness -0.0611 0.204 -0.0393 0.003 Average Precipitation 0.000593 0.226 0.000601 0.220 Average TEMP_MEAN_AVG (deg C) -0.0588 0.216 -0.0603 0.203 Average FREEZE_INDEX -0.000179 0.797 -
0.000203 0.770
Average FREEZE_THAW -0.01586 0.108 -0.01617 0.100 Average TEMP_MAX 0.1089 0.002 0.1089 0.002 Average TEMP_MIN 0.0275 0.171 0.0278 0.166 Average DAYS_ABOVE_32_C -0.00323 0.377 -0.00316 0.387 Average DAYS_BELOW_0_C 0.00836 0.328 0.00860 0.313 Feature -0.146 0.309 -0.146 0.304 Subgrade Strength -0.165 0.852 0.468 0.006 Average Precipitation*Average TEMP_MEAN_AVG (deg C)
Coef P Coef P Constant -1.361 -0.798 Years Since Major Work Actual 0.01106 0.000 0.01071 0.000 Thickness -0.0394 0.002 -0.0387 0.003 Average Precipitation 0.000654 0.149 0.000634 0.161 Average TEMP_MEAN_AVG (deg C) -0.0572 0.216 -0.0595 0.195 Average FREEZE_INDEX Average FREEZE_THAW -0.01360 0.002 -0.01202 0.002 Average TEMP_MAX 0.1072 0.002 0.0863 0.000 Average TEMP_MIN 0.0294 0.127 0.0278 0.144 Average DAYS_ABOVE_32_C -0.00299 0.406 Average DAYS_BELOW_0_C 0.00645 0.130 0.00583 0.164 Feature -0.146 0.305 -0.141 0.317 Subgrade Strength 0.466 0.006 0.465 0.005 Average Precipitation*Average TEMP_MEAN_AVG (deg C)
5 ------Step 5----- ------Step 6----- Coef P Coef P Constant -0.508 -0.487 Years Since Major Work Actual 0.01059 0.000 0.01061 0.000 Thickness -0.0398 0.002 -0.0418 0.001 Average Precipitation 0.000249 0.136 0.000236 0.157 Average TEMP_MEAN_AVG (deg C) -0.0908 0.003 -0.0905 0.003 Average FREEZE_INDEX Average FREEZE_THAW -0.01127 0.003 -0.01139 0.003 Average TEMP_MAX 0.0920 0.000 0.0910 0.000 Average TEMP_MIN 0.0295 0.120 0.0292 0.123 Average DAYS_ABOVE_32_C Average DAYS_BELOW_0_C 0.00498 0.221 0.00509 0.211 Feature -0.142 0.319 Subgrade Strength 0.466 0.005 0.469 0.004 Average Precipitation*Average TEMP_MEAN_AVG (deg C)
------Step 7----- ------Step 8----- Coef P Coef P Constant 0.010 0.022 Years Since Major Work Actual 0.01080 0.000 0.01095 0.000 Thickness -0.0408 0.001 -0.0404 0.002 Average Precipitation 0.000187 0.244 0.000155 0.321 Average TEMP_MEAN_AVG (deg C) -0.0900 0.003 -0.0699 0.001 Average FREEZE_INDEX Average FREEZE_THAW -0.00782 0.002 -0.00828 0.001 Average TEMP_MAX 0.0778 0.000 0.0671 0.000 Average TEMP_MIN 0.0127 0.343 Average DAYS_ABOVE_32_C Average DAYS_BELOW_0_C Feature Subgrade Strength 0.462 0.003 0.458 0.003 Average Precipitation*Average TEMP_MEAN_AVG (deg C)
6 ------Step 9----- Coef P Constant 0.261 Years Since Major Work Actual 0.01087 0.000 Thickness -0.0391 0.002 Average Precipitation Average TEMP_MEAN_AVG (deg C) -0.0603 0.002 Average FREEZE_INDEX Average FREEZE_THAW -0.00774 0.001 Average TEMP_MAX 0.0593 0.000 Average TEMP_MIN Average DAYS_ABOVE_32_C Average DAYS_BELOW_0_C Feature
160
Subgrade Strength 0.467 0.003 Average Precipitation*Average TEMP_MEAN_AVG (deg C)
α to remove = 0.1 If a term has more than one coefficient, the largest in magnitude is shown.
Response Information
Variable Value Count Unhealthy vs Healthy
1 1719 (Event)
0 618 Total 2337
Regression Equation
P(1) = exp(Y')/(1 + exp(Y'))
Subgrade Strength A Y' = 0.2611 + 0.01087 Years Since Major Work Actual - 0.03912 Thickness
- 0.06033 Average TEMP_MEAN_AVG (deg C) - 0.007736 Average FREEZE_THAW + 0.05930 Average TEMP_MAX
B Y' = 0.3477 + 0.01087 Years Since Major Work Actual - 0.03912 Thickness
- 0.06033 Average TEMP_MEAN_AVG (deg C) - 0.007736 Average FREEZE_THAW + 0.05930 Average TEMP_MAX
C Y' = 0.7279 + 0.01087 Years Since Major Work Actual - 0.03912 Thickness
- 0.06033 Average TEMP_MEAN_AVG (deg C) - 0.007736 Average FREEZE_THAW + 0.05930 Average TEMP_MAX
Coefficients
Term Coef SE Coef VIF Constant 0.261 0.417 Years Since Major Work Actual 0.01087 0.00276 1.06 Thickness -0.0391 0.0127 1.07 Average TEMP_MEAN_AVG (deg C)
-0.0603 0.0194 4.58
161
Average FREEZE_THAW -0.00774
0.00240 3.54
Average TEMP_MAX 0.0593 0.0143 1.95 Subgrade Strength B 0.087 0.181 3.23 C 0.467 0.202 3.44
Odds Ratios for Continuous Predictors
Odds Ratio 95% CI Years Since Major Work Actual 1.0109 (1.0055,
1.0164) Thickness 0.9616 (0.9380,
0.9859) Average TEMP_MEAN_AVG (deg C)
0.9415 (0.9064, 0.9779)
Average FREEZE_THAW 0.9923 (0.9876, 0.9970)
Average TEMP_MAX 1.0611 (1.0317, 1.0913)
Odds Ratios for Categorical Predictors
Level A Level B Odds Ratio 95% CI Subgrade Strength
Wald Test Source DF Chi-Square P-Value Regression 7 67.34 0.000
162
Years Since Major Work Actual
1 15.49 0.000
Thickness 1 9.48 0.002 Average TEMP_MEAN_AVG (deg C)
1 9.71 0.002
Average FREEZE_THAW 1 10.39 0.001 Average TEMP_MAX 1 17.14 0.000 Subgrade Strength 2 11.54 0.003
163
164
Distress 66 Small Patch
During the first iteration, Average Precipitation*Average TEMP_MEAN_AVG (deg C) had a VIF of 23.72 and was removed from the predictor list. The second iteration had all predictors with a VIF less than 10 and are below.
Method
Link function Logit Categorical predictor coding
(1, 0)
Rows used 2337 Backward Elimination of Terms
Candidate terms: Years Since Major Work Actual, Thickness, Average Precipitation, Average TEMP_MEAN_AVG (deg C), Average FREEZE_INDEX, Average FREEZE_THAW, Average TEMP_MAX, Average TEMP_MIN, Average DAYS_ABOVE_32_C, Average DAYS_BELOW_0_C, Feature, Subgrade Strength, Thickness*Subgrade Strength
------Step 1------ ------Step 2------ ------Step 3------ Coef P Coef P Coef P Constant 0.87 1.01 0.643 Years Since Major Work Actual 0.03129 0.000 0.03128 0.000 0.03130 0.000 Thickness 0.0578 0.309 0.0573 0.313 0.0551 0.332 Average Precipitation -
Wald Test Source DF Chi-Square P-Value Regression 6 115.79 0.000 Years Since Major Work Actual
1 95.42 0.000
Thickness 1 9.17 0.002 Average Precipitation 1 14.21 0.000 Average DAYS_ABOVE_32_C
1 19.72 0.000
Feature 2 21.00 0.000
168
169
170
Distress 41 Alligator Cracking
During the first iteration, 'Average DAYS_BELOW_0_C' had a VIF of 126.65 and was removed from the predictor list. The second iteration Average Precipitation*Average TEMP_MEAN_AVG (deg C) had a VIF of 20.56 and was removed. The third iteration had all predictors with a VIF less than 10 and are below.
Method
Link function Logit Categorical predictor coding
(1, 0)
Rows used 1064 Backward Elimination of Terms
Candidate terms: Years Since Major Work Actual, Thickness, Average Precipitation, Average TEMP_MEAN_AVG (deg C), Average FREEZE_INDEX, Average FREEZE_THAW, Average TEMP_MAX, Average TEMP_MIN, Average DAYS_ABOVE_32_C, Feature, Subgrade Strength, Surface Type - Current, Thickness*Subgrade Strength
------Step 1----- ------Step 2----- ------Step 3----- Coef P Coef P Coef P Constant -9.53 -9.45 -9.41 Years Since Major Work Actual 0.02454 0.001 0.02554 0.000 0.02479 0.000 Thickness -0.0102 0.805 -0.0099 0.811 0.0174 0.526 Average Precipitation 0.000457 0.176 0.000363 0.247 0.000392 0.208 Average TEMP_MEAN_AVG (deg C)
3 -----Step 4----- -----Step 5----- -----Step 6----- Coef P Coef P Coef P
171
Constant -9.28 -8.93 -8.36 Years Since Major Work Actual 0.02455 0.001 0.02488 0.000 0.02666 0.000 Thickness Average Precipitation 0.000371 0.231 Average TEMP_MEAN_AVG (deg C)
Average FREEZE_INDEX 0.000840 0.037 0.000657 0.078 0.000244 0.213 Average FREEZE_THAW 0.01029 0.022 0.00737 0.053 0.00352 0.153 Average TEMP_MAX 0.1905 0.000 0.1964 0.000 0.1791 0.000 Average TEMP_MIN 0.0382 0.098 0.0285 0.190 Average DAYS_ABOVE_32_C -0.00897 0.082 -0.01200 0.008 -0.01150 0.012 Feature -0.394 0.131 -0.399 0.129 -0.381 0.168 Subgrade Strength 0.938 0.001 0.931 0.001 0.925 0.001 Surface Type - Current -0.464 0.004 -0.459 0.005 -0.497 0.002 Thickness*Subgrade Strength Deviance R-Sq 9.94% 9.80% 9.63% Deviance R-Sq(adj) 8.64% 8.59% 8.53% AIC 924.46 923.89 923.54 AICc 924.87 924.24 923.84 BIC 994.04 988.50 983.18 -----Step 7----- -----Step 8----- Coef P Coef P Constant -7.37 -7.45 Years Since Major Work Actual 0.02640 0.000 0.03018 0.000 Thickness Average Precipitation Average TEMP_MEAN_AVG (deg C)
Average FREEZE_INDEX Average FREEZE_THAW 0.00456 0.048 0.00531 0.020 Average TEMP_MAX 0.1498 0.000 0.1459 0.000 Average TEMP_MIN Average DAYS_ABOVE_32_C -0.00933 0.026 -0.00947 0.024 Feature -0.384 0.176 Subgrade Strength 0.920 0.001 0.893 0.002 Surface Type - Current -0.518 0.001 -0.511 0.002 Thickness*Subgrade Strength Deviance R-Sq 9.49% 9.13% Deviance R-Sq(adj) 8.48% 8.33% AIC 923.00 922.57 AICc 923.25 922.74 BIC 977.67 967.30
α to remove = 0.1 If a term has more than one coefficient, the largest in magnitude is shown.
172
Response Information
Variable Value Count Unhealthy vs Healthy
1 189 (Event)
0 875 Total 1064
Regression Equation
P(1) = exp(Y')/(1 + exp(Y'))
Subgrade Strength
Surface Type - Current
A AAC Y' = -7.448 + 0.03018 Years Since Major Work Actual + 0.005305 Average FREEZE_THAW + 0.1459 Average TEMP_MAX - 0.009471 Average DAYS_ABOVE_32_C
A AC Y' = -7.078 + 0.03018 Years Since Major Work Actual
+ 0.005305 Average FREEZE_THAW + 0.1459 Average TEMP_MAX - 0.009471 Average DAYS_ABOVE_32_C
A APC Y' = -7.960 + 0.03018 Years Since Major Work Actual
+ 0.005305 Average FREEZE_THAW + 0.1459 Average TEMP_MAX - 0.009471 Average DAYS_ABOVE_32_C
B AAC Y' = -7.250 + 0.03018 Years Since Major Work Actual
+ 0.005305 Average FREEZE_THAW + 0.1459 Average TEMP_MAX - 0.009471 Average DAYS_ABOVE_32_C
B AC Y' = -6.880 + 0.03018 Years Since Major Work Actual
+ 0.005305 Average FREEZE_THAW + 0.1459 Average TEMP_MAX - 0.009471 Average DAYS_ABOVE_32_C
B APC Y' = -7.761 + 0.03018 Years Since Major Work Actual
+ 0.005305 Average FREEZE_THAW + 0.1459 Average TEMP_MAX - 0.009471 Average DAYS_ABOVE_32_C
C AAC Y' = -6.556 + 0.03018 Years Since Major Work Actual
+ 0.005305 Average FREEZE_THAW + 0.1459 Average TEMP_MAX - 0.009471 Average DAYS_ABOVE_32_C
173
C AC Y' = -6.186 + 0.03018 Years Since Major Work Actual + 0.005305 Average FREEZE_THAW + 0.1459 Average TEMP_MAX - 0.009471 Average DAYS_ABOVE_32_C
C APC Y' = -7.067 + 0.03018 Years Since Major Work Actual
+ 0.005305 Average FREEZE_THAW + 0.1459 Average TEMP_MAX - 0.009471 Average DAYS_ABOVE_32_C
Coefficients
Term Coef SE Coef VIF Constant -7.45 1.06 Years Since Major Work Actual
0.03018 0.00657 1.06
Average FREEZE_THAW 0.00531 0.00227 1.26 Average TEMP_MAX 0.1459 0.0334 3.83 Average DAYS_ABOVE_32_C
-0.00947
0.00420 4.11
Subgrade Strength B 0.198 0.200 1.32 C 0.893 0.255 1.33 Surface Type - Current AC 0.370 0.257 1.90 APC -0.511 0.329 1.99
Odds Ratios for Continuous Predictors
Odds Ratio 95% CI Years Since Major Work Actual
1.0306 (1.0174, 1.0440)
Average FREEZE_THAW 1.0053 (1.0009, 1.0098)
Average TEMP_MAX 1.1571 (1.0838, 1.2353)
Average DAYS_ABOVE_32_C
0.9906 (0.9824, 0.9988)
Odds Ratios for Categorical Predictors
Level A Level B Odds Ratio 95% CI Subgrade Strength B A 1.2191 (0.8242,
Wald Test Source DF Chi-Square P-Value Regression 8 71.08 0.000 Years Since Major Work Actual
1 21.09 0.000
Average FREEZE_THAW 1 5.45 0.020 Average TEMP_MAX 1 19.11 0.000 Average DAYS_ABOVE_32_C
1 5.08 0.024
Subgrade Strength 2 12.54 0.002 Surface Type - Current 2 12.50 0.002
175
176
177
Distress 76 Alkali Silica Reaction
During the first iteration, 'Average DAYS_BELOW_0_C' had a VIF of 2157.50 and was removed from the predictor list. The second iteration Average TEMP_MIN had a VIF of 24.97 and was removed. The third iteration Average DAYS_ABOVE_32_C had a VIF of 12.08 and was removed. The fourth iteration had all predictors with a VIF less than 10 and are below.
Method
Link function Logit Categorical predictor coding
(1, 0)
Rows used 2337 Backward Elimination of Terms
Candidate terms: Years Since Major Work Actual, Thickness, Average Precipitation, Average TEMP_MEAN_AVG (deg C), Average FREEZE_INDEX, Average FREEZE_THAW, Average TEMP_MAX, Feature, Subgrade Strength, Average Precipitation*Average TEMP_MEAN_AVG (deg C), Thickness*Subgrade Strength
------Step 1----- -----Step 2----- Coef P Coef P Constant -12.05 -13.33 Years Since Major Work Actual 0.01770 0.000 0.01764 0.000 Thickness -0.150 0.294 -0.0509 0.024 Average Precipitation -0.00226 0.076 -0.00225 0.077 Average TEMP_MEAN_AVG (deg C) 0.1177 0.216 0.1153 0.225 Average FREEZE_INDEX -0.00265 0.038 -0.00265 0.038 Average FREEZE_THAW 0.03867 0.000 0.03846 0.000 Average TEMP_MAX 0.1820 0.000 0.1818 0.000 Feature -0.233 0.385 -0.233 0.375 Subgrade Strength -0.93 0.813 0.806 0.052 Average Precipitation*Average TEMP_MEAN_AVG (deg C)
0.000101 0.183 0.000102 0.182
Thickness*Subgrade Strength 0.106 0.765 Deviance R-Sq 19.65% 19.60% Deviance R-Sq(adj) 18.38% 18.51% AIC 916.41 912.98 AICc 916.62 913.13 BIC 1002.76 987.81 -----Step 3----- ------Step 4----- Coef P Coef P Constant -13.32 -14.30 Years Since Major Work Actual 0.01732 0.000 0.01788 0.000 Thickness -0.0532 0.017 -0.0504 0.024
178
Average Precipitation -0.00232 0.068 -0.000620 0.050 Average TEMP_MEAN_AVG (deg C) 0.1114 0.240 0.1956 0.007 Average FREEZE_INDEX -0.00257 0.044 -0.00271 0.033 Average FREEZE_THAW 0.03837 0.000 0.03983 0.000 Average TEMP_MAX 0.1831 0.000 0.1717 0.000 Feature Subgrade Strength 0.795 0.046 0.721 0.063 Average Precipitation*Average TEMP_MEAN_AVG (deg C)
α to remove = 0.1 If a term has more than one coefficient, the largest in magnitude is shown.
Response Information
Variable Value Count Unhealthy vs Healthy
1 148 (Event)
0 2189 Total 2337
Regression Equation
P(1) = exp(Y')/(1 + exp(Y'))
Subgrade Strength A Y' = -14.30 + 0.01788 Years Since Major Work Actual
- 0.05044 Thickness - 0.000620 Average Precipitation + 0.1956 Average TEMP_MEAN_AVG (deg C) - 0.002707 Average FREEZE_INDEX + 0.03983 Average FREEZE_THAW + 0.1717 Average TEMP_MAX
B Y' = -13.99 + 0.01788 Years Since Major Work Actual
- 0.05044 Thickness - 0.000620 Average Precipitation + 0.1956 Average TEMP_MEAN_AVG (deg C) - 0.002707 Average FREEZE_INDEX
179
+ 0.03983 Average FREEZE_THAW + 0.1717 Average TEMP_MAX
C Y' = -13.57 + 0.01788 Years Since Major Work Actual
- 0.05044 Thickness - 0.000620 Average Precipitation + 0.1956 Average TEMP_MEAN_AVG (deg C) - 0.002707 Average FREEZE_INDEX + 0.03983 Average FREEZE_THAW + 0.1717 Average TEMP_MAX
Coefficients
Term Coef SE Coef VIF Constant -14.30 2.05 Years Since Major Work Actual 0.01788 0.00468 1.13 Thickness -0.0504 0.0223 1.10 Average Precipitation -
0.000620 0.000316 1.64
Average TEMP_MEAN_AVG (deg C)
0.1956 0.0725 8.88
Average FREEZE_INDEX -0.00271 0.00127 3.23 Average FREEZE_THAW 0.03983 0.00563 5.39 Average TEMP_MAX 0.1717 0.0451 2.39 Subgrade Strength B 0.304 0.542 9.02 C 0.721 0.549 9.24
Odds Ratios for Continuous Predictors
Odds Ratio 95% CI Years Since Major Work Actual 1.0180 (1.0087,
1.0274) Thickness 0.9508 (0.9101,
0.9933) Average Precipitation 0.9994 (0.9988,
1.0000) Average TEMP_MEAN_AVG (deg C)
1.2160 (1.0550, 1.4017)
Average FREEZE_INDEX 0.9973 (0.9948, 0.9998)
Average FREEZE_THAW 1.0406 (1.0292, 1.0522)
Average TEMP_MAX 1.1873 (1.0868, 1.2970)
Odds Ratios for Categorical Predictors
Level A Level B Odds Ratio 95% CI Subgrade Strength