A Predictive Model for Structural Tornado Damage to Residential Structures Using Housing Data from the 2011 Joplin, Mo Tornado

A PREDICTIVE MODEL FOR STRUCTURAL TORNADO DAMAGE TO RESIDENTIAL STRUCTURES USING HOUSING DATA FROM THE 2011 JOPLIN, MO TORNADO

ALYSSA C EGNEW

A THESIS PRESENTED TO THE UNDERGRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR SUMMA CUM LAUDE IN ENGINEERING

UNIVERSITY OF FLORIDA

2016

To my Lord and Savior, Jesus Christ, in whom I can do all things, and to my parents who keep me sane in the meantime.

ACKNOWLEDGMENTS

I would like to thank Dr. David O. Prevatt for the opportunity to work under his supervision with the UF Wind Hazard Damage Assessment Group, and David Roueche for his indispensable guidance through this research project. I would like to thank Dr. Kurtis Gurley and Dr. Curtis Taylor for agreeing to be on the panel for the thesis defense. I would also like to thank all of those who helped augment the database, specifically Malcolm Ammons, Austin Bouchard, and Jeandona

Doreste. And a final thank you to the UF Center for Undergraduate Research, which funded this investigation through the University Scholars Program.

TABLE OF CONTENTS

page

ACKNOWLEDGMENTS ...... 4

LIST OF TABLES ...... 6

LIST OF FIGURES ...... 7

LIST OF ABBREVIATIONS ...... 8

ABSTRACT ...... 9

INTRODUCTION ...... 10

BACKGROUND ...... 14

METHODOLOGY ...... 16

RESULTS ...... 20

CONCLUSION ...... 35

FUTURE WORK ...... 36

REFERENCES ...... 37

APPENDIX

A: Metadata on the 488 Homes Used in this Study ...... 40

B: MATLAB R2015 Script Used to Generate Graphs of Parameters ...... 49

C: MATLAB R2015 Script Used to Generate Multinomial Logistic Regression with Random Input ...... 51

D: MATLAB R2015 Script Used to Generate Multinomial Logistic Regression with Significant Parameters Only ...... 52

LIST OF TABLES

Table page

1 EF-Scale Wind Speed Ranges ...... 15

2 Degree of Damage Description ...... 16

3 Building Code History of Joplin, Missouri ...... 26

4 Y-Intercepts and Coefficients from the Proportional Odds Model ...... 31

5 Testing the Proportional Odds Likelihood of Damage Output ...... 32

6 Comparison of Findings to Literature ...... 33

LIST OF FIGURES

Figure page

1 Screenshot of the Beacon GIS Site ...... 17

2 Example of Geo-Tagged Survey Imagery ...... 18

3 Screenshot of Google Street View® imagery ...... 18

4 Square Footage Histogram ...... 21

5 Appraised Value Histogram ...... 22

6 Year Built Histogram ...... 22

7 Number of Homes with One Story Versus Two Stories ...... 23

8 Distance from Tornado Centerline Histogram ...... 23

9 Degree of Damage Bar Graph ...... 24

10 Comparison of Year Built Between the Sample Set and the Entire Population ...... 25

11 Percentage of Homes Built Under Each New Building Code Adoption ...... 27

12 Linear Regression of Degree of Damage and Number of Stories ...... 28

13 Linear Regression of DOD and Wind Speed ...... 28

14 Linear Regression of DOD and Appraised Value ...... 29

15 Linear Regression of DOD and Square Footage ...... 29

16 Linear Regression of DOD and Year Built ...... 30

LIST OF ABBREVIATIONS

EF-Rating Enhanced Fujita scale rating of a tornado’s severity; used when estimating wind speeds based on damage to a particular Damage Indicator

DOD-rating Degree of Damage rating for a particular structure type relating its level of structural damage to a wind speed range

Abstract of Thesis Presented to the Undergraduate School of the University of Florida in Partial Fulfillment of the Requirements for Summa Cum Laude in Engineering

A PREDICTIVE MODEL FOR STRUCTURAL TORNADO DAMAGE TO RESIDENTIAL STRUCTURES USING HOUSING DATA FROM THE 2011 JOPLIN, MO TORNADO

Alyssa C Egnew

March 2016

Chair: David O. Prevatt Major: Civil Engineering

On May 22, 2011, an EF-5 tornado struck Joplin, Missouri, leaving 158 fatalities and over 1000 injuries in its aftermath (National Weather Service, 2011, para. 1-2). The damaged residential structures were surveyed by a reconnaissance team under Dr. David O. Prevatt just days later. This investigation used the extracted empirical data from the tornado path to find trends in the damage for future applications. In order to use the collected information, the database of damaged homes first needed to be augmented, one by one, to contain street addresses and parcel IDs that could be cross referenced with the Jasper County Tax Assessor’s database of house characteristics. In this way, the year built, appraised value, square footage, and number of stories for each home was obtained for a final sample size of 488 homes. The maximum wind speed encountered by each home was assigned using each home’s distance from the tornado centerline (from the geo-tagged imagery taken by the reconnaissance team) and the near-surface wind model of the Joplin tornado developed by Lombardo, Roueche, and Prevatt (2015). To see how each of these parameters influences the expected level of damage in a home, a multinomial logistic regression (“proportional odds model”) with an ordinal response was developed for this dataset. A multiple linear regression could not have been used because of the non-continuous categories of degree of damage (as described by McDonald, Mehta, and Mani, 2004). Hence, a proportional odds model best fit the data type and allowed for the varying wind speed with distance from the tornado centerline to be more accurately accounted for. The output of this model is the odds of the expected level of damage being less than or equal to a reference damage level, as compared to greater than that reference level. According to the model, the number of stories in a home was rejected as being a significant predictor of damage level. However, an increase in year built, wind speed, and square footage all result in greater odds of having a higher state of damage. On the other hand, an increase in appraised value results in lower odds of having a higher state of damage. The most influential parameter on damage was the one with the opposite trend, appraised value. These results can be further investigated regarding the underlying correlations to other parameters; perhaps the appraised value of the house is significant because of better maintenance, which allows it to perform better in a tornado than a house with decay. This proportional odds model, when coupled with other related studies, would be useful for city officials to forecast weak residential areas in their cities.

Introduction

Tornadoes are one of the most potent natural disasters experienced in the United States. From

1993 to 2012, tornadoes accounted for 36% of insured catastrophe losses in the United States, which is more than winter storms, terrorism, geological events, wind, hail, fires, and floods combined (The

Property Claims Services, 2014). "A total of 1,625 tornadoes occurred in the United States in 2011, resulting in economic losses that exceeded $25 billion” (Prevatt et al., 2012, p. 254). Tornadoes in

Tuscaloosa, Alabama, on April 27 and Joplin, Missouri, on May 22 caused more than half of those

2011 losses, with a combined effect of 223 fatalities and more than 13,000 damaged buildings

(Prevatt et al., 2012). Such significant damage and loss of human life merits consideration of whether the current building codes, which do not consider tornadoes in their construction requirements, are appropriate for tornado-prone regions without further strengthening. Regardless of any future advances in building codes, however, there exists a legacy of nearly 132 million homes in the US that are highly vulnerable to tornado damage. It is important for community decision makers to be aware of this vulnerability, and what portions of their community are most vulnerable, so that they can appropriately allocate mitigation and first response resources.

In order to pinpoint vulnerable areas, though, an understanding of tornadoes and the risks associated with them is needed. There has been a significant amount of research dedicated to this; as early as 1897, there have been studies on the wind pressures of tornadoes and the direct need for wind bracing in taller structures (Baier, 1897). The focus in the mid-twentieth century turned to tornado mechanics studies (e.g. wind velocities, pressure differentials, etc.) (Melaragno, 1968). In recent decades, researchers have been trying to model the risk of tornado outbreak during any time of the year for anywhere in the contiguous United States (Brooks, Doswell, & Kay, 2003), what the recurring patterns are in supercell storm tracks (Hocker & Basara, 2008), and what the strengths and

10 weaknesses are of in-home storm shelters (Masters, Gurley, & Prevatt, 2014). Moreover, many studies in this field incorporate mathematical models to increase understanding of trends in tornado outbreaks (Boruff et al., 2003; Hocker & Basara, 2008; Schaefer et al., 1986; Schaefer et al., 2002).

Other research has been dedicated to improving near-surface tornado wind models by incorporating tree-fall data (Lombardo, Roueche, & Prevatt, 2015).

Additionally, there have been efforts to analyze the spatial and temporal trends of tornado hazards using GIS technology (Boruff et al., 2003) and to adjust paradigms on the tornado rating system (Schaefer, Schneider, & Kay, 2002). The Fujita Scale, which became the official tornado rating system in the early 1970s, generally over-estimated wind speeds, and was replaced in 2007 by the Enhanced Fujita (EF) Scale as described by McDonald, Mehta, and Mani (2004), and provides more accurate wind estimations (Doswell, Brooks, & Dotzek, 2009, pp. 555-556). Despite these improvements, though, the tornado rating system is still subjective because of its use of damage to estimate wind speeds. There is no way to account for whether or not the building code of the time was enforced or if the building had preexisting damages that made it susceptible even to lower wind speeds.

In addition to understanding the mechanics behind tornadoes and their path characteristics, an understanding of structural damage patterns in tornadoes is necessary to locate regions of particular vulnerability. For example, wind tunnel tests on finite element models of homes are being used to predict their damage potential and stress distribution, which will reveal the sequence and type of failures within the homes (Kumar, Dayal, & Sarkar, 2012). Roueche and Prevatt identified seven common failure mechanisms due to tornado wind hazards in residential structures and established correlations between them (2013, p. 5). De Silva, Kruse, and Wang have investigated the

“debris effect” that occurs during a tornado outbreak when debris is picked up and turned into a

11 missile, creating further damage (2008, p. 318). Damage surveys after major tornado outbreaks have become increasingly common, as well. One such survey in Joplin, Missouri was conducted by the

National Institute of Standards and Technology ([NIST], 2013). Their report reconstructs the proceedings of the tornado outbreak and responses to advance warnings using a collection of photos, videos, building plans, wind models, and interviews. The report also describes the wind pressures and fields of the tornado, the damage associated with flying debris, the emergency communication systems in place and how people responded, the factors affecting survival and injury, and the need for safety code revisions. In doing so, they present recommendations that range from new methods for tornado-resistant design of buildings, to improved measurement and characterization of tornado hazards, and improved emergency communication systems.

Because tornado strength decreases with distance from the tornado centerline, improved construction techniques could help reduce damage on the peripheries of even an EF-5 tornado

(Sutter, DeSilva, & Kruse, 2009, p. 114). Sutter et al. investigated this application to tornadoes by performing a benefit-cost analysis of retrofitting measures (such as hurricane clips, anchor bolts, and directional nailing), and concluded that it “may be cost effective” in mitigating damage for states with a high-risk of tornadoes (2009, pp. 113, 119). A more recent benefit-cost analysis corroborated these findings; the benefits of adopting wind-resistant building codes was shown to outweigh the costs by a factor of 3 to 1, showing that improved construction and even retrofitting measures can help mitigate tornado damage (Simmons, Kovacs, & Kopp, 2015). It has also been shown by the

Federal Emergency Management Agency that structural retrofitting can help reduce the risk of damage to buildings in hurricane prone regions, which further validates their use in other high wind load situations, such as tornadoes ([FEMA], 2010).

Despite all of this research on structural damage mitigation, there have not been considerations for tornado wind loads in building codes until recently. Previously, the design wind speed was 90 miles per hour, but in 2014, Moore, Oklahoma adopted the first building code for wind speeds of 135 miles per hour (City of Moore, Oklahoma, 2014, p. 1). This code incorporates mitigation techniques based on structural retrofitting for hurricanes (i.e. hurricane clips) to help reduce the risk of structural damage from tornadoes (p. 1).

This mitigation effort can be further narrowed by targeting more specific trends in structural damage. De Silva, Kruse, and Wang’s general spatial model (GSM) identified house characteristics that tended to cause greater loss when present in a structure; specifically, when a house is larger, is single-story (versus multi-story), has a hip-only roof, has a slab foundation (versus a conventional foundation), has any other exterior besides frame hardboard or stucco, or is newer, it is at a greater risk of economic loss (2008, p. 328). They corroborate the claim that newer houses are at a greater risk of loss with Fronstin and Holtmann’s (1994) explanation of lack of code enforcement and deterioration of construction quality in recent decades. Thus, for a tornado outbreak, it has been shown that certain house characteristics are associated with greater economic loss, and that structural damage is also caused by air-born debris, not just direct tornado impact. There is no quantized correlation between house characteristics and structural damage, though, particularly with respect to distance from the tornado centerline. This would certainly be a useful tool for city officials to identify vulnerable areas in their region.

Hence, this research was conducted to determine the extent to which building construction characteristics correlate to the damage in the residential structures struck by the 2011 Joplin,

Missouri tornado. In this way, future mitigation efforts, building codes, and construction methods can target these features of tornado damage, and awareness can be raised about which existing

13 homes are most at risk. Furthermore, any government official can use the findings from this investigation to pinpoint vulnerable homes in their jurisdiction, since the basic parameters (year built, square footage, number of stories, and appraised value) are readily accessible through any tax assessor’s database. Other house characteristics, such as home orientation with respect to the tornado path and roof construction, are useful to engineers, but are not readily available for city officials; these other characteristics are therefore not considered in this investigation, since their use would require additional time and money on the part of city officials. However, additional data regarding wind speed was readily available for this set of 488 homes, and is included in this investigation.

Thus, the scope of this research is limited to how year built, square footage, appraised value, maximum encountered wind speed, and number of stories influence the expected level of tornado damage.

Background

The tornado that struck Joplin, Missouri on May 22, 2011 was rated as an EF-5 tornado, and caused 158 fatalities and over 1000 injuries; the damage path of this tornado was approximately six miles long and three-quarters of a mile in width within Joplin (NWS, 2011, para. 1-2). Of the 7500 residential structures that were damaged, about 4000 were destroyed, which left an estimated 9200 people displaced (Onstot, 2013, p.2).

From May 30 to June 1, 2011, a reconnaissance team headed by Dr. David O. Prevatt from the University of Florida, and funded by the American Society of Civil Engineers and the Structural

Engineering Institute, set out to survey the damage (Prevatt et al., 2011). The survey team documented the damage to 1,394 structures using 8,750 geo-tagged photographs (p. 12). A database of these damaged structures was created with reference to their geo-tagged imagery, the coordinates of which were used to determine each home’s distance from the centerline of the tornado. The

14 maximum wind speed was determined for each home using its distance from the tornado centerline in conjunction with the near-surface wind model of the Joplin tornado from Lombardo, Roueche, and Prevatt (2015). The number of stories each home had was also previously retrieved from the Tax

Assessor database (Jasper County Tax Assessor Office, n.d.).

The database also includes the manually-assigned damage level for each home. In this investigation, the damage levels are based on the Enhanced Fujita (EF) scale and Degree of Damage

(DOD) scale for Damage Indicator 2, “One- or Two-Family Residences” (FR12), as described by

McDonald, Mehta, and Mani (2004, pp. 7, 8, 11), and are shown in Tables 1 and 2 below.

Table 1: EF classification scale used when estimating wind speeds based on damage to a particular Damage Indicator EF-Scale Wind Speed Ranges EF Classes 3-Second Gust Speed, mph EF0 65-85 EF1 86-110 EF2 111-135 EF3 136-165 EF4 166-200 EF5 >200

Table 2: Degrees of Damage (DOD) descriptions for one- or two-family residences, with expected (EXP), lower bound (LB), and upper bound (UB) wind speeds (in mph) for each DOD

DOD* Damage description EXP LB UB 1 Threshold of visible damage 65 53 80 2 Loss of roof covering material (<20%), gutters 79 63 97 and/or awning; loss of vinyl or metal siding 3 Broken glass in doors and windows 96 79 114 4 Uplift of roof deck and loss of significant roof 97 81 116 covering material (>20%); collapse of chimney; garage doors collapse inward or outward; failure of porch or carport 5 Entire house shifts off foundation 121 103 141 6 Large sections of roof structure removed; most 122 104 142 walls remain standing 7 Top floor exterior walls collapsed 132 113 153 8 Most interior walls of top story collapsed 148 128 173 9 Most walls collapsed in bottom floor, except small 152 127 178 interior rooms 10 Total destruction of entire building 170 142 198 *DOD is degree of damage

Methodology

Once the database of damaged structures included EF-ratings and DODs, other parameters were needed to describe them. The database from the ASCE damage survey had to be augmented to contain specific house characteristics that could be analyzed for trends with respect to the damage.

To get the house characteristics, the addresses of the houses first needed to be assigned. To do so, the GPS coordinates for a house from the damage survey would be searched for in Google Maps® to find the general area in which the house is located. Then, the street that the house is on would be pinpointed in the “Beacon” GIS site for Jasper County, Missouri, as demonstrated in Figure 1. The

“Beacon” account created for the research team granted access to aerial imagery of the tornado damage and a layer on the map showing the location where each geo-tagged photo of a damaged home was taken during the ASCE survey.

Figure 1: Screenshot of the Beacon GIS site used to find the address of a home surveyed by the ASCE damage assessment team; each geo-tagged photo location is demarked by a yellow triangle as shown

The GPS coordinates do not always line up directly with a specific home, so Pictometry

Online®, Zillow.com, and Google Street View® were used to confirm the address of the home by cross referencing the landmarks from the survey imagery with the online imagery (Figures 2 and 3).

The address and parcel ID of the home would then be obtained from the “Beacon” GIS site and cross-referenced with the Jasper County Tax Assessor’s database of construction characteristics

(Jasper County Tax Assessor Office, n.d.). The four house characteristics that are readily available in any tax assessor’s database are number of stories, year built, square footage, and appraised value.

These were assigned to each house in our set to determine if they are reliable predictors of tornado damage. This entire process is lengthy, though, so due to time constraints, only 488 houses were assigned street addresses and were cross-referenced with the county’s database to obtain their construction characteristics.

Figure 2: The geo-tagged, survey imagery of a home that was taken by the ASCE damage assessment team

Figure 3: Screenshot of the Google Street View® imagery used to confirm the address of the home in Figure 2

To analyze these parameters’ effects on damage, linear regressions were created for each parameter independently (for example, Area vs DOD) using Minitab17. However, a more rigorous statistical approach was needed to take into account the varying wind speeds with distance from the tornado centerline and the non-continuous nature of DOD categories.

A multinomial logistic regression with an ordinal response was therefore developed to more adequately test whether or not these parameters influence the damage level and in what way. Linear regressions could not account for the categorical nature of DOD, but multinomial logistic regressions

18 can. This method takes into account the change in wind speed with distance from the tornado centerline (something difficult to achieve when just grouping wind speeds into broad ranges based on distance from the centerline). The ordinal response type takes into account the DOD not being a continuous scale, but having a clear progression to its categories (a DOD of 9 has more damage than a DOD of 8) (The MathWorks, Inc., 2016). This multinomial logistic regression is different than a simple linear regression, where the output is the actual DOD and shows how much the parameter influences the damage directly. Here, the multinomial logistic regression gives an output that is a number. This number is the odds of the DOD for a given home being less than or equal to a given reference DOD; the output number is not the DOD itself, but rather the odds of it being less than or equal to that reference DOD.

Using MATLAB R2015, the model was created using mnrfit (see Appendices B and C for the scripts). In addition to providing p-values to test the significance of each parameter, this mnrfit gives an equation for each DOD-rating that is a “proportional odds model” for likelihood of damage.

It is considered a “proportional odds model,” in that the equations have the same slope, but are just offset by different y-intercepts (The MathWorks, Inc., 2016). The model produces one less number of intercepts than number of input categories, because there is no category beyond the greatest DOD- value; hence, the 9 categories of DOD require only 8 intercept values (and accordingly only 8 equations), since you cannot have odds comparing the highest category to nonexistent higher categories of DOD.

The form of the proportional odds model equation based off of the generated parameters is as follows:

ln( )= bi + c1p1 + c2p2 + …+cnpn (1)

where the left-hand side of Equation (1) is the natural log of the probability that the actual

DOD is less than or equal to the reference DOD, versus greater than that reference DOD; bi is the y- intercept corresponding to the reference DOD being examined; c1, c2, …, cn are the constants assigned to each predictor, p1, p2, …, pn. If, for example, the equation for a reference DOD of 5 is used, then the output would be a number that represents the odds of the DOD being less than or equal to 5, as compared to greater than 5. So if this output is 2, then the home is two times as likely to have a DOD less than or equal to 5, than to have a DOD greater than 5.

It is important to note that the coefficients express the “relative risk or log odds” associated with each predictor; so if all else is held constant, then a unit change to p1, for example, will result in a change of the odds outcome by a factor of � (The MathWorks, Inc., 2016). The coefficients are the same from one reference DOD-rating to the next, and from one house to the next, since the model generates these coefficients based off of the given data to demonstrate how each predictor influences the level of damage.

A random number generator was included as one of the predictor variables in order to test how accurately the p-values accept or reject the significance of the predictor variables (Appendix C).

The parameters that were accordingly rejected were removed, and the significant parameters were adjusted one by one, while holding all else constant, to observe the influence each one had on the likelihood output of the equation generated for a reference DOD-ranking. The influence that each parameter had on the odds of a higher damage state was compared to findings from other research.

Results

The basic parameters of these 488 houses are shown in Figures 4 through 9. The MATLAB

R2015 script to create the graphs is given in Appendix B; the homes in the sample set tend to be inexpensive (less than $24,000) and not very large (less than 1700 ft2). The low home values are due

20 to the entire property value being split between the building and the land values; the building value is what is being used for this investigation. Distance from the tornado centerline has been included

(Figure 8), since wind speeds decrease with distance from the center of a tornado, and therefore have varying effects on the level of damage incurred in structures.

Figure 4: Square footage histogram

Figure 5: Appraised value histogram in thousands of $US

Figure 6: Year built histogram

Figure 7: Number of houses with one story versus two stories

Figure 8: Distance from tornado centerline histogram

Figure 9: Degree of Damage bar graph

The housing age distributions for the set of 488 homes and for the entire population of Joplin,

Missouri as of 2009 are shown in Figure 10.

Cumulative Distribution of "Year Built" for Joplin, MO as Compared to the Sample Set of 488 Homes

120

100

20 Cumulative Percentage 0 < 1940 < 1950 < 1960 < 1970 < 1980 < 1990 < 2000 < 2010

Cumulative Distribution of 22677 Homes Based on Year Built (%)

Cumulative Distribution of 488 Homes Based on Year Built (%)

Figure 10: Cumulative distribution of year built for the entire city of Joplin, Missouri (22677 homes) as compared to the sample set of homes used in this investigation (488 homes) (factfinder.census.gov, Jan. 2016).

Figure 10 demonstrates how the 488 homes in the sample set tend to be older than the entire population of 22,677 homes in Joplin, Missouri (as of 2009). This should be considered before applying the results to the greater population of Joplin. Because most of the homes in Joplin,

Missouri are relatively old, they were consequently constructed under outdated building codes. Table

3 lists each building code adopted by Joplin, Missouri. Accordingly, Figure 11 displays the percentage of 2,757 homes from the Jasper County Tax Assessor’s database that were built to each code in Joplin (Jasper County Tax Assessor Office, n.d.).

Table 3: The building codes adopted by the city of Joplin, along with year of adoption and ordinance numbers; retrieved October 10, 2013 from the Joplin City Building Department; revised February 20, 2014 with information from the NIST investigation (2013, pp. 397-401) Building Code History of Joplin, Missouri Year The Edition Adopted Ordinance Adopted Number 1877 Some form of building code existed; updated every few years; Earliest known use of building codes in Joplin 1940 Adopted their own written building code, “1940 City Code of Joplin” 17707 1955 1955 BOCA National Building Code with amendments 22699 1959 1957 Code of the City of Joplin. Codified Chapters 1 to 57. 24113 1961 1960 BOCA National Building Code 24491 1966 1965 BOCA National Building Code with amendments 25573 1970 1970 BOCA National Building Code with amendments 26132 1972 Amending and repealing sections of the 1970 BOCA Building Code 26653 1972 1970 Supplement to the 1970 BOCA Building Code 26660 1972 Amending the 1970 BOCA Building Code by adding sections to 26666 provide code coverage for structures used for non-residential purposes. 1973 1972 Supplement to the 1970 BOCA Basic Building Code. 26877 1974 1973 Supplement to the 1970 BOCA Building Code 27087 1980 1978 BOCA National Building Code 80-106 1984 1984 BOCA National Building Code 84-76 1990 1990 BOCA National Building Code 90-179 1991 All precedent subsequent Supplements or Amendments to the 1990 91-155 BOCA National Building Code 1993 Amending the 1990 BOCA Building Code Chapter 9, Article 4, 93-6 Section 9-62, specifically in reference to Snow and Wind loads. 1997 1996 BOCA National Building Code 97-091 2003 2000 International Building Code 2003-049 2003 2000 International Residential Code 2003-050 2008 2006 International Building Code, 2006 International Residential 2008-068 Code

40%

35%

30%

25%

20%

15%

Percentage of Homes 10%

0% No 1940 1955 1961 1966 1970 1980 1984 1990 1993 1997 2003 2008 Code Year of Building Code Adoption

Figure 11: Percentage of the 2,757 homes available from the Jasper County Tax Assessor’s office that were built under each new building code adoption (Jasper County Tax Assessor Office, n.d.)

As seen in Figure 11, Joplin was exceptionally vulnerable to tornado damage, since about one-third of the homes in Joplin were built to no code at all. Besides, many of the homes that were constructed to a building code are relatively old (built nearly 50 years ago), and there is no way to guarantee that the outdated codes were enforced. In fact, each home in the city was vulnerable regardless of which building code it was built under, because none of the codes accounted for tornado wind loads. So in addition to this vulnerability, older homes likely contained preexisting damage due to decades of wear, and newer homes likely suffered from deterioration of construction quality in recent decades, as mentioned previously (Fronstin and Holtmann, 1994).

Two approaches were taken to describe the influence each parameter has on structural damage—linear regression and multinomial logistic regression. The linear regression for each parameter was generated using Minitab17, and the results are shown in Figures 12 through 16 below.

Figure 12: Linear Regression of Degree of Damage and Number of Stories

Figure 13: Linear Regression of DOD and Wind Speed

Figure 14: Linear Regression of DOD and Appraised Value

Figure 15: Linear Regression of DOD and Square Footage

Figure 16: Linear Regression of DOD and Year Built

As can be seen by Figures 12 through 16, the multiple linear regression approach was found to be inadequate for this investigation, since DOD values are not a continuous range of numbers (a

DOD of 4.8 has no meaning). Its discrete nature does not produce a smooth correlation to the input variables. Wind speed was the only parameter with a linear regression having an obvious trend to it

(Figure 13), as the damage clearly increases with an increase in wind speed. Hence, a more rigorous statistical approach was needed to take into account the non-continuous nature of DOD.

A multinomial logistic regression was therefore developed using MATLAB R2015; its output includes p-values describing the chance of error within each parameter’s result. Generally, predictor variables are accepted within a 5% chance of error, so a p-value of 0.05 was taken as the threshold for significance for each predictor variable; using this standard, the model rejected two predictors, deeming them as insignificant—the random number generator (p-value of 0.9385) and the number of stories the home has (p-value of 0.3618). It was known that the random number generator has no correlation to DOD, so a high p-value was expected. Because the model rejected

30 the random number generator as being a significant predictor of damage, this gives greater confidence in the use of the model.

The output of the multinomial logistic regression also includes coefficients and intercepts to form proportional odds models for each DOD. Upon removing the rejected predictors, the resulting set of coefficients (constant for each DOD-rating) and y-intercepts (different for each DOD-rating), as shown in Table 4, can be used for analyzing the likelihood of a house have a reference level of damage.

Table 4: Y-intercept and coefficient values for the likelihood of damage equations generated by the proportional odds model. Y-Intercepts and Coefficients from the Proportional Odds Model

DOD-Rating Intercept 1 28.8807 2 32.5987 Predictor Coefficient 3 34.0259 Year Built (YB) -0.0150 4 34.9812 Square Footage (SF) -0.0007 5 34.9938 Appraised Value (Val) 0.0247 6 37.2411 ($USD thousand) 7 37.9106 Wind Speed (WS) -0.0465 8 38.7719 9 ---

As an example, the equation for a reference DOD of 3 would be as follows:

( ) ln( )=34.0259 − 0.0150�� − 0.0007�� + 0.0247�� − 0.0465�� (2) ()

The ordinal response model was tested on a home as shown in Table 5; the MATLAB R2015 script is found in Appendix D. The equation for a DOD-rating of 3 was used in this case to test the effects of each predictor variable on the likelihood output when all other variables are held constant.

Table 5: Example home to test the likelihood of damage output when changing the input values of the predictor variables. The original value for each predictor variable is included, and then each predictor was varied by a percentage of the range of values in the database of 488 homes, while all else was held constant at the original value. The likelihood outputs for each case are given.

Likelihood of Damage Output, (predictor variables listed in order of most impactful to least impactful on likelihood)

Predictor Variable -20% of -10% of original +10% of +20% of Being Adjusted range range range range

Appraised Value 0.0883 0.2041 0.4719 1.0910 2.5223 ($USD thousands) (37.4) (71.4) (105.4) (139.3) (173.3)

Wind Speed 1.1609 0.7402 0.4719 0.3009 0.1918 (mph) (96.4) (106.1) (115.8) (125.5) (135.2)

Square Footage 1.0765 0.7128 0.4719 0.3125 0.2069 (2279.4) (2873.7) (3468) (4062.3) (4656.6)

Year Built 0.6946 0.5725 0.4719 0.3890 0.3206 (1949.2) (1962.1) (1975) (1987.9) (2000.8)

When using the original values of the example home, the likelihood is 0.4719, as shown in

Table 5, meaning there’s a 47.2% chance the damage is less than or equal to DOD3 rather than greater than DOD3. From there, each predictor variable was adjusted by +/-10% and +/-20% of the range of values in the samples set of 488 homes, while all else was held at the original value. When the wind speed, for instance, was increased by 10% of its range of values in the database, the likelihood output changed to 0.3009. This means that the odds of DOD being less than or equal to 3 versus greater than 3 decreased. This indicates that higher wind speeds will likely cause higher levels of damage in homes, which is exactly what one would expect. A summary of each predictor variable’s influence is given in Table 6.

Table 6: Comparison of this investigation’s findings to findings from literature regarding the influence of different parameters on expected level of structural damage.

The Effects of Increasing Each Predictor Variable on the Odds of Having a Higher Final Damage State and Comparison to Results from Literature Variable Influence on Odds Literature Results from of Higher Damage Literature Appraised Value Decrease ------Wind Speed Increase McDonald, Mehta, Increase and Mani (2004) Square Footage Increase De Silva, Kruse, Increase and Wang (2008) Year Built Increase Fronstin and Increase Holtmann (1994) Number of Stories None De Silva, Kruse, Decrease and Wang (2008)

All the predictor variables with negative coefficients shared the same trend, as hypothesized, that increasing the predictor variable increases the odds of higher damage. Namely, the newer homes, along with homes having greater square footage, and the homes encountering higher wind speeds, will likely have more damage. The opposite was true for homes having greater appraisal values, as would be expected, since its coefficient was the only positive one, while all the other coefficients were less than zero. Hence, the greater the home value, the less likely it is to have high damage, according to this model. A house with good upkeep and maintenance would be appraised at a higher value than a similar house with rot and decay, so it would be expected that the house with the higher value would perform better in the event of a tornado.

Two other test homes were used to verify the influence that each predictor variable has on the odds of having higher damage, and it was found that these trends are consistent across each sample home; not only were the likelihood output patterns for each predictor variable the same, but the ordering of most impactful predictor variable to least impactful predictor variable was also consistent from one sample home to another. The most impactful parameter on the outcome of the proportional odds model, surprisingly, was appraised value and the least impactful was year built.

These findings seem to line up with previous research, though nothing was found in literature to confirm that an increase in a house’s appraised value will decrease its likelihood of high damage.

However, this outcome is reasonable, since well-maintained houses will have a higher appraised value, and will also perform better in a tornado than poorly-maintained houses having lower appraised values. As for square footage, the findings in previous research corroborate the findings in this study that an increase in square footage corresponds to higher levels of tornado damage (De

Silva, Kruse, and Wang, 2008). This outcome is also reasonable, since larger houses with greater surface area will act as more blunt obstacles in the path of tornado winds than smaller houses; smaller houses would have less surface area to oppose the tornado winds and be less at risk of high levels of damage. As for number of stories, our findings do not match up with literature (De Silva,

Kruse, and Wang, 2008), though this could be due to the fact that so few multi-story homes were present in our dataset. As for the wind speed parameter, it has already been well documented that higher wind speeds correlate to higher levels of structural damage (McDonald, Mehta, and Mani,

2004); this is the fundamental idea behind the EF-scale and DOD rating system. The lack of building codes that address these tornado wind loads is problematic; with the exception of the codes adopted by Moore, Oklahoma in 2014, building codes do not account for tornado wind loads, and even these building codes may not have been strictly enforced.

As for year built, the findings from this study seem to line up with Fronstin and Holtmann’s

(1994) claim that homes built in the past few decades are at higher risk of damage due to lack of code enforcement and degradation of construction quality. De Silva et al. (2008) also showed that certain house characteristics are associated with greater economic loss, and structurally this may be true. Their claim that newer houses and larger houses are at a greater risk of economic loss seems to hold ground for structural damage based on the findings of this research (p. 328). They also found

34 that when a house is single-story (versus multi-story), has a hip-only roof, has a slab foundation

(versus a conventional foundation), or has any other exterior besides frame hardboard or stucco, it is at risk of greater economic loss, but these relations are outside the scope of this study.

Conclusion

By extracting empirical data on 488 homes that were impacted by the 2011, EF-5 tornado outbreak in Joplin, Missouri, a multinomial logistic regression was developed to investigate how certain construction characteristics influence the expected level of structural damage, and then have these trends for future applications. This “proportional odds model” considers readily accessible predictor variables that city officials could potentially use to identify vulnerable areas in their cities, especially once further parameters are included to make the model more robust. The findings from this study are not absolute, since they only represent 488 homes in one city impacted by one tornado.

The findings do, however, indicate general trends that point to other interrelated causes of damage.

For example, the strong influence of appraised home value on the damage could be related to material quality, maintenance and upkeep, etc. There are numerous other factors lying behind these parameters being used, so these results are only generic expressions of more complex relationships that are beyond the scope of this investigate. The key findings from this investigation are as follows:

• The proportional odds model behaves as expected from findings in other research. • The model successfully rejected the unrelated random number generator as being significant, adding further merit to these findings. • An increase in appraised home value indicates a decreased likelihood of having a higher state of damage. • An increase in wind speed indicates an increased likelihood of having a higher state of damage. • An increase in square footage indicates an increased likelihood of having a higher state of damage. • An increase in year built indicates an increased likelihood of having a higher state of damage.

• The most influential parameter appeared to be appraised home value. Future Work

A closer look should be taken at environmental layout and its relation to structural failure; shielding may occur from one structure to another, which ties into De Silva et al.’s (2008) “debris effect,” where debris is launched as a projectile causing further damage. Other variables that were beyond the scope of this investigation (such as construction materials, house orientation with respect to the tornado centerline, pressure differentials, vertical wind loads, and more detailed wind field models) should also be considered as factors when analyzing tornado damage.

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Appendix A: Metadata on the 488 homes used in this study

Address DOD- Year Appraised House Square Stories Wind Speed Rating Built Value ($USD) Footage 2117 S MOFFET 3 1880 30,290.00 1,452.00 1.5 87.8 2209 EMPIRE 2 1885 27,650.00 854 1 91.0 2526 VIRGINIA 9 1890 11,240.00 1,301.00 1 170.1 2020 GRAND 6 1890 22,440.00 1,437.00 1 107.1 2523 EMPIRE 3 1895 16,470.00 1,005.00 1 171.3 1812 GRAND 2 1895 45,340.00 1,281.00 1.5 82.0 2810 W 26TH ST 2 1895 12,110.00 964 1 128.4 2409 S EMPIRE 3 1895 11,160.00 736 1 141.1 2006 S BYERS 3 1900 26,850.00 1,914.00 2 77.2 2528 BIRD 8 1900 6,960.00 1,000.00 1 171.0 2222 EMPIRE 2 1900 8,100.00 858 1 94.7 2121 S BYERS 3 1900 34,260.00 1,084.00 1 92.9 2023 S MOFFET 2 1900 46,520.00 2,244.00 1.5 80.8 2529 S WILLARD 4 1900 9,400.00 696 1 155.5 2124 S BYERS AVE 4 1900 8,940.00 982 1 90.9 2206 EMPIRE 3 1900 22,040.00 1,350.00 1.5 88.3 2121 S MOFFET 4 1900 24,800.00 1,687.00 1.5 90.6 2111 S BYERS 2 1900 45,620.00 1,244.00 1 89.8 2305 EMPIRE 4 1900 12,890.00 952 1 107.9 2127 S MOFFET 2 1900 11,580.00 1,087.00 1 93.1 2301 EMPIRE 4 1900 7,250.00 973 1 103.0 2431 S PICHER 5 1900 7,640.00 756 1 163.2 2010 S BYERS 3 1900 18,530.00 1,052.00 1 79.3 2526 MURPHY 9 1900 17,300.00 1,008.00 1 172.2 2015 S BYERS 4 1900 26,200.00 1,034.00 1 79.6 2329 EMPIRE AVE 6 1900 9,580.00 1,610.00 1.5 120.8 2201 & 2203 S MOFFET 3 1900 24,240.00 644 1 96.7 2325 S PICHER 6 1900 21,220.00 1,156.00 1 129.5 2202 KENTUCKY 6 1900 28,390.00 2,053.00 1.8 151.5 2421 EMPIRE 6 1905 8,610.00 624 1 158.2 2116 GRAND 6 1905 15,660.00 1,288.00 1 134.2 2315 S PICHER 4 1905 4,350.00 476 1 120.8 2319 EMPIRE AVE 4 1905 3,590.00 645 1 120.8 2227 EMPIRE 3 1905 55,990.00 872 1 98.3 2425 EMPIRE 4 1905 17,360.00 1,216.00 1 163.2 2215 EMPIRE 3 1905 26,850.00 2,086.00 1 91.0 2424 S TYLER 3 1905 15,430.00 1,036.00 1 140.5 2531 VIRGINIA 9 1905 15,320.00 806 1 157.3 2102 GRAND 9 1905 13,880.00 2,009.00 1.5 118.4 2524 KENTUCKY 9 1905 19,520.00 1,080.00 1.5 142.6 2425 S PICHER 4 1906 12,580.00 1,071.00 1 158.2 2008 GRAND 2 1910 22,430.00 1,877.00 1 102.0 2829 S JOPLIN 2 1910 10,010.00 620 1 101.0 2016 GRAND 3 1910 24,120.00 1,262.00 1 107.1 2006 GRAND 7 1910 21,520.00 1,676.00 2 98.6 2317 EMPIRE 4 1910 14,790.00 1,125.00 1 113.8 2005 KENTUCKY AVE 6 1910 19,160.00 1,368.00 1 97.0 2006 KENTUCKY 3 1910 17,070.00 1,208.00 1 93.5 2110 GRAND 6 1910 11,840.00 980 1 125.5 2030 GRAND 6 1910 18,600.00 1,496.00 1 111.9 2417 EMPIRE 6 1915 4,180.00 672 1 150.8 2528 EMPIRE 9 1915 11,160.00 1,250.00 1.5 172.8 2115 S MOFFET 2 1915 19,530.00 1,574.00 1.8 87.8 2126 GRAND 6 1915 11,860.00 910 1 145.5 2006 PENNSYLVANIA 3 1915 12,470.00 1,162.00 1 89.7 2007 S BYERS 2 1915 35,320.00 546 1 77.6 2407 S PICHER 6 1915 14,130.00 784 1 141.1

2120 GRAND 6 1915 17,500.00 1,726.00 1 145.5 2114 GRAND 6 1915 12,440.00 1,490.00 1 134.2 2528 PENNSYLVANIA 9 1915 14,560.00 960 1 153.2 1824 GRAND 2 1915 28,810.00 1,480.00 1 84.2 2202 S MOFFET 3 1918 19,760.00 1,212.00 1 95.2 2201 S BIRD 3 1920 68,850.00 1,050.00 1 88.5 2115 S BYERS 3 1920 32,150.00 1,440.00 1 89.8 2201 S SERGEANT 3 1920 4,460.00 593 1 93.0 2021 S MOFFET 2 1920 16,980.00 1,180.00 1 80.8 2827 S OLIVER 9 1920 7,390.00 1,108.00 1 143.3 2202 S PEARL 2 1920 25,120.00 1,496.00 2 101.0 2411 S WILLARD 6 1920 4,490.00 660 1 110.7 2405 EMPIRE 6 1920 10,170.00 748 1 141.1 2110 S BYERS 3 1920 29,860.00 1,590.00 1.5 85.9 2003 PENNSYLVANIA 3 1920 8,780.00 896 1 91.0 2201 KENTUCKY 7 1920 20,000.00 1,944.00 1.8 155.8 2026 GRAND 2 1920 14,670.00 1,045.00 1 111.9 2202 VIRGINIA 7 1920 21,070.00 1,221.00 1 120.5 2130 GRAND 6 1922 24,770.00 1,212.00 1 153.2 2513 EMPIRE AVE 3 1925 18,270.00 1,012.00 1 169.3 2401 S PICHER 6 1925 46,840.00 984 1 141.1 2225 S PICHER 2 1925 16,840.00 936 1 98.3 2323 S PICHER 3 1925 18,370.00 1,364.00 1 120.8 2212 GRAND 6 1925 15,180.00 1,136.00 1 161.8 2802 S OLIVER 6 1928 19,450.00 896 1 164.9 2305 S PICHER 2 1930 16,970.00 1,008.00 1 107.9 2521 S WALL 9 1930 28,830.00 1,539.00 1.5 173.5 2024 W 26TH 9 1930 10,390.00 1,038.00 1 167.5 2017 S FLORIDA 4 1930 19,680.00 1,260.00 1 165.7 2518 E 20TH 7 1930 22,390.00 1,748.00 1 170.2 1123 W 26TH 9 1930 7,480.00 660 1 171.3 2701 IRON GATES RD 2 1930 26,240.00 1,092.00 1 158.6 2920 E 22ND 1 1930 10,970.00 756 1 106.2 2301 S PICHER 4 1935 19,190.00 1,209.00 1 103.0 2830 S JOPLIN 6 1935 15,060.00 804 1 102.4 2444 W 26TH 6 1938 43,640.00 1,899.00 1 144.6 2715 S OLIVER 6 1940 8,250.00 850 1 170.6 2833 S WALL 3 1940 25,450.00 1,818.00 1 103.3 2202 W 26TH 6 1940 12,550.00 1,040.00 1 165.3 417 E 23RD 7 1940 54,670.00 4,400.00 2 165.0 3827 E 20TH 6 1940 23,660.00 1,448.00 1 173.6 2831 S PEARL 6 1941 28,570.00 2,052.00 1 105.8 2125 S BYERS 2 1941 53,700.00 921 1 92.9 2230 W 26TH 7 1941 19,870.00 1,297.00 1 164.1 2216 W 26TH 7 1941 21,790.00 1,347.00 1 164.7 2330 E 20TH 9 1943 11,290.00 780 1 170.2 2217 EMPIRE 2 1944 26,480.00 1,158.00 1 94.7 2529 KENTUCKY 7 1944 25,970.00 1,466.00 1 145.7 2922 E 22ND 2 1945 10,600.00 832 1 106.2 2805 S OLIVER 6 1946 28,100.00 1,394.00 1 154.4 2725 S OLIVER AVE 7 1946 52,450.00 952 1 166.3 2703 S OLIVER 7 1946 15,920.00 1,308.00 1 172.8 2521 CONNOR 6 1950 10,890.00 696 1 173.0 2136 ARIZONA 6 1950 25,410.00 2,366.00 1 113.5 2520 E 20TH 9 1950 13,030.00 1,050.00 1 170.2 2133 MISSISSIPPI 6 1950 33,060.00 1,812.00 1 113.5 2911 E 15TH 2 1950 39,550.00 1,304.00 1 93.8 2921 E 15TH 4 1950 21,650.00 832 1 93.8 2925 E 15TH 3 1950 17,360.00 1,080.00 1 93.8 2920 S PEARL 2 1950 78,420.00 1,673.00 1 101.4 2636 E 20TH 7 1950 29,460.00 1,427.00 1 170.2 2112 MISSISSIPPI 4 1950 28,740.00 1,677.00 1 122.9

2002 ARIZONA 6 1950 18,280.00 1,552.00 1 170.2 2003 MISSISSIPPI 4 1950 26,840.00 1,948.00 1 170.2 2028 MISSISSIPPI 8 1950 29,280.00 1,511.00 1 144.7 2039 MISSISSIPPI 8 1950 25,010.00 1,294.00 1 136.3 2036 MISSISSIPPI 6 1950 23,700.00 1,284.00 1 144.7 2202 S OZARK 2 1950 59,530.00 1,588.00 1 106.2 2004 MISSISSIPPI 6 1950 25,060.00 1,348.00 1 170.2 2202 MISSISSIPPI 2 1950 16,720.00 972 1 106.2 2020 MISSISSIPPI 8 1950 25,370.00 1,562.00 1 155.7 2012 MISSISSIPPI 6 1950 26,650.00 1,344.00 1 165.7 2825 PENNSYLVANIA 2 1950 48,920.00 1,057.00 1 95.6 2830 VIRGINIA 3 1950 19,020.00 1,014.00 1 99.1 2014 DELAWARE AVE 7 1950 20,360.00 1,130.00 1 165.8 1938 S PARKWOOD LN 4 1950 32,840.00 1,085.00 1 94.7 2425 S DUQUESNE RD 3 1950 17,880.00 1,548.00 1 102.4 2510 S DUQUESNE RD 4 1950 67,720.00 1,767.00 1 94.3 4005 E 20TH 4 1950 31,030.00 2,392.00 1 169.5 2626 E 20TH 6 1951 28,410.00 1,262.00 1 170.2 2831 VIRGINIA 3 1951 7,040.00 920 1 98.1 3853 E 20TH 3 1951 17,050.00 1,086.00 1 171.9 2829 E 15TH 6 1952 31,760.00 1,529.00 1 93.8 2029 MISSISSIPPI 9 1952 25,740.00 1,539.00 1 144.7 2616 E 20TH ST 4 1952 23,690.00 1,320.00 1 170.2 2002 S HIGHVIEW 9 1953 24,550.00 1,550.00 1 170.2 2104 MISSISSIPPI 6 1953 40,640.00 2,667.00 1 129.0 2604 W 26TH 4 1953 36,740.00 1,392.00 1 154.2 2120 MISSISSIPPI AVE 6 1953 29,900.00 1,772.00 1 118.2 2724 S GRAND 3 1953 18,670.00 1,231.00 1 100.9 2102 S BROWNELL 6 1953 36,340.00 2,183.00 1 146.6 2016 S HIGHVIEW 6 1953 24,950.00 1,614.00 1 155.7 2725 S KENTUCKY 3 1953 16,130.00 1,056.00 1 102.8 2107 ALABAMA 6 1953 38,540.00 1,959.00 1 122.9 2515 EMPIRE 3 1954 18,640.00 1,300.00 1 171.3 1136 W 26TH ST 9 1954 20,070.00 936 1 174.0 2044 MISSISSIPPI 6 1954 25,440.00 1,469.00 1 136.3 2121 MISSISSIPPI AVE 6 1954 21,550.00 1,283.00 1 122.9 2503 EMPIRE 6 1954 25,490.00 1,184.00 1 166.6 3819 E 20TH 6 1954 30,930.00 1,592.00 1 173.9 2143 S BROWNELL 6 1955 25,840.00 1,280.00 1 113.5 2103 MISSISSIPPI 6 1955 27,270.00 1,824.00 1 129.0 2021 MISSISSIPPI 6 1955 33,670.00 1,834.00 1 155.7 2726 MISSOURI 3 1955 51,920.00 1,356.00 1 98.8 2026 ARIZONA 6 1955 22,550.00 1,232.00 1 144.7 2024 GRAND 2 1955 9,800.00 576 1 107.1 2001 ARIZONA 7 1955 22,530.00 1,410.00 1 170.2 2029 S FLORIDA 6 1955 25,070.00 1,399.00 1 155.7 2027 MISSISSIPPI 6 1955 35,230.00 2,363.00 1 144.7 2415 S PICHER 3 1955 12,520.00 792 1 150.8 2103 S FLORIDA AVE 6 1955 31,470.00 1,632.00 1 144.7 2032 ARIZONA 6 1955 21,010.00 1,240.00 1 144.7 2122 S FLORIDA 6 1955 26,690.00 1,479.00 1 122.9 2035 S OZARK 9 1955 19,510.00 1,248.00 1 136.3 2035 ARIZONA 6 1955 21,570.00 1,299.00 1 136.3 2020 ARIZONA 4 1955 26,860.00 1,712.00 1 155.7 2118 S FLORIDA 6 1955 30,530.00 1,833.00 1 129.0 2135 S BROWNELL 6 1955 29,020.00 1,452.00 1 118.2 2136 S FLORIDA AVE 9 1955 27,970.00 1,323.00 1 118.2 2729 S GRAND 3 1955 13,610.00 1,236.00 1 99.8 4313 E 20TH ST 6 1955 49,370.00 1,598.00 1 114.1 2417 PICHER 6 1956 13,900.00 804 1 150.8 2131 S OZARK 6 1956 33,780.00 2,128.00 1 113.5 2131 S FLORIDA 4 1956 29,080.00 1,509.00 1 118.2

2006 S OZARK 9 1956 55,840.00 4,155.00 1 144.7 2201 MISSISSIPPI AVE 1 1956 80,210.00 1,555.00 1 106.2 2729 S MISSOURI 3 1956 41,850.00 1,166.00 1 98.1 4317 E 20TH 6 1956 31,600.00 1,825.00 1 113.5 2023 ARIZONA 4 1957 24,900.00 1,671.00 1 144.7 2011 ARIZONA 6 1957 20,090.00 1,473.00 1 165.7 2008 ARIZONA 4 1957 25,290.00 1,356.00 1 165.7 2005 ARIZONA 6 1957 21,980.00 1,312.00 1 165.7 2123 S BROWNELL 8 1957 26,170.00 1,405.00 1 122.9 2029 ARIZONA 4 1957 25,300.00 1,489.00 1 144.7 2104 S FLORIDA 6 1957 34,430.00 1,452.00 1 144.7 2204 S FLORIDA 3 1957 39,560.00 1,652.00 1 106.2 2018 S FLORIDA AVE 9 1957 25,410.00 1,622.00 1 165.7 2515 S PICHER 9 1958 20,750.00 1,066.00 1 171.3 2101 TEXAS 4 1958 27,830.00 1,549.00 1 129.0 2134 MISSISSIPPI 6 1958 29,010.00 1,666.00 1 113.5 2142 S FLORIDA 6 1958 34,170.00 1,605.00 1 113.5 2816 W 26TH 6 1958 21,270.00 1,372.00 1 125.8 2039 S OZARK 6 1958 22,650.00 1,356.00 1 136.3 2001 S OZARK 6 1958 27,270.00 1,518.00 1 170.2 2110 S BROWNELL 4 1958 29,720.00 1,426.00 1 137.6 2507 S PICHER 6 1958 24,350.00 1,708.00 1 169.3 2014 ARIZONA 8 1958 22,490.00 1,546.00 1 165.7 2121 S FLORIDA 6 1958 32,080.00 1,736.00 1 122.9 2036 S OZARK 4 1958 63,990.00 4,456.00 1 144.7 2521 WISCONSIN AVE 4 1958 32,040.00 2,150.00 2 94.8 2129 S BROWNELL 6 1958 27,680.00 1,534.00 1 118.2 2117 S BROWNELL 6 1958 27,770.00 1,460.00 1 129.0 2730 S IOWA 3 1958 24,970.00 1,410.00 1 94.9 2103 ALABAMA 6 1958 20,590.00 1,066.00 1 129.0 2830 W 26TH 6 1959 27,570.00 1,192.00 1 119.4 2140 S BROWNELL 6 1959 30,130.00 1,473.00 1 113.6 2101 ARIZONA 6 1959 47,040.00 1,454.00 1 129.0 2112 S FLORIDA AVE 6 1959 29,640.00 1,609.00 1 136.3 2111 S FLORIDA 6 1959 31,590.00 1,712.00 1 136.3 0 S BROWNELL 6 1959 28,850.00 1,510.00 1 136.3 2103 S BROWNELL 6 1959 30,990.00 1,543.00 1 144.7 2526 ILLINOIS 3 1959 42,290.00 3,141.00 1 104.1 2201 ALABAMA 6 1959 28,090.00 1,502.00 1 106.2 2119 ALABAMA AVE 6 1959 42,080.00 2,712.00 1 113.5 2115 ALABAMA 6 1959 32,240.00 1,393.00 1 118.2 2111 ALABAMA 6 1959 33,350.00 1,915.00 1 122.9 2615 W 32ND 4 1960 27,290.00 1,800.00 2 110.9 2106 S OZARK 6 1960 31,360.00 1,785.00 1 129.0 2107 S OZARK 4 1960 30,440.00 1,777.00 1 129.0 2108 ARIZONA 8 1960 22,660.00 1,316.00 1 122.9 2608 E 20TH 6 1960 18,530.00 1,536.00 1 170.2 2501 S PICHER 6 1960 17,750.00 960 1 166.6 2602 E 20TH ST 7 1960 17,060.00 1,032.00 1 170.2 2104 ALABAMA 6 1960 30,090.00 1,766.00 1 129.0 2044 S HIGHVIEW 6 1960 27,830.00 1,776.00 2 129.0 2041 ARIZONA 6 1960 29,110.00 1,742.00 1 129.0 2130 S OZARK 4 1960 35,530.00 1,740.00 1 113.5 2001 MARYLAND 4 1960 21,440.00 1,120.00 1 172.0 2005 S OZARK 6 1960 31,320.00 1,826.00 1 165.7 2020 S HIGHVIEW 6 1960 18,570.00 1,368.00 1 144.7 2021 S OZARK 6 1960 47,540.00 2,891.00 1 155.7 2107 ARIZONA 8 1960 19,700.00 1,371.00 1 122.9 2104 S HIGHVIEW 6 1960 25,750.00 1,366.00 1 129.0 2121 S OZARK AVE 4 1960 23,400.00 1,380.00 1 118.2 2116 S BROWNELL 6 1960 30,090.00 1,463.00 1 130.2 2122 ARIZONA 4 1960 27,610.00 1,638.00 1 118.2

2006 S HIGHVIEW AVE 6 1960 18,730.00 1,124.00 1 165.7 2133 S FLORIDA AVE 6 1960 32,160.00 1,589.00 1 113.5 2110 S OZARK 3 1960 32,450.00 1,414.00 1 122.9 2109 S OZARK 4 1960 23,440.00 1,288.00 1 122.9 2004 S OZARK 4 1960 27,770.00 1,224.00 1 155.7 2010 HIGHVIEW 6 1960 20,600.00 1,428.00 1 165.7 2102 ARIZONA 6 1960 22,510.00 1,281.00 1 129.0 2211 ARIZONA 6 1960 88,170.00 1,638.00 1 106.2 2120 S BROWNELL 8 1960 30,250.00 1,380.00 1 123.8 2120 S OZARK 4 1960 39,040.00 1,614.00 1 118.2 2111 ARIZONA 6 1960 20,910.00 1,260.00 1 118.2 2115 ARIZONA 3 1960 22,140.00 1,621.00 1 113.5 2112 ALABAMA 4 1960 27,800.00 1,467.00 1 118.2 2036 TEXAS 6 1960 24,010.00 1,558.00 1 144.7 2205 S BROWNELL 6 1960 28,850.00 1,508.00 1 106.2 2202 S HIGHVIEW 2 1960 39,510.00 2,304.00 1 106.2 2038 S HIGHVIEW 9 1960 21,360.00 1,426.00 1 136.3 2017 ARIZONA 6 1960 22,080.00 1,356.00 1 155.7 2527 ILLINOIS 2 1960 36,760.00 1,943.00 1 98.6 2128 S HIGHVIEW 8 1960 28,410.00 1,638.00 1 113.5 2119 ARIZONA 4 1960 27,920.00 1,768.00 1 113.5 2128 S BROWNELL 6 1960 29,010.00 1,394.00 1 118.4 2134 S BROWNELL 6 1960 37,830.00 1,623.00 1 118.4 1321 E 26TH 4 1960 41,840.00 1,680.00 1 90.6 2024 S FLORIDA AVE 8 1960 34,160.00 1,742.00 1 155.7 1423 E 26TH 3 1960 33,950.00 900 1 87.3 2205 S OZARK 4 1960 35,220.00 2,594.00 1 106.2 2102 ALABAMA 6 1960 68,820.00 1,888.00 1 144.7 2014 S FLORIDA 8 1960 20,570.00 1,374.00 1 165.7 4575 E 20TH ST 3 1960 28,180.00 1,571.00 1 101.1 2044 ARIZONA 4 1961 22,440.00 1,342.00 1 129.0 3029 W 27TH 2 1961 56,920.00 2,804.00 1 129.7 2127 S FLORIDA AVE 6 1961 30,780.00 1,745.00 1 122.9 2108 ALABAMA 6 1961 27,300.00 1,420.00 1 122.9 2118 ALABAMA 6 1961 33,490.00 1,401.00 1 118.2 2031 S OZARK 9 1961 27,670.00 1,763.00 1 144.7 2021 ALABAMA 6 1961 39,270.00 2,078.00 1 155.7 2122 ALABAMA 6 1962 31,430.00 1,467.00 1 113.5 2204 S BROWNELL 2 1962 36,710.00 1,836.00 1 106.2 2102 TEXAS 4 1962 24,070.00 1,532.00 1 129.0 2844 W 26TH 4 1962 42,520.00 1,770.00 1 109.6 2000 S OZARK 6 1962 34,380.00 1,976.00 1.5 170.2 4549 E 20TH 6 1962 25,550.00 1,456.00 1 106.6 1824 W 26TH 9 1963 9,200.00 802 1 168.9 2503 PICHER 6 1963 22,970.00 1,556.00 1 166.6 2102 S OZARK 6 1963 30,510.00 1,876.00 2 136.3 2128 ARIZONA 4 1963 26,420.00 1,545.00 1 113.5 2125 MISSISSIPPI 4 1963 24,160.00 1,287.00 1 118.2 2038 ARIZONA 4 1963 19,690.00 1,282.00 1 136.3 2731 IOWA AVE 2 1963 16,090.00 1,250.00 1 93.9 2201 S FLORIDA 4 1963 31,540.00 1,604.00 1 106.2 2027 ALABAMA 6 1963 34,860.00 1,960.00 1 144.7 2101 ALABAMA 6 1963 27,840.00 1,474.00 1 136.3 2525 NEW HAMPSHIRE 3 1963 19,170.00 1,650.00 1 88.1 4631 E 20TH ST 6 1963 41,230.00 2,056.00 1 87.4 2110 S HIGHVIEW 6 1964 19,060.00 1,176.00 1 122.9 2030 S HIGHVIEW AVE 8 1964 21,320.00 1,292.00 1 144.7 2531 KANSAS 4 1964 48,930.00 1,230.00 1 91.1

2223 W 26TH 7 1965 39,920.00 2,772.00 2 141.5 2611 S OLIVER 6 1965 29,670.00 1,215.00 1 172.0 2626 MINNESOTA AVE 3 1965 53,520.00 1,248.00 1 104.7 2113 TEXAS 4 1965 28,740.00 1,673.00 1 122.9 1219 E 26TH 3 1965 46,050.00 1,185.00 1 92.6 1211 E 26TH ST 3 1965 21,890.00 1,680.00 1 94.0 2122 TEXAS 3 1965 29,410.00 1,442.00 1 118.2 2120 DELAWARE 7 1965 21,230.00 1,458.00 1 131.0 2124 DELAWARE 8 1965 27,820.00 1,475.00 1 131.0 2131 TEXAS 6 1965 28,400.00 1,504.00 1 113.5 2602 MINNESOTA 3 1965 44,570.00 1,144.00 1 112.8 2630 S MINNESOTA AVE 2 1965 17,250.00 988 1 102.0 2024 ALABAMA 6 1965 22,740.00 1,165.00 1 144.7 2107 TEXAS 6 1966 26,130.00 1,365.00 1 129.0 2201 MC CONNELL 7 1966 35,230.00 1,772.00 1 111.6 2120 S HIGHVIEW 8 1966 34,010.00 2,020.00 1 118.2 2124 S HIGHVIEW 6 1966 24,290.00 1,512.00 1 113.5 2403 WILLARD 3 1967 9,360.00 930 1 106.2 2423 S PICHER 3 1967 18,010.00 1,242.00 1 158.2 2204 S PATTERSON 4 1967 35,620.00 1,762.00 1 111.0 2608 S MINNESOTA AVE 3 1967 34,690.00 980 1 111.0 2547 MISSOURI 6 1967 35,060.00 1,425.00 1 123.4 2548 MISSOURI 7 1967 26,730.00 1,384.00 1 127.5 2926 S MONROE 6 1968 32,130.00 1,844.00 1 127.4 902 E 24TH 7 1968 37,410.00 2,572.00 2 139.3 2402 INDIANA 4 1968 70,480.00 3,096.00 1 136.6 2202 ALABAMA 4 1968 25,470.00 1,372.00 1 106.2 2520 INDIANA 3 1968 36,840.00 1,752.00 1 108.3 4021 E 25 TH ST 6 1968 28,760.00 1,688.00 1 107.3 2828 S WALL 6 1969 40,400.00 2,240.00 2 104.8 2116 DELAWARE 7 1969 15,380.00 1,036.00 1 138.3 3016 S MONROE 6 1969 34,410.00 1,716.00 1 121.6 2130 DELAWARE 7 1969 34,460.00 1,850.00 1 124.7 4111 E 20TH 6 1969 44,820.00 2,612.00 1 125.9 2702 S MONROE 6 1970 46,360.00 2,426.00 1 173.7 2431 ADELE 4 1970 19,420.00 800 1 125.7 2712 S MONROE 6 1970 40,670.00 1,430.00 1 173.7 2027 TEXAS 8 1970 19,670.00 986 1 144.7 2114 TEXAS 2 1970 25,370.00 1,558.00 1 122.9 2525 MURPHY 8 1970 29,190.00 1,636.00 1 172.3 3102 S MONROE 6 1970 30,630.00 1,542.00 1 112.2 2302 W 29TH 7 1970 38,790.00 2,490.00 1 142.3 2028 TEXAS 6 1970 27,240.00 1,606.00 1 144.7 2039 TEXAS 6 1970 28,460.00 1,614.00 1 136.3 2108 TEXAS 6 1970 30,600.00 1,424.00 1 122.9 2040 TEXAS 9 1970 30,540.00 1,343.00 1 136.3 1435 E 26TH 3 1970 42,640.00 1,550.00 1 86.3 1501 E 26TH 4 1970 15,370.00 1,036.00 1 85.6 2530 GRAND 9 1970 20,130.00 1,168.00 1 134.9 1437 E 26TH 3 1970 51,980.00 1,036.00 1 86.3 4201 E 25TH ST 6 1970 22,550.00 1,200.00 1 116.0 4027 E 25TH ST 2 1970 76,500.00 1,716.00 1 110.0 4023 E 25TH ST 6 1970 26,040.00 1,200.00 1 108.0

4015 E 25TH ST 3 1970 49,510.00 1,188.00 1 108.7 4225 E 25TH ST 6 1970 36,360.00 1,536.00 1 125.4 4101 E 20TH 6 1970 49,290.00 2,136.00 1 130.3 4129 E 25TH ST 4 1970 27,420.00 1,330.00 1 112.5 3122 S MONROE 2 1971 33,190.00 1,800.00 1 101.9 2402 MONTANA 8 1971 18,840.00 1,192.00 1 114.3 2412 MONTANA 3 1971 26,920.00 1,568.00 1 102.4 2547 GRAND 6 1971 25,730.00 1,342.00 1 129.4 2110 DELAWARE AVE 8 1971 18,360.00 1,128.00 1 147.1 2406 MONTANA 2 1971 21,230.00 1,036.00 1 109.7 2525 OHIO 3 1971 52,610.00 1,669.00 1 109.7 2408 MONTANA 2 1971 18,250.00 1,036.00 1 106.3 2404 MONTANA PL 4 1971 32,080.00 1,591.00 1 113.5 2015 MARYLAND 6 1971 43,230.00 2,426.00 1 168.7 4221 E 25TH ST 3 1971 49,450.00 1,511.00 1 123.0 4421 E 25TH ST 6 1971 65,400.00 1,518.00 1 153.6 3106 S MONROE 3 1972 31,390.00 1,360.00 1 108.4 2804 S OLIVER 8 1972 22,670.00 1,756.00 1 155.0 3026 S MONROE 6 1972 31,750.00 1,474.00 1 116.6 2106 ALABAMA 6 1972 30,000.00 1,610.00 1 136.3 4501 E 25TH ST 8 1972 20,360.00 1,408.00 1 167.7 2202 TEXAS 3 1973 37,330.00 1,744.00 1 106.2 3112 S MONROE 3 1973 72,280.00 1,306.00 1 104.9 4011 E 25TH ST 6 1973 80,820.00 2,153.00 1 104.1 4571 E 25TH ST 6 1973 22,130.00 1,050.00 1 163.9 4561 E 25TH ST 8 1973 24,870.00 1,330.00 1 165.7 4431 E 25TH ST 6 1973 35,790.00 1,400.00 1 164.8 4471 E 25TH ST 8 1973 27,530.00 1,300.00 1 173.6 2505 S WILLARD 7 1974 18,510.00 962 1 132.5 4211 E 25TH ST 6 1974 23,610.00 1,440.00 1 117.9 0 E 25TH ST 7 1974 21,490.00 1,050.00 1 147.7 4401 E 25TH ST 6 1974 18,860.00 1,075.00 1 139.5 4521 E 25TH ST 6 1974 36,720.00 2,126.00 1 173.0 4581 E 25TH ST 6 1974 33,060.00 1,550.00 1 158.5 4461 E 25TH ST 9 1974 25,220.00 1,260.00 1 172.1 4451 E 25TH ST 7 1974 32,160.00 1,437.00 1 171.1 11 BRIARWOOD LN 6 1975 105,350.00 3,468.00 1 115.8 2145 -2149 W 32ND 4 1975 35,640.00 1,848.00 1 90.3 2134 TEXAS 6 1975 39,450.00 1,830.00 1 113.5 2128 TEXAS AVE 4 1975 28,260.00 1,542.00 1 113.5 2123 TEXAS 6 1975 29,500.00 1,463.00 1 113.5 2202 ARIZONA 3 1975 78,500.00 1,718.00 1 106.2 2201 TEXAS 6 1975 33,040.00 1,640.00 1 109.3 2016 DELAWARE 8 1975 21,420.00 1,560.00 1 158.0 4229 E 25TH ST 6 1975 42,090.00 1,628.00 1 130.6 4551 E 25TH ST 6 1975 21,030.00 1,050.00 1 169.0 4511 E 25TH ST 9 1975 32,600.00 1,676.00 1 173.9 4441 E 25TH ST 6 1975 19,640.00 1,075.00 1 168.9 2126 S REINMILLER RD 4 1975 33,430.00 1,738.00 1 94.9 2606 JEFFERSON 6 1976 52,670.00 2,592.00 1 151.5 2122 PATTERSON 6 1976 30,330.00 1,417.00 1 120.1 2603 S MONROE 8 1976 38,460.00 2,115.00 1 163.0 2831 S MONROE 4 1976 47,750.00 2,736.00 2 166.5

2201 S PATTERSON 7 1976 36,190.00 1,424.00 1 110.2 4239 E 25TH ST 6 1976 31,100.00 1,589.00 1 133.4 4541 E 25TH ST 6 1976 24,320.00 1,392.00 1 170.3 4531 E 25TH ST 8 1976 37,680.00 1,741.00 1 166.1 3132 S MONROE 6 1977 125,680.00 2,848.00 2 96.5 2634 S MONROE 6 1977 36,700.00 1,380.00 1 170.9 2730 S MONROE 8 1977 43,540.00 2,010.00 1 173.7 2107 S PATTERSON 9 1977 42,720.00 1,800.00 1 137.7 2125 S PATTERSON 6 1977 42,160.00 2,187.00 1 119.2 2117 S PATTERSON 9 1977 33,510.00 1,572.00 1 131.2 2127 S PATTERSON AVE 9 1977 32,300.00 1,485.00 1 114.4 2118 S PATTERSON 8 1978 31,600.00 1,401.00 1 125.7 2121 S PATTERSON 8 1978 38,260.00 1,855.00 1 124.8 2722 S MONROE 7 1979 35,430.00 1,538.00 1 174.0 2110 S PATTERSON 7 1979 35,680.00 1,442.00 1 131.2 2126 S PATTERSON 7 1979 35,940.00 1,590.00 1 115.2 2626 MONROE 9 1979 31,950.00 1,380.00 1 168.6 2121 TEXAS 6 1979 30,000.00 1,496.00 1 118.2 2106 S PATTERSON 9 1979 35,140.00 1,489.00 1 138.8 2114 S PATTERSON AVE 8 1979 35,600.00 1,412.00 1 124.8 2102 S PATTERSON 8 1979 36,620.00 1,893.00 1 147.9 2828 S OLIVER 6 1980 26,790.00 1,225.00 1 149.3 2101 S PATTERSON 8 1980 35,140.00 1,480.00 1 146.6 2033 TEXAS 6 1980 30,140.00 1,606.00 1 144.7 2812 MONROE 6 1981 48,440.00 2,138.00 1 170.4 2602 ADELE 9 1981 36,740.00 1,920.00 2 166.7 2020 ALABAMA 6 1981 41,170.00 1,674.00 1 155.7 2001 TEXAS 7 1983 24,430.00 1,302.00 1 170.2 2002 TEXAS 9 1983 28,870.00 1,302.00 1 170.2 2804 S MONROE 7 1984 65,790.00 2,440.00 1 172.5 2531 EMPIRE 9 1984 31,950.00 1,848.00 1 172.8 2008 TEXAS 8 1984 28,370.00 1,330.00 1 165.7 2013 TEXAS 9 1984 26,120.00 1,302.00 1 165.7 2019 TEXAS 9 1984 29,720.00 1,302.00 1 155.7 2019 & 2021 MARYLAND 8 1984 67,840.00 1,736.00 1 160.8 2820 S MONROE 8 1985 36,550.00 1,489.00 1 164.9 2402 GRAND 9 1986 54,370.00 3,115.00 1 173.9 2702 S OLIVER 7 1986 36,410.00 1,476.00 1 173.5 2231 W 29TH 8 1986 34,870.00 1,435.00 1 164.9 2914 E 22ND 6 1986 36,340.00 1,265.00 1 106.2 2902 E 22ND 6 1986 29,550.00 1,200.00 1 106.2 2410 S TYLER 3 1988 25,380.00 1,081.00 1 114.1 2302 W 25TH 2 1988 47,020.00 2,286.00 1 124.4 2501 DELAWARE 2 1988 73,320.00 1,404.00 1 77.5 2307 CONNECTICUT 6 1988 25,260.00 1,104.00 1 104.3 4581 E 24TH ST 3 1988 28,080.00 1,144.00 1 127.3 4580 E 24TH ST 4 1989 30,790.00 1,137.00 1 145.8 2201 E 26TH 2 1990 75,600.00 1,168.00 1 79.5 2020 W 26TH 8 1992 47,400.00 1,836.00 1 168.0 3061 S DAY RD 7 1994 29,980.00 1,344.00 1 169.3 2930 S OLIVER 3 1995 52,130.00 1,947.00 1 119.8 2202 E 22ND 7 1995 43,790.00 1,714.00 1 113.0 3030 ABIGAIL LN 6 1996 136,820.00 4,001.00 1.5 169.3

2214 W 29TH 4 1996 30,290.00 1,234.00 1 135.7 2321 WILLARD AVE 2 1997 67,200.00 1,155.00 1 94.3 2230 WILLARD 2 1997 82,000.00 1,372.00 1 86.1 2208 E 22ND ST 6 1997 37,190.00 1,474.00 1 113.0 2413 EMPIRE 3 1997 22,370.00 1,050.00 1 150.8 3018 SUNSET W DR 6 1998 148,250.00 3,964.00 2 172.3 3102 ABIGAIL ST 7 1998 131,300.00 4,488.00 2 159.7 2107 E 26TH ST 3 1998 84,420.00 1,452.00 1 79.8 2017 E 26TH ST 2 1998 84,140.00 1,448.00 1 81.3 2214 E 22ND ST 6 1998 35,140.00 1,340.00 1 112.3 3030 JESSICA DR 7 1998 159,680.00 5,608.00 1.5 169.3 3101 ABIGAIL LN 7 1999 122,430.00 2,482.00 1 159.7 3110 SUNSET DR 6 1999 139,860.00 4,033.00 2 159.7 2101 E 26TH 2 2000 86,560.00 1,452.00 1 81.0 3018 JESSICA DR 8 2000 126,060.00 4,570.00 1 173.6 3131 KELLEY 6 2003 127,310.00 2,634.00 1 132.5 3118 KELLEY DR 3 2003 154,120.00 3,921.00 1.5 139.2 2228 W 29TH ST 2 2003 104,440.00 1,574.00 1 145.7 3031 KELLEY DR 7 2003 126,710.00 3,345.00 1 169.3 2221 W 29TH ST 9 2003 39,020.00 1,288.00 1 159.5 2601 JEFFERSON 7 2004 41,110.00 1,405.00 1 147.1 3130 KELLY DR 2 2004 343,520.00 3,312.00 1 132.5 3117 S KELLEY DR 7 2005 110,890.00 2,554.00 1 139.2 2225 S HARLEM 2 2006 33,940.00 1,324.00 1 94.7 1224 24THST 6 2006 35,300.00 1,222.00 1 129.5 3102 SUNSET EAST DR 7 2007 191,930.00 6,419.00 1 148.3 2702 S WASHINGTON 4 2007 74,470.00 2,079.00 1 151.2 2631 OLIVER 7 2009 85,840.00 1,505.00 1 173.9

Appendix B: MATLAB R2015 script used to generate graphs of parameters

%Histograms and bar graphs of parameters

%Alyssa Egnew

%Revised March 2, 2016 clc load('Joplin488.mat') figure(1) hist(Distance,2*length(Distance)^(1/3)) title('Distance from Tornado Centerline Distribution') xlabel('Distance (ft)') ylabel('Number of Homes')

%Generates histogram of Distance %Number of bins typically taken as 2*length(Variable)^(1/3)

figure(2) for jj= 1:10

index = find(DOD == jj);

DOD_Counts(jj) = length(index); end %Finds how many instances of each DOD rating there are in the set of homes bar(1:10,DOD_Counts) title('Degree of Damage Distribution') xlabel('DOD Rating') ylabel('Number of Homes')

%Generates bar graph of the number of instances in each DOD rating

figure(3) hist(YearBuilt,2*length(YearBuilt)^(1/3)) title('Year Built Distribution') xlabel('Year Built') ylabel('Number of Homes')

%Generates histogram of Year Built

figure(4)

hist(APRBLDG,2*length(APRBLDG)^(1/3)) title('Appraised Value Distribution') xlabel('Appraised Value') ylabel('Number of Homes')

%Generates histogram of Appraised Value figure(5) hist(SFLA,2*length(SFLA)^(1/3)) title('Square Footage Distribution') xlabel('Square Footage') ylabel('Number of Homes')

%Generates histogram of Square Footage

figure(6) hist(WindSpeed,2*length(WindSpeed)^(1/3)) title('Maximum Wind Speeds Distribution') xlabel('Wind Speed') ylabel('Number of Homes')

%Generates histogram of maximum wind speeds encountered by the homes

for kk= 1:2

index2 = find(Stories == kk);

Stories_Counts(kk) = length(index2); end %Finds how many instances of each number of stories there are in the set of homes

figure(7) bar(1:2,Stories_Counts) title('Number of Stories Distribution') xlabel('Number of Stories') ylabel('Number of Homes')

%Generates bar graph of stories distribution

Appendix C: MATLAB R2015 script used to generate multinomial logistic regression with random input

%Multinomial Logistic Regression with an Ordinal Response and Random %Predictor Variable to Test Significance of Predictors in Likelihood %Model

%Alyssa Egnew

%Revised December 13, 2015 clc clear all load Joplin488.mat random = randn(488,1); %Dummy variable to check method. %p-value for this variable should be high since we know it has no correlation. %.05 p-value for significance (less than .05 used)

X = [Stories YearBuilt SFLA APRBLDG WindSpeed random]; %Create predictor variables (input variables) categories = [1,2,3,4,5,6,7,8,9]; damage = ordinal(DOD,{'1','2','3','4','5','6','7','8','9'},categories); %Create an ordinal object based on categories 1 through 9. %This is your response variable.

[B,dev,stats] = mnrfit(X,damage,'model','ordinal'); %Fit your predictor variables and ordinal response variable using multinomial %logistic regression

B stats.p %B gives coefficients and y-intercepts for likelihood equation %stats.p gives p-values for significance of B-values

Appendix D: MATLAB R2015 script used to generate multinomial logistic regression with significant parameters only

%Multinomial Logistic Regression with an Ordinal Response to Create a %Sample Likelihood Model for DOD 3

%Alyssa Egnew

%Revised February 22, 2016

clc % clear all % load('Joplin488.mat')

X = [YearBuilt SFLA APRBLDG/1000 WindSpeed]; %Create predictor variables (input variables); APRBLDG/1000 gives home values in xx thousands of $US categories = [1,2,3,4,5,6,7,8,9]; damage = ordinal(DOD,{'1','2','3','4','5','6','7','8','9'},categories); %Create an ordinal object based on categories 1 through 9. %This is your response variable.

[B,dev,stats] = mnrfit(X,damage,'model','ordinal'); %Fit your predictor variables and ordinal response variable using multinomial logistic regression

B; stats.p; %B gives coefficients and y-intercepts for likelihood equation %stats.p gives p-values for significance of B-values

[B(1:8)'; repmat(B(9:end),1,8)] %Displays full matrix of B for clarity

%Example (House #317 from the set of 488) % YB = 1975; % SF = 3468; % Val = 105350; % WS = 115.7957; %These are the actual values for each predictor variable. The full list of trial inputs is in the comments below.

Likelihood = exp(B(3) + B(9)*YB + B(10)*SF + B(11)*Val + B(12)*WS) % Multinomial logistic regression equation for DOD 3 (DOD 3 as an example to test with)

% Checking for limits of inputs and 10% of each range based on database: % Year Built: 1880-2009 % range: 129 % 10% of range: 12.9 % Square Footage: 476-6419

% range: 5943 % 10% of range: 594.3 % Value: $3590-$343520 % range: 339930 % 10% of range: 33993 % Wind Speed: 77.1530-174.0000 % range: 96.847 % 10% of range: 9.6847

% Home 317 input values: % Year Built: 1949.2, 1962.1, 1975, 1987.9, 2000.8 % Square Footage: 2279.4, 2873.7, 3468, 4062.3, 4656.6 % Value: 37364, 71357, 105350, 139343, 173336 % Wind Speed: 96.4263, 106.1110, 115.7957, 125.4804, 135.1651