# How to Predict a Fire in Hartford

# Introduction

Time sensitive industries the world over are constantly trying to innovate new ways to maximize their staffing efficiency, making sure to have the exact number of needed personnel on hand at all times. Too many people incurs unnecessary costs, while too few guarantees poor output.

Nobody knows this need better then those working in emergency services. Too many people on the clock at once can lay waste to a fragile operating income, while too few at the wrong time can spell disaster for those in need of emergency services.

# Methodology

Using data from Axibase Dataset Catalog released by the City of Hartford, call volume to the local fire department can be analyzed and visualized to predict future infrastructural needs in one of the most vital sectors of the city. The data is divided to indicate whether the call is about a fire incident or routed to the paramedics' Emergency Services Department, which includes Medical First Response and Emergency Medical Services (EMS).

The data is parsed and examined to note trends based on the day of the week of calls, monthly and annual figures, and compared to Year 2017 data to determine whether the volume is on pace with previous years, in decline, or experiencing growth.

Predicting future personnel and supply needs is a vital step in readiness preparation but making such judgments is impossible without the needed data, and in the case of emergency services this preparation can literally be the difference between life and death.

# Data

Visualizations created using ChartLab

From just a glance at the above visualization, it is obvious that the number of calls being placed to the Hartford Fire Department is on the rise. Unfortunately, this knowledge alone is insufficient to determine the rate at which the number of calls is increasing, and even less helpful in making predictions about future call volume. Readiness is an essential skill set for those working in emergency services, and thanks to an increased focus on data tracking, that readiness can be buttressed by sound data analysis.

Using the SQL Console in ATSD to query the dataset:

# Call Numbers by Year

SELECT  date_format(time, 'yyyy') AS "Year", sum(value) AS "Total Calls"
  FROM total_number_of_calls
GROUP BY period(1 year)
  ORDER BY 'Year' ASC

Year	Total Calls
2014	22196
2015	23829
2016	27267
2017*	4266

While undoubtedly important, the annual information here is not scalable to an applicable level. Using yearly increments of calls cannot provide insight about seasonal increases and decreases, and certainly cannot be used to predict an increase in type of calls made to the Hartford Fire Department.

*Year 2017 data is indexed until February 25

# Call Numbers by Month

SELECT  date_format(time, 'MM, yyyy') AS "Month, Year", sum(value) AS "Total Calls"
  FROM total_number_of_calls
GROUP BY period(1 month)
  ORDER BY time ASC

Month, Year	Total Calls
01, 2014	2029
02, 2014	1673
03, 2014	1827
04, 2014	1810
05, 2014	1946
06, 2014	1892
07, 2014	1885
08, 2014	1960
09, 2014	1835
10, 2014	1829
11, 2014	1730
12, 2014	1780
01, 2015	1810
02, 2015	1763
03, 2015	1934
04, 2015	1875
05, 2015	2100
06, 2015	1952
07, 2015	2083
08, 2015	2120
09, 2015	2058
10, 2015	2075
11, 2015	2060
12, 2015	1999
01, 2016	1975
02, 2016	2182
03, 2016	2129
04, 2016	2206
05, 2016	2275
06, 2016	2378
07, 2016	2494
08, 2016	2302
09, 2016	2312
10, 2016	2415
11, 2016	2213
12, 2016	2386
01, 2017	2362
02, 2017	1904

While this visualization shows that despite an overall increase in calls to the department has been observed throughout the entire observation period, recently, the data shows a certain amount of stability and even decline.

# Call Numbers by Day of the Week

Diurnal analysis shows that instances of calls to the Hartford Fire Department remain fairly consistent throughout the week, and while the highest volume of calls came on Friday, the deviation from the average is quite low. Likewise, the lowest call volume, which came on Sunday, did not significantly deviate from the average either.

SELECT  date_format(time, 'E') AS "Day of the Week", sum(value)/1000 AS "Total Calls (Thousand)"
  FROM total_number_of_calls
GROUP BY date_format(time, 'E'), date_format(time, 'u')
  ORDER BY date_format(time, 'u') ASC

Day of the Week	Total Calls (Thousand)
Mon	33.16
Tue	33.47
Wed	33.41
Thu	33.42
Fri	34.46
Sat	33.37
Sun	31.39

Open ChartLab with the button above and navigate through time using the drop-down list.

Despite consistent overall call numbers throughout the week, it is interesting to note that the number of fire-related calls made to the Hartford Fire Department is the highest on Sundays:

SELECT  date_format(time, 'E') AS "Day of the Week", sum(value) AS "Fire Calls"
  FROM fire_calls
GROUP BY date_format(time, 'E'), date_format(time, 'u')
  ORDER BY date_format(time, 'u') ASC

Day of the Week	Fire Calls
Mon	591
Tue	564
Wed	562
Thu	546
Fri	600
Sat	648
Sun	696

Additionally, the number of EMS calls is highest on Mondays:

SELECT  date_format(time, 'E') AS "Day of the Week", sum(value)/1000 AS "EMS Calls (Thousand)"
  FROM ems_calls
GROUP BY date_format(time, 'E'), date_format(time, 'u')
  ORDER BY date_format(time, 'u') ASC

Day of the Week	EMS Calls (Thousand)
Mon	18.56
Tue	15.95
Wed	16.05
Thu	15.82
Fri	16.38
Sat	15.33
Sun	14.61

# EMS Calls by Year

SELECT  date_format(time, 'yyyy') AS "Year", sum(value) AS "Total Calls"
  FROM ems_calls
GROUP BY period(1 year)
  ORDER BY 'Year' ASC

Year	Total Calls
2014	15563
2015	16797
2016	19499
2017	3164

# Fire Calls by Year

SELECT  date_format(time, 'yyyy') AS "Year", sum(value) AS "Total Calls"
  FROM fire_calls
GROUP BY period(1 year)
  ORDER BY 'Year' ASC

Year	Total Calls
2014	566
2015	702
2016	760
2017	58

# EMS Calls by Month

SELECT  date_format(time, 'MM, yyyy') AS "Month, Year", sum(value) AS "Total Calls"
  FROM ems_calls
GROUP BY period(1 month)
  ORDER BY time ASC

Month, Year	Total Calls
01, 2014	1367
02, 2014	1188
03, 2014	1332
04, 2014	1288
05, 2014	1387
06, 2014	1357
07, 2014	1287
08, 2014	1344
09, 2014	1313
10, 2014	1245
11, 2014	1188
12, 2014	1267
01, 2015	1285
02, 2015	1207
03, 2015	1374
04, 2015	1344
05, 2015	1451
06, 2015	1391
07, 2015	1419
08, 2015	1460
09, 2015	1480
10, 2015	1474
11, 2015	1477
12, 2015	1435
01, 2016	1418
02, 2016	1385
03, 2016	1590
04, 2016	1656
05, 2016	1625
06, 2016	1691
07, 2016	1781
08, 2016	1690
09, 2016	1658
10, 2016	1713
11, 2016	1587
12, 2016	1705
01, 2017	1744
02, 2017	1420

# Fire Calls by Month

SELECT  date_format(time, 'MM, yyyy') AS "Month, Year", sum(value) AS "Total Calls"
  FROM fire_calls
GROUP BY period(1 month)
  ORDER BY time ASC

Month, Year	Total Calls
01, 2014	40
02, 2014	46
03, 2014	43
04, 2014	50
05, 2014	50
06, 2014	53
07, 2014	62
08, 2014	53
09, 2014	38
10, 2014	47
11, 2014	47
12, 2014	37
01, 2015	32
02, 2015	41
03, 2015	34
04, 2015	58
05, 2015	141
06, 2015	45
07, 2015	55
08, 2015	68
09, 2015	74
10, 2015	64
11, 2015	52
12, 2015	38
01, 2016	43
02, 2016	32
03, 2016	55
04, 2016	69
05, 2016	76
06, 2016	105
07, 2016	95
08, 2016	69
09, 2016	76
10, 2016	55
11, 2016	49
12, 2016	36
01, 2017	27
02, 2017	31

# Analysis

The percent by year change in number of calls received by the Hartford Fire Department is shown below:

# Previous Year Baseline

Year	EMS	Fire	Other	Total
2015	+7.33%	+19.37%	+4.15%	+6.85%
2016	+13.86%	+7.63%	+9.67%	+12.61%

# First Year Baseline

Year	EMS	Fire	Other	Total
2015	+7.33%	+19.37%	+4.15%	+6.85%
2016	+18.59%	+20.19%	+25.52%	+13.43%

# Average Value Baseline

Year	EMS	Fire	Other	Total
Baseline	17,286	676	6,468	24,430
2014	-9.97%	-5.98%	-6.20%	-9.14%
2015	-2.83%	+3.85%	+2.13%	+2.46%
2016	+12.8%	+12.42%	+8.35%	+11.61%

Based on the first two baseline tables, predicting fire call growth is difficult due to the irregularly large amount of calls received in 2015, however, when modeling using an average value baseline, consistent 8% annual growth is shown.

# Median Value Baseline

Year	EMS	Fire	Other	Total
Baseline	16,797	702	6330	23,829
2014	-7.34%	-19.37%	-4.15%	-6.85%
2015*	0%	0%	0%	0%
2016	+16.01%	+8.26%	+10.71%	+14.43%

2015 is the median baseline

# Growth Rates

Baseline	Average Percent Growth Per Year
Previous Year	+9.73%
First Year	+10.14%
Average Value	+7.34%*
Median Value	+7.09%*

*Absolute value of percent change is used for percent growth calculations.

# Validation

Since data is already available for the first two months of 2017, but not included in the above calculations, it can be used as holdout data and used to test the validity of the above models. Likewise, this exercise can be used to demonstrate the potential scalability of such modeling:

# January (2014-2017)

SELECT date_format(time, 'MM, yyyy') AS "Month, Year", SUM(value) AS "Total Calls"
  FROM total_number_of_calls WHERE date_format(time, 'MM') = '01'
GROUP BY 'Month, Year'

Month, Year	Total Calls
01, 2014	2029
01, 2015	1810
01, 2016	1975
01, 2017	2362

The expected total calls for January 2017 are predicted using each of the models:

PYB	FYB	AVB*	MVB*
2,167	2,646	2,477	2,454

*AVB and MVB values for one month are taken by dividing the year total AVB and MVB by twelve. The average value is 2,036. The median value is 1,986.

Observed Growth Rates:

Year	Total Calls	PYB	FYB	AVB*	MVB*
2014	2,029	+0%	+0%	-0.07%	+1.33%
2015	1,810	-12.01%	-12.01%	-11.45%	-10.60%
2016	1,975	+9.11%	-2.73 %	-3.38%	-1.37%
2017	2,362	+19.60%	+16.41%	+15.56%	+17.98%

*The average value is 2,044. The median value is 2,002.

Error Calculations:

Baseline	Average Percent Growth Per Year	Baseline Error	Model Error	p-value*
Previous Year	+10.81%	+11.10%	-8.26%	p > 0.20
First Year	+7.78%	-23.27%	+12.02%	p > 0.20
Average Value	+7.6%	+3.68%	+4.87%	0.025 > p > 0.02
Median Value	+7.82%	+10.30%	+3.92%	0.10 > p > 0.05

*p-value is calculated using the expected versus actual measurements. For these values, there is one degree of freedom.

# February (2014-2017)

SELECT date_format(time, 'MM, yyyy') AS "Month, Year", SUM(value) AS "Total Calls"
  FROM total_number_of_calls WHERE date_format(time, 'MM') = '02'
GROUP BY 'Month, Year'

Month, Year	Total Calls
02, 2014	1673
02, 2015	1763
02, 2016	2182
02, 2017	1904

The expected total calls for February 2017 are predicted using each of the models:

PYB	FYB	AVB*	MVB*
2384	1,836	2,087	2,095

Observed Growth Rates:

Year	Total Calls	PYB	FYB	AVB*	MVB*
2014	1,673	+0%	+0%	-12.43%	-9.63%
2015	1,763	+5.10%	+5.10%	-6.27%	-3.87%
2016	2,182	+27.77%	+30.45%	+16.00%	+18.98%
2017	1,904	-12.74%	+13.81%	+1.22%	+3.82%

*The average value is 1,881. The median value is 1,834.

Error Calculations:

Baseline	Average Percent Growth Per Year	Baseline Error	Model Error	p-value
Previous Year	+11.40%	+17.16%	+25.21%	p > 0.20
First Year	+15.45%	+52.36%	-3.57%	0.20 > p > 0.10
Average Value	+8.98%	+22.34%	+11.40%	p > 0.20
Median Value	+9.08%	+28.01%	+10.03%	p > 0.20

Based on the results of the validation testing, the Average Value Baseline model is alternatively successful and unsuccessful in predicting the number of calls placed to the Hartford Fire Department; 100% prediction accuracy is almost impossible to achieve without drastically overfitting the model to the data, which is also undesirable. Here, when the data showed a sub-standard level of consistency to the trend with a major outlier point (January), the model is effectively able to negotiate the irregularity and still predict the number of calls placed in the holdout data to within 5%. When the target variable itself is the outlier (February) the error percentage of this model grew to almost 12%. This shows that the model itself is unable to predict whether or not the target data point is an outlier or not, and the very definition of an outlier makes its prediction near impossible.

# Implementation

Continuing to manually input this data for the remaining ten months would be a practice in patience, but the AVB model just effectively demonstrated above is the same method used to predict future values with the Forecast feature in the Axibase Time Series Database. The visualizations have been converted to display average monthly values.

Note the model error here is consistent with the error demonstrated in the Validation section above.

Data Forecasting has the scalability to render predictions for any amount of time, in this case, the numerical predictions in ChartLab are given for the day as such they are on the order of 10 x 10^0.

Below are the anticipated levels of fire-related calls yet-to-be received for the remainder of 2017:

The forecast feature is able to both effectively predict the increase in fire-related calls the Hartford Fire Department is likely to receive during the summer and demonstrate its ability to scale to smaller problems.

Because of the recent trend of increased call volume to the Fire Department Emergency Medical Services Department, a lower scoring interval is applied to this data set. The scoring interval determines the weight of recent data compared to the entire set. A lower scoring interval, like that which is used in this case, applies a stronger weight to recent data. The low scoring interval here is demonstrated by the replication of the patterns seen throughout the year 2016.

Because the third category of calls placed to the Department is titled "All Other Calls," analysis is not performed because of the ambiguous nature of such a category. Additional data would be needed, for example, about Fire Department events or public outreach efforts since likely such a category contains calls of a non-emergency nature.

# Conclusion

This particular data set is extremely responsive to the Average Value Baseline modeling techniques demonstrated above and the number of calls to be placed to the Hartford Fire Department about its most serious responsibilities modeled to anticipate the future needs of the department.

Often, such models are extremely case-sensitive and are unable to significantly generalize to either a larger population, or a different set of data, but the techniques demonstrated above can be applied to a different instance of the same type of data, or even an entirely different dataset should the need arise.

Forecast settings used here are contained in the Resources folder. Launch the Forecast feature with the .xml file contained there by opening your instance of ATSD and following the path Configuration > Forecasts. At the bottom of the screen click import and launch the Forecast feature with the provided .xml file. Contact Axibase with any questions.