Predicting Federal Emergency Management Agency Funding for U.S. Disasters

1 Supplemental Information

This document represents additional information about the data and results. The full code and detailed explanation of the figures can be found at the GitHub repository.

1.1 Exploratory analysis

The processed data were explored to characterize and summarize the relevant features, which can be found below.

Table ?? reflects the results of the exploratory data analysis. Between February 2012 and November 2021, there were 446 disaster declarations for states and territories. Funds requested by states or territories for FEMA ranged from -$855,200.3 to $4,388,540,486, with an average of $29,673,687, and FEMA funds obligated to the states and territories after reconciliation ranged from -$855,200.3 to $440,842,4297 with an average of $29,744,109.

	Overall (N=326)
Requested FEMA Funds
Mean (SD)	40600000 (255000000)
Median [Min, Max]	420000 [0.000000000000455, 4390000000]
Obligated FEMA Funds
Mean (SD)	40700000 (256000000)
Median [Min, Max]	434000 [0.000000000000455, 4410000000]
Average FEMA Cost Share
Mean (SD)	0.964 (0.0573)
Median [Min, Max]	1.00 [0.675, 1.00]
Federal Agencies Involved
Mean (SD)	6.23 (7.03)
Median [Min, Max]	3.00 [1.00, 55.0]
Percent of Counties Awarded IH
Mean (SD)	0.338 (1.59)
Median [Min, Max]	0.00197 [0, 27.7]
Percent of Counties Awarded PA
Mean (SD)	0.594 (1.56)
Median [Min, Max]	0.357 [0, 27.3]
Percent of Counties Awarded HM
Mean (SD)	0.476 (1.56)
Median [Min, Max]	0.207 [0, 27.3]
Response Duration (days)
Mean (SD)	1400 (898)
Median [Min, Max]	1180 [70.0, 3590]
Incident Duration (days)
Mean (SD)	136 (250)
Median [Min, Max]	14.0 [0, 660]
Declaration Month
January	71 (21.8%)
February	22 (6.7%)
March	22 (6.7%)
April	24 (7.4%)
May	22 (6.7%)
June	25 (7.7%)
July	13 (4.0%)
August	32 (9.8%)
September	31 (9.5%)
October	41 (12.6%)
November	9 (2.8%)
December	14 (4.3%)
Incident Year
Mean (SD)	2020 (2.89)
Median [Min, Max]	2020 [2010, 2020]
Incident Type
Biological	60 (18.4%)
Earthquake	4 (1.2%)
Fire	20 (6.1%)
Flood	61 (18.7%)
Hurricane	73 (22.4%)
Other	15 (4.6%)
Severe Ice Storm	4 (1.2%)
Severe Storm(s)	82 (25.2%)
Tornado	7 (2.1%)
Declaration Type
DR	261 (80.1%)
EM	65 (19.9%)
FEMA Region
Region I	27 (8.3%)
Region II	19 (5.8%)
Region III	25 (7.7%)
Region IV	62 (19.0%)
Region IX	31 (9.5%)
Region V	37 (11.3%)
Region VI	54 (16.6%)
Region VII	20 (6.1%)
Region VIII	24 (7.4%)
Region X	27 (8.3%)
Counties per State
Mean (SD)	75.3 (53.5)
Median [Min, Max]	67.0 [1.00, 254]
State Population
Mean (SD)	9310000 (10300000)
Median [Min, Max]	5710000 [577000, 39500000]

Figure 1.1 shows the FEMA Regions by state.

Figure 1.1: FEMA Regions

Figure 1.2 shows the number of disaster declarations per year, and Figure 1.3 shows the total FEMA funds (both requested and obligated) by states per year. The substantial peak in 2020 corresponds to the COVID-19 pandemic, and the one in 2017 represents the hurricane season with Hurricanes Irma, Harvey, and Maria. These characteristics can also be seen in Table 1.1, which represents FEMA Funding for the 3 Costliest Years (2012 - 2021).

Figure 1.2: Number of disaster declarations per year 2012 - 2021

Figure 1.3: State or territory requested FEMA funds and obligated FEMA funds by year 2012 - 2021

Table 1.1: Table 2. FEMA Funding for the 3 Costliest Years (2012 - 2021)

Variable	Year
	2012, N = 331	2017, N = 361	2020, N = 851
Requested Funds	11,106,321 (55,959,108)	155,310,630 (735,733,161)	74,188,913 (115,267,136)
Obligated Funds	11,388,973 (56,050,414)	155,887,178 (739,000,529)	74,194,235 (115,269,357)
1 Mean (SD)

Figure 1.4 shows the number of disaster declarations per month, and Figure 1.5 shows the total FEMA funds (both requested and obligated) by states per month. The substantial peak in January likely corresponds to the COVID-19 pandemic, and the ones in August, September, and October represent the peak hurricane season. These characteristics can also be seen in Table 1.2, which represents FEMA Funding for the 3 Costliest Months.

Figure 1.4: Number of disaster declarations per month for years 2012 - 2021

Figure 1.5: State or territory requested FEMA funds and obligated FEMA funds by month for 2012 - 2021

Table 1.2: Table 3. FEMA Funding for the 3 Costliest Months (2012 - 2021)

Variable	Month
	Jan1	Sept1	Oct1
Requested Funds	63,229,783 (111,136,115)	100,831,890 (639,779,995)	22,992,573 (101,460,411)
Obligated Funds	63,239,449 (111,135,744)	101,252,822 (642,677,256)	23,165,582 (101,470,263)
1 Mean (SD)

All 50 states as well as Washington, DC were included in the final, combined dataset. Table 1.3 provides the five most disaster-prone states and summarizes their requested FEMA funding and received FEMA funding over the study period.

Table 1.3: Table 4. FEMA Funding for 5 Most Disaster-Prone States 2012 - 2021

Variable	State					SD, N = 101	TX, N = 161	WA, N = 111	WV, N = 101
	CA, N = 191	FL, N = 131	LA, N = 161	MN, N = 101	OK, N = 101
Requested Funds	65,900,489 (173,898,625)	37,851,532 (78,320,708)	47,187,723 (104,127,805)	4,758,425 (13,184,247)	6,413,888 (14,086,311)	2,727,818 (7,026,623)	48,019,502 (135,429,624)	14,599,599 (47,096,442)	10,655,340 (32,155,687)
Obligated Funds	65,900,489 (173,898,625)	37,851,532 (78,320,708)	47,187,723 (104,127,805)	4,758,425 (13,184,247)	6,413,888 (14,086,311)	2,727,818 (7,026,623)	48,087,226 (135,451,571)	14,599,599 (47,096,442)	10,656,415 (32,155,346)
1 Mean (SD)

Incident duration ranged from zero days to 660 days (or almost two years), as seen by Figure 1.6. The incident duration of 660 days likely corresponds to the COVID-19 pandemic, which is an ongoing incident of almost two years. Further analysis of all variables can be found in the supplementary information.

Figure 1.6: Incident duration for requested FEMA funds and obligated FEMA funds under $1 billion for 2012 - 2021

1.2 Modeling Analysis

Prior to fitting the data to machine learning models, standard simple and multivariable regression models were fitted using the tidymodels framework in RStudio 4.1. Both outcomes of interest were fitted, using incident duration as the primary predictor of interest. Figure @ref(fig:req_MVR_bp) and @ref(fig:obl_MVR_bp) show the significant variables fitted in the multivariable regression models for requested and obligated FEMA funds, respectively. There are simply too many variables to be able to report all variables on one figure.

(#fig:req_MVR_bp)Significant predictors in multivariate regression model for requested FEMA funds

(#fig:obl_MVR_bp)Significant predictors in multivariate regression model for obligated FEMA funds

Table 1.4 shows the comparisons of the models, using the root mean square error (RMSE) and r-squared statistics. The requested and obligated funding models performed almost identically. None of the models fit the data well, which suggests more sophisticated modeling practices are necessary to adequately characterize the data.

Table 1.4: Linear model comparisons

	Obligated	Requested
MVR: rmse	3.2825340	3.2821346
MVR: rsq	0.5767613	0.5765888
SLR: rmse	4.6045374	4.6012644
SLR: rsq	0.1672034	0.1678456

1.3 Machine Learning Models

The identified decision tree model for each outcome is illustrated by Figures 1.7 and 1.8.

Figure 1.7: Selected decision tree for predicting requested FEMA funds

Figure 1.8: Selected decision tree for predicting obligated FEMA funds

The most important variables in the identified random forest model for each outcome is illustrated by Figures 1.9 and 1.10.

Figure 1.9: 20 most important variables for the random forest model for requested FEMA funds

Figure 1.10: 20 most important variables for the random forest model for obligated FEMA funds

The most important variables in the identified elastic net model for each outcome is illustrated by Figures 1.11 and 1.12.

Figure 1.11: 20 most important variables for the elastic net model for requested FEMA funds

Figure 1.12: 20 most important variables for the elastic net model for obligated FEMA funds

The most important variables in the identified LASSO model for each outcome is illustrated by Figures 1.13 and 1.14.

Figure 1.13: 20 most important variables for the LASSO model for requested FEMA funds

Figure 1.14: 20 most important variables for the LASSO model for obligated FEMA funds

Table 1.5 shows the model comparisons for estimating requested FEMA funding, and Table 1.6 similarly shows the model comparisons for estimating obligated FEMA funding.

Table 1.5: ML model comparison for requested FEMA funding

rmse	SE	model
5.388000	2.3019	LASSO
5.394000	2.3023	EN
5.552000	2.2316	RF
5.679000	2.1802	Tree
5.276854	0.0000	Null - Train

Table 1.6: ML model comparison for obligated FEMA funding

rmse	SE	model
5.38900	2.3020	LASSO
5.39500	2.3023	EN
5.55200	2.2302	RF
5.70700	2.1712	Tree
5.27838	0.0000	Null - Train

Once the random forest was fit to the test data, the following diagnostic plots were created for each outcome.

For Requested FEMA Funding:

Figure 1.15: Actual vs predicted log(requested FEMA funds) for the random forest test model

Figure 1.16: Requested FEMA funds residuals for the random forest test model

Figure 1.17: Residuals versus fitted values of the log(requested FEMA funds) for the random forest test model

For Obligated FEMA Funding:

Figure 1.18: Actual vs predicted log(obligated FEMA funds) for the random forest test model

Figure 1.19: Obligated FEMA funds residuals for the random forest test model

Figure 1.20: Residuals versus fitted values of the log(obligated FEMA funds) for the random forest test model