Project 3

Author

Sajutee Mukrabine

Research Question: Which factors (height, speed, phase_of_flt, sky, and time_of_day) predict whether a wildlife strike results in a negative effect on the flight?

Inroduction

Introduction. This project aims to answer the following research question: Which factors (height, speed, phase_of_flt, sky, and time_of_day) predict whether a wildlife strike results in a negative effect on the flight? This question matters because a wildlife strike can endanger an airplane.

For this project, we have the dataset that will be called birds. It has 19,302 rows and 17 variables. Each row displays a report of an aircraft hitting a bird or other wildlife. The dataset does have the data about the aircraft, the weather, and what happened after the strike. This project relies on five variables: height, speed, phase_of_flt, sky, and time_of_day. The dependent variable is effect, which indicates whether the strike created a problem for the flight.

The data comes from the FAA Wildlife Strike Database and it can be found at: https://datahub.transportation.gov/Aviation/Aircraft-Wildlife-Strike-Data-Search-Tool-FAA-Wild/jhay-dgxy

Load Packages

library(tidyverse)
── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
✔ dplyr     1.1.4     ✔ readr     2.1.5
✔ forcats   1.0.0     ✔ stringr   1.5.1
✔ ggplot2   3.5.2     ✔ tibble    3.3.0
✔ lubridate 1.9.4     ✔ tidyr     1.3.1
✔ purrr     1.1.0     
── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
✖ dplyr::filter() masks stats::filter()
✖ dplyr::lag()    masks stats::lag()
ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors
library(dplyr)

##Load the Dataset

setwd("C:/Users/sajut/OneDrive/Desktop/DATA_101")

Birds <- read.csv("birds.csv")
head(Birds)
  opid                 operator      atype                remarks phase_of_flt
1  AAL        AMERICAN AIRLINES      MD-80              NO DAMAGE      Descent
2  USA               US AIRWAYS FK-28-4000    2 BIRDS, NO DAMAGE.        Climb
3  AAL        AMERICAN AIRLINES  B-727-200                   <NA>     Approach
4  AAL        AMERICAN AIRLINES      MD-82                   <NA>        Climb
5  AAL        AMERICAN AIRLINES      MD-82              NO DAMAGE        Climb
6  GFT GULFSTREAM INTL AIRLINES      BE-99 FLT 714.  TIME = 1951Z Landing Roll
  ac_mass num_engs            date time_of_day state height speed effect
1       4        2  9/30/1990 0:00       Night    IL   7000   250   <NA>
2       4        2 11/29/1993 0:00         Day    MD     10   140   None
3       4        3  8/13/1993 0:00         Day    TN    400   140   None
4       4        2  10/7/1993 0:00         Day    VA    100   200   None
5       4        2  9/25/1993 0:00         Day    SC     50   170   None
6       2        2  9/20/1993 0:00         Day    FL      0    40   None
         sky               species birds_seen birds_struck
1   No Cloud UNKNOWN BIRD - MEDIUM       <NA>            1
2   No Cloud UNKNOWN BIRD - MEDIUM     10-Feb       10-Feb
3 Some Cloud  UNKNOWN BIRD - SMALL     10-Feb            1
4   Overcast  UNKNOWN BIRD - SMALL       <NA>            1
5 Some Cloud  UNKNOWN BIRD - SMALL     10-Feb            1
6 Some Cloud                 HAWKS       <NA>            1
str(Birds)
'data.frame':   19302 obs. of  17 variables:
 $ opid        : chr  "AAL" "USA" "AAL" "AAL" ...
 $ operator    : chr  "AMERICAN AIRLINES" "US AIRWAYS" "AMERICAN AIRLINES" "AMERICAN AIRLINES" ...
 $ atype       : chr  "MD-80" "FK-28-4000" "B-727-200" "MD-82" ...
 $ remarks     : chr  "NO DAMAGE" "2 BIRDS, NO DAMAGE." NA NA ...
 $ phase_of_flt: chr  "Descent" "Climb" "Approach" "Climb" ...
 $ ac_mass     : int  4 4 4 4 4 2 4 2 4 2 ...
 $ num_engs    : int  2 2 3 2 2 2 2 1 3 2 ...
 $ date        : chr  "9/30/1990 0:00" "11/29/1993 0:00" "8/13/1993 0:00" "10/7/1993 0:00" ...
 $ time_of_day : chr  "Night" "Day" "Day" "Day" ...
 $ state       : chr  "IL" "MD" "TN" "VA" ...
 $ height      : int  7000 10 400 100 50 0 4000 100 200 3000 ...
 $ speed       : int  250 140 140 200 170 40 230 50 130 NA ...
 $ effect      : chr  NA "None" "None" "None" ...
 $ sky         : chr  "No Cloud" "No Cloud" "Some Cloud" "Overcast" ...
 $ species     : chr  "UNKNOWN BIRD - MEDIUM" "UNKNOWN BIRD - MEDIUM" "UNKNOWN BIRD - SMALL" "UNKNOWN BIRD - SMALL" ...
 $ birds_seen  : chr  NA "10-Feb" "10-Feb" NA ...
 $ birds_struck: chr  "1" "10-Feb" "1" "1" ...

Data Analysis

In this project, I processed the dataset to study what factors cause a negative effect from wildlife strikes. First, I cleaned the variable names and kept only the important columns. Then I grouped and summarized the data to look at patterns in flight phase, height, and speed. I also cleaned the outcome variable and changed it into a factor in order to be used in the logistic regression model. I will make bar charts for categories and histograms or boxplots for numbers like height and speed. This helps me check the data and find important variables for the model.

Clean variable names

names(Birds) <- gsub("[(). \\-]", "_", names(Birds)) 
names(Birds) <- gsub("_$", "", names(Birds))  
names(Birds) <- tolower(names(Birds))         

head(Birds) 
  opid                 operator      atype                remarks phase_of_flt
1  AAL        AMERICAN AIRLINES      MD-80              NO DAMAGE      Descent
2  USA               US AIRWAYS FK-28-4000    2 BIRDS, NO DAMAGE.        Climb
3  AAL        AMERICAN AIRLINES  B-727-200                   <NA>     Approach
4  AAL        AMERICAN AIRLINES      MD-82                   <NA>        Climb
5  AAL        AMERICAN AIRLINES      MD-82              NO DAMAGE        Climb
6  GFT GULFSTREAM INTL AIRLINES      BE-99 FLT 714.  TIME = 1951Z Landing Roll
  ac_mass num_engs            date time_of_day state height speed effect
1       4        2  9/30/1990 0:00       Night    IL   7000   250   <NA>
2       4        2 11/29/1993 0:00         Day    MD     10   140   None
3       4        3  8/13/1993 0:00         Day    TN    400   140   None
4       4        2  10/7/1993 0:00         Day    VA    100   200   None
5       4        2  9/25/1993 0:00         Day    SC     50   170   None
6       2        2  9/20/1993 0:00         Day    FL      0    40   None
         sky               species birds_seen birds_struck
1   No Cloud UNKNOWN BIRD - MEDIUM       <NA>            1
2   No Cloud UNKNOWN BIRD - MEDIUM     10-Feb       10-Feb
3 Some Cloud  UNKNOWN BIRD - SMALL     10-Feb            1
4   Overcast  UNKNOWN BIRD - SMALL       <NA>            1
5 Some Cloud  UNKNOWN BIRD - SMALL     10-Feb            1
6 Some Cloud                 HAWKS       <NA>            1
Birds_clean <- Birds |>
  select(phase_of_flt, time_of_day, height, speed, effect, sky, birds_struck)
Birds_clean |>
  group_by(effect) |> 
  summarize(
  n = n(),
  mean_height = mean(height),
  mean_speed = mean(speed)
  )
# A tibble: 6 × 4
  effect                    n mean_height mean_speed
  <chr>                 <int>       <dbl>      <dbl>
1 Aborted Take-off        544          NA         NA
2 Engine Shut Down        116          NA         NA
3 None                  11611          NA         NA
4 Other                   348          NA         NA
5 Precautionary Landing   965          NA         NA
6 <NA>                   5718          NA         NA

The last step is cleaning “effect”, replace 0 and 1

unique(Birds_clean$effect)
[1] NA                      "None"                  "Precautionary Landing"
[4] "Other"                 "Aborted Take-off"      "Engine Shut Down"     
Birds_clean$negative_effect <- ifelse(Birds_clean$effect %in% c("Precautionary Landing",
                                                                "Aborted Take-off", 
                                                                "Engine Shut Down"),1,0)
#Help from https://sscc.wisc.edu/sscc/pubs/dwr/06_logical.html?utm_source=chatgpt.com
Birds_clean$negative_effect <- as.factor(Birds_clean$negative_effect)  # convert to a factor

Finaly

str(Birds_clean)
'data.frame':   19302 obs. of  8 variables:
 $ phase_of_flt   : chr  "Descent" "Climb" "Approach" "Climb" ...
 $ time_of_day    : chr  "Night" "Day" "Day" "Day" ...
 $ height         : int  7000 10 400 100 50 0 4000 100 200 3000 ...
 $ speed          : int  250 140 140 200 170 40 230 50 130 NA ...
 $ effect         : chr  NA "None" "None" "None" ...
 $ sky            : chr  "No Cloud" "No Cloud" "Some Cloud" "Overcast" ...
 $ birds_struck   : chr  "1" "10-Feb" "1" "1" ...
 $ negative_effect: Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...

Regression Analysis

To address my research question, I employed the logistic regression model using the glm() function. This model is used to calculate if a wildlife strike had a negative impact on a flight. I applied five predictors: height, speed, phase_of_flt, sky, and time_of_day.

I am using this logistic regression model in this study as negative_effect is a binary variable, whether a wildlife strike caused a problem (yes/no). Logistic regression is the best statistical approach to estimate a yes/no outcome and to see what makes a yes/no outcome more likely and why. I hope to test this effect on my observation on how much height, speed, phase_of_flt, sky, and time_of_day modify the probability of the negative effect, so logistic regression will be my fit.

logistic <- glm(negative_effect ~ height + speed + phase_of_flt + sky + time_of_day,
  data = Birds_clean,
  family = "binomial")

summary(logistic)

Call:
glm(formula = negative_effect ~ height + speed + phase_of_flt + 
    sky + time_of_day, family = "binomial", data = Birds_clean)

Coefficients:
                           Estimate Std. Error z value Pr(>|z|)    
(Intercept)              -2.395e+00  2.396e-01  -9.996  < 2e-16 ***
height                    1.322e-04  2.758e-05   4.794 1.63e-06 ***
speed                    -1.508e-02  1.081e-03 -13.958  < 2e-16 ***
phase_of_fltClimb         2.832e+00  1.330e-01  21.296  < 2e-16 ***
phase_of_fltDescent       7.921e-01  3.529e-01   2.244 0.024807 *  
phase_of_fltEn Route      2.805e+00  1.899e-01  14.767  < 2e-16 ***
phase_of_fltLanding Roll -9.251e-01  2.876e-01  -3.217 0.001296 ** 
phase_of_fltParked       -1.221e+01  3.943e+02  -0.031 0.975304    
phase_of_fltTake-off run  2.907e+00  1.345e-01  21.623  < 2e-16 ***
phase_of_fltTaxi         -1.179e+01  2.035e+02  -0.058 0.953789    
skyOvercast               3.326e-01  9.188e-02   3.620 0.000294 ***
skySome Cloud             9.082e-02  8.267e-02   1.099 0.271923    
time_of_dayDay           -1.652e-01  1.581e-01  -1.045 0.295941    
time_of_dayDusk           6.642e-01  2.066e-01   3.215 0.001304 ** 
time_of_dayNight          1.107e-01  1.779e-01   0.622 0.533746    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 6951.7  on 11663  degrees of freedom
Residual deviance: 5352.3  on 11649  degrees of freedom
  (7638 observations deleted due to missingness)
AIC: 5382.3

Number of Fisher Scoring iterations: 13
r_square <- 1 - (logistic$deviance / logistic$null.deviance)
r_square
[1] 0.230073
colSums(is.na(Birds_clean))
   phase_of_flt     time_of_day          height           speed          effect 
           1783            2077            3193            7008            5718 
            sky    birds_struck negative_effect 
           3579              39               0 

Interpretation

In the logistic regression, the intercept is the log-odds of the outcome when all of the predictor variables are zero. In this model the intercept is -2.395. Which indicates that, with height and speed equal to zero, phase_of_flt is the reference category (Approach), sky is No Cloud and time_of_day is the baseline category (Dawn), that is the log-odds of a negative effect occurring is -2.395. Turning this into a probability indicates, based on these baseline conditions, that the chance of a negative effect is approximately 8.3%. The intercept therefore reflects the baseline risk of a negative effect before considering the impact of any other factors.

Logistic Regression:

model_data <- logistic$model

predicted.data <- data.frame(
  probability.of.negative_effect = logistic$fitted.values,
  negative_effect = model_data$negative_effect
)

predicted.data
      probability.of.negative_effect negative_effect
1                       1.290167e-02               0
2                       1.372319e-01               0
3                       1.068628e-02               0
4                       8.324672e-02               0
5                       1.002088e-01               0
6                       1.802837e-02               0
7                       8.876070e-02               0
8                       3.848675e-01               0
9                       1.104716e-02               0
11                      1.139029e-02               0
14                      1.904229e-01               0
16                      1.468149e-01               0
17                      1.827102e-01               1
18                      8.230851e-03               0
20                      9.896312e-03               0
23                      3.199305e-01               0
24                      9.370028e-03               0
27                      2.851014e-01               0
29                      1.820475e-01               0
30                      1.054737e-02               0
33                      3.634588e-02               0
34                      4.294695e-03               0
36                      1.317034e-02               0
37                      6.731117e-02               0
38                      9.391211e-03               0
39                      1.006373e-02               0
40                      7.243361e-01               1
42                      2.890905e-01               0
44                      7.371722e-03               0
45                      2.091247e-02               0
46                      2.384919e-01               0
47                      1.174778e-02               0
49                      1.501502e-01               0
50                      2.676856e-01               1
51                      1.276673e-02               0
53                      1.050028e-02               0
54                      1.767077e-01               0
59                      3.104182e-01               1
60                      1.240464e-02               0
62                      1.242798e-02               0
63                      2.640153e-01               0
64                      2.890905e-01               0
71                      3.641092e-01               0
72                      7.724400e-02               0
74                      1.704276e-02               0
75                      5.148524e-02               1
76                      1.459323e-02               0
77                      1.084576e-02               0
78                      1.159416e-02               0
79                      7.371722e-03               0
80                      4.340542e-03               0
83                      2.594090e-02               0
84                      1.657238e-02               0
85                      1.906450e-02               0
86                      1.002497e-02               0
88                      1.063795e-01               0
89                      6.473633e-03               0
90                      4.523286e-03               0
91                      9.941870e-03               0
92                      1.735530e-02               0
94                      1.265647e-02               0
95                      1.167127e-02               0
96                      1.487954e-02               0
99                      1.389086e-01               1
100                     7.371722e-03               0
101                     6.934702e-03               0
102                     2.702553e-02               0
103                     1.243489e-02               0
104                     1.692714e-02               0
105                     2.170050e-01               0
106                     2.157743e-02               0
107                     2.553757e-01               0
109                     1.082700e-02               0
110                     6.736025e-03               0
111                     2.130277e-01               0
112                     1.387585e-02               0
114                     7.632558e-03               0
115                     1.476699e-02               0
118                     6.249712e-03               0
119                     4.593579e-03               0
120                     2.434001e-02               0
123                     9.881594e-03               0
124                     2.723833e-02               1
127                     3.137734e-01               0
128                     1.056565e-02               0
129                     2.825065e-01               0
131                     3.972151e-02               0
132                     1.928297e-01               0
133                     7.054449e-03               0
134                     1.076432e-01               0
135                     1.703752e-02               0
136                     2.023227e-01               0
137                     1.564687e-02               0
138                     1.643879e-02               0
139                     9.805584e-03               0
146                     1.451569e-02               0
147                     3.079695e-02               1
149                     1.511131e-02               0
152                     1.250860e-02               0
153                     1.230137e-01               0
154                     5.500359e-02               0
155                     1.384311e-02               0
156                     2.861257e-02               0
157                     7.790287e-02               0
163                     5.462337e-03               0
164                     9.691070e-03               0
165                     1.803708e-02               0
166                     1.670635e-02               0
167                     1.097516e-02               0
168                     3.974646e-01               0
169                     6.736025e-03               0
171                     3.695567e-03               0
172                     1.283714e-02               0
173                     6.946189e-03               0
174                     1.062957e-02               0
175                     9.183949e-03               0
177                     2.332966e-02               0
178                     3.581560e-01               0
180                     1.317034e-02               0
188                     1.020493e-01               0
189                     1.352105e-02               0
190                     3.902258e-02               0
193                     2.816935e-01               1
195                     9.172880e-03               0
196                     4.990468e-03               0
204                     1.208348e-01               0
206                     1.682456e-01               0
207                     6.856613e-03               0
209                     2.273774e-01               0
211                     1.405683e-02               0
215                     6.818970e-02               0
217                     1.439529e-02               0
222                     1.523820e-02               0
223                     1.308788e-01               0
227                     9.567761e-03               0
231                     2.524588e-01               0
232                     1.193896e-02               0
234                     4.990468e-03               0
235                     2.976584e-02               0
236                     3.050487e-02               0
239                     3.369941e-01               0
240                     1.611010e-02               0
241                     1.661019e-01               0
245                     1.696246e-01               0
247                     1.005073e-01               0
248                     2.109214e-02               0
249                     1.146541e-01               0
250                     4.701087e-03               0
251                     8.735969e-03               0
254                     1.035304e-01               0
256                     1.921303e-01               0
257                     1.131451e-02               0
262                     1.144111e-01               0
263                     1.228496e-02               0
264                     2.412995e-01               0
266                     2.588459e-01               0
269                     1.880605e-01               0
270                     1.868161e-02               0
271                     1.684451e-02               0
272                     1.204707e-02               0
273                     3.254221e-02               1
275                     4.294695e-03               0
277                     4.186242e-02               0
279                     1.744968e-02               0
283                     3.067234e-02               0
285                     3.332511e-02               0
290                     1.218270e-02               0
292                     8.482518e-03               0
293                     1.552330e-02               0
294                     1.981903e-01               0
295                     4.693948e-03               0
296                     8.183753e-03               0
297                     1.240464e-02               0
298                     1.005026e-01               0
300                     1.504310e-02               0
301                     3.716068e-01               1
302                     7.711937e-02               1
303                     1.000095e-02               0
307                     2.023227e-01               0
308                     3.368225e-01               1
311                     1.459156e-02               0
312                     1.389283e-02               0
313                     2.259188e-01               0
316                     2.686714e-02               0
319                     1.787447e-01               1
323                     2.553757e-01               1
324                     1.076432e-01               1
325                     1.993287e-02               0
326                     4.990468e-03               0
327                     1.315873e-02               0
328                     1.386702e-02               0
329                     1.691709e-01               0
330                     1.926347e-01               0
331                     1.171062e-02               0
333                     2.622389e-02               0
334                     5.979388e-03               0
335                     1.579532e-01               0
336                     5.728662e-02               1
347                     1.448403e-02               0
349                     1.172053e-02               0
351                     2.974920e-01               1
352                     1.333157e-02               0
353                     7.395223e-03               0
354                     1.153145e-02               0
355                     7.925233e-03               0
356                     9.767569e-03               0
357                     4.071427e-01               0
358                     1.219385e-02               0
359                     1.696898e-02               0
362                     1.661019e-01               0
363                     2.851014e-01               0
365                     8.933471e-03               0
367                     8.255125e-02               0
368                     1.155716e-01               0
369                     1.973973e-03               0
370                     6.736025e-03               0
371                     1.005346e-02               0
372                     2.332966e-02               0
373                     2.432148e-02               0
374                     2.139983e-02               0
375                     9.661255e-03               0
376                     8.878112e-03               0
377                     1.136428e-02               0
378                     1.085180e-02               0
380                     1.124402e-01               0
381                     2.030095e-02               0
382                     1.221097e-01               0
383                     1.094854e-02               0
384                     2.584375e-02               0
386                     1.304282e-01               1
387                     4.216745e-01               0
388                     3.192088e-01               0
395                     1.099557e-02               0
396                     4.990468e-03               0
398                     1.790660e-01               0
402                     1.083992e-01               0
404                     1.036073e-02               0
405                     2.324697e-02               0
406                     1.283971e-01               0
407                     1.273344e-02               0
408                     2.170390e-01               0
409                     1.060413e-02               0
410                     5.345394e-01               0
411                     1.020787e-02               0
412                     1.472033e-02               0
413                     1.196177e-02               0
414                     9.366410e-02               0
415                     1.133989e-02               0
416                     1.697005e-01               1
422                     2.384919e-01               0
423                     1.431817e-02               0
425                     1.267837e-01               0
427                     1.041025e-02               0
431                     1.746738e-01               0
432                     2.974920e-01               1
438                     1.224722e-02               0
439                     4.990468e-03               0
440                     8.939187e-03               0
441                     5.379324e-03               0
442                     9.926851e-03               0
445                     1.462453e-01               0
447                     3.713013e-01               1
448                     5.065934e-03               0
451                     1.703752e-02               0
452                     1.512370e-02               0
453                     1.462453e-01               0
454                     1.093757e-01               0
456                     1.348176e-01               1
457                     1.504310e-02               0
458                     9.154822e-03               0
460                     9.767569e-03               0
461                     6.736025e-03               0
462                     1.850668e-02               0
463                     2.295225e-02               0
464                     1.346634e-02               0
465                     1.266454e-02               0
466                     7.155132e-02               0
467                     1.087830e-02               0
468                     1.579532e-01               0
470                     2.297162e-01               0
471                     1.054737e-02               0
473                     4.711733e-01               1
474                     7.497734e-03               0
476                     1.733807e-02               0
478                     1.262714e-02               0
479                     1.823431e-01               0
481                     1.369943e-02               0
482                     1.121666e-02               0
483                     1.024459e-02               0
484                     2.072286e-02               0
485                     7.298778e-03               0
487                     1.667493e-02               0
489                     9.767569e-03               0
491                     1.612943e-01               0
492                     1.478481e-02               0
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1900                    1.167127e-02               0
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1918                    5.383420e-03               0
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1927                    2.462622e-01               1
1929                    3.168150e-01               1
1931                    2.853174e-01               1
1933                    6.581914e-02               0
1934                    1.163070e-02               0
1938                    5.637699e-02               0
1939                    6.450528e-03               0
1940                    2.783722e-02               0
1943                    1.422514e-02               0
1944                    1.704311e-01               0
1946                    6.700347e-03               0
1947                    1.114356e-02               0
1948                    1.293025e-02               0
1949                    1.068628e-02               0
1950                    1.270023e-02               0
1952                    1.295936e-01               0
1953                    1.340251e-02               0
1954                    1.850668e-02               0
1956                    1.953766e-02               0
1958                    8.003376e-02               0
1959                    4.863961e-03               0
1960                    7.371722e-03               0
1961                    3.610128e-02               0
1963                    1.000488e-02               0
1964                    2.079805e-02               0
1965                    1.108095e-01               1
1967                    1.530587e-02               0
1969                    8.561710e-03               0
1970                    1.083253e-02               0
1975                    1.119258e-02               0
1976                    2.573602e-02               0
1978                    3.168150e-01               1
1979                    1.319099e-02               0
1981                    3.299478e-01               0
1983                    2.448565e-02               0
1984                    2.553757e-01               1
1986                    1.317666e-02               0
1987                    5.239651e-03               0
1988                    2.148333e-01               0
1989                    3.165841e-01               0
1990                    1.337340e-01               0
1991                    1.637045e-01               1
1992                    1.133989e-02               0
1993                    6.736025e-03               0
1994                    6.090066e-02               0
1996                    8.707886e-03               0
1998                    1.675484e-02               0
1999                    4.187277e-03               0
2001                    2.077142e-02               0
2002                    4.119138e-02               0
2003                    3.197986e-02               0
2004                    1.093136e-02               0
2005                    1.300123e-01               0
2007                    2.218346e-01               1
2008                    9.086566e-03               0
2009                    2.023227e-01               0
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2012                    3.284955e-02               0
2013                    1.556555e-02               0
2014                    1.439529e-02               0
2015                    1.230137e-01               0
2016                    2.877474e-02               0
2017                    2.524588e-01               0
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2022                    1.981903e-01               0
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2205                    1.654339e-01               0
2206                    1.790660e-01               0
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18860                   1.365738e-01               0
18861                   1.003200e-01               1
18863                   8.829877e-03               0
18865                   8.965659e-03               0
18866                   4.990468e-03               0
18867                   1.225773e-02               0
18868                   4.187252e-01               1
18873                   1.579532e-01               0
18876                   2.851014e-01               1
18877                   5.798304e-03               0
18878                   9.941942e-02               0
18882                   2.253513e-02               0
18883                   1.241888e-02               0
18884                   1.023805e-02               0
18885                   2.249794e-02               0
18888                   1.404903e-02               0
18889                   2.851014e-01               0
18890                   2.335981e-02               0
18891                   9.314627e-02               0
18892                   9.084470e-03               0
18897                   2.668859e-02               0
18906                   2.062284e-01               1
18910                   1.007174e-01               0
18913                   5.603402e-03               0
18914                   6.736025e-03               0
18915                   1.121543e-02               0
18917                   1.282280e-02               0
18918                   6.266652e-02               0
18919                   2.149477e-02               0
18921                   1.077742e-01               0
18925                   1.794992e-01               1
18926                   1.640461e-02               0
18927                   1.577917e-02               0
18930                   1.673670e-02               0
18931                   6.041309e-01               1
18933                   1.404623e-02               0
18936                   2.159699e-02               0
18937                   2.606558e-02               0
18941                   5.798304e-03               0
18948                   1.431817e-02               0
18949                   4.879291e-02               0
18950                   1.020787e-02               0
18951                   1.266454e-02               0
18952                   1.313254e-02               0
18954                   1.691709e-01               0
18956                   9.226258e-03               0
18957                   2.145933e-01               0
18958                   5.734947e-03               0
18961                   1.124402e-01               1
18962                   2.384919e-01               0
18966                   1.998491e-01               0
18967                   2.441554e-01               1
18971                   4.990468e-03               0
18972                   1.137123e-01               1
18973                   5.226810e-03               0
18979                   1.146831e-02               0
18981                   1.145707e-02               0
18987                   1.266454e-02               0
18988                   3.035052e-01               1
18989                   1.403374e-02               0
18993                   1.585599e-01               0
18994                   6.736025e-03               0
18997                   6.983967e-03               0
19003                   2.174006e-01               0
19008                   1.250024e-02               0
19009                   1.234679e-02               0
19010                   2.611017e-01               0
19012                   1.880605e-01               0
19014                   1.445105e-02               0
19015                   2.880365e-01               0
19020                   9.329896e-03               0
19025                   2.018098e-02               0
19029                   4.990468e-03               0
19032                   1.131703e-02               0
19033                   9.470532e-03               0
19037                   2.023227e-01               0
19041                   1.836689e-01               0
19042                   1.072176e-01               0
19051                   1.337293e-02               0
19054                   8.923698e-03               0
19055                   4.730595e-07               0
19059                   7.247309e-03               0
19060                   1.351855e-02               0
19064                   2.298261e-02               0
19065                   1.382507e-02               0
19066                   9.503569e-03               0
19069                   1.703671e-01               0
19072                   1.185022e-02               0
19073                   1.243203e-02               0
19076                   1.661019e-01               0
19077                   3.193980e-02               1
19078                   1.002088e-01               0
19079                   1.011949e-02               0
19084                   1.566139e-02               0
19085                   1.208477e-02               0
19092                   1.411096e-02               0
19094                   1.076432e-01               0
19096                   1.283714e-02               0
19097                   1.908288e-01               0
19098                   2.946383e-02               0
19100                   9.470532e-03               0
19102                   1.042570e-01               0
19104                   2.763356e-02               0
19108                   3.571614e-01               0
19109                   3.832299e-03               0
19110                   3.055461e-02               0
19113                   4.701087e-03               0
19114                   1.004878e-02               0
19117                   2.559908e-01               1
19118                   1.490131e-01               0
19120                   3.367540e-02               0
19121                   9.941870e-03               0
19123                   9.332786e-03               0
19124                   1.305783e-01               0
19126                   1.266454e-02               0
19128                   1.077742e-01               0
19129                   1.619558e-02               0
19130                   1.040181e-01               0
19132                   3.120652e-02               0
19135                   9.154822e-03               0
19136                   1.022124e-02               0
19138                   1.589451e-02               0
19139                   1.797359e-02               0
19141                   9.605027e-03               0
19143                   1.111396e-02               0
19144                   1.982021e-02               0
19148                   1.125122e-02               0
19149                   2.728053e-01               1
19150                   1.148912e-02               0
19152                   6.072733e-01               0
19153                   1.044026e-01               0
19154                   1.532785e-02               0
19157                   4.990468e-03               0
19158                   1.349982e-01               0
19160                   3.021093e-01               0
19161                   3.713013e-01               0
19163                   1.348164e-02               0
19164                   1.054737e-02               0
19165                   7.162382e-02               0
19166                   1.273581e-01               0
19168                   1.346634e-02               0
19171                   1.319021e-02               0
19173                   2.401901e-01               1
19174                   2.021547e-01               0
19175                   2.669569e-01               0
19176                   1.849984e-02               0
19177                   8.574085e-03               0
19178                   1.389086e-01               0
19182                   1.162864e-02               0
19184                   8.684438e-03               0
19187                   3.400369e-01               0
19188                   1.542659e-01               0
19192                   1.028444e-02               0
19193                   2.051019e-01               0
19197                   4.988981e-02               0
19198                   8.574324e-02               0
19199                   2.206456e-01               0
19200                   1.880605e-01               0
19202                   5.323933e-03               0
19203                   1.650306e-02               0
19205                   2.496397e-02               0
19206                   1.372319e-01               0
19211                   3.469835e-01               1
19212                   2.907461e-02               0
19215                   1.108122e-02               0
19217                   1.225040e-01               0
19218                   2.974920e-01               1
19219                   9.932835e-03               0
19220                   1.389086e-01               0
19221                   1.481032e-02               0
19222                   6.736025e-03               0
19223                   1.223683e-01               1
19224                   2.142754e-02               0
19226                   2.384919e-01               0
19229                   2.668280e-02               0
19231                   1.488901e-02               0
19235                   4.990468e-03               0
19236                   2.829173e-02               0
19241                   1.161800e-02               0
19243                   1.300581e-02               0
19244                   1.153270e-01               0
19245                   1.304893e-02               0
19247                   1.756271e-01               0
19250                   1.215941e-01               0
19251                   1.178074e-02               0
19254                   2.395257e-02               0
19255                   1.351855e-02               0
19257                   1.579532e-01               0
19260                   1.681000e-01               0
19262                   6.444802e-03               0
19263                   1.211658e-01               0
19264                   3.290870e-01               0
19265                   1.777761e-01               0
19266                   1.403374e-02               0
19268                   9.391211e-03               0
19269                   2.273774e-01               0
19270                   1.828861e-02               0
19272                   1.087830e-02               0
19275                   3.503276e-01               1
19276                   1.185602e-01               0
19278                   3.089589e-02               0
19281                   1.367610e-01               0
19283                   1.405683e-02               0
19284                   1.661019e-01               0
19286                   4.363776e-01               0
19287                   1.803726e-01               0
19290                   3.481010e-03               0
19292                   3.518308e-01               1
19295                   1.363209e-02               0
19299                   1.340749e-02               0
19300                   5.013206e-03               0
# Keep only rows with no missing values in Glucose, BMI, or Age
Birds_subset <- Birds_clean[complete.cases(Birds_clean[, c("height", "speed", "phase_of_flt", "sky",
                                                           "time_of_day")]), ]

# Predicted probabilities
predicted.probs <- logistic$fitted.values

# Convert predicted probabilities to classes 
predicted.classes <- ifelse(predicted.probs >= 0.5, 1, 0)

# Confusion matrix 
confusion <- table(
  Predicted = factor(predicted.classes, levels = c(0, 1)),
  Actual  = factor(Birds_subset$negative_effect, levels = c(0, 1))
)

confusion
         Actual
Predicted     0     1
        0 10616  1002
        1    21    25

The ROC Curve and Report the AUC Value

# Load package
library(pROC)
Warning: package 'pROC' was built under R version 4.5.2
Type 'citation("pROC")' for a citation.

Attaching package: 'pROC'
The following objects are masked from 'package:stats':

    cov, smooth, var
# ROC curve & AUC on full data
roc_obj <- roc(response  = Birds_subset$negative_effect,
               predictor = logistic$fitted.values,        
               levels = c("0", "1"),                                
               direction = "<")

# Print AUC value
auc_val <- auc(roc_obj); auc_val
Area under the curve: 0.8445
# Plot ROC with AUC displayed
plot.roc(roc_obj, print.auc = TRUE, legacy.axes = TRUE,
         xlab = "False Positive Rate (1 - Specificity)",
         ylab = "True Positive Rate (Sensitivity)")

The AUC shows how well does the model distinguish between wildlife strikes that cause a negative effect. For example, a 0.5 AUC means the model is not doing any better than random guesses. The model predicts perfectly if it is 1.0. Higher AUC means better performance. If the AUC is close to 0.80, it means the model does a good job overall at identifying strikes that are likely to cause problems.

Conclusion and Future Directions

According to the logistic regression, there are several factors that have a significant effect on the likelihood of a negative effect of a wildlife strike. The height and speed of the aircraft, phase of flight, sky conditions, and time of day factor into the numbers. These are all critical in that strikes during Climb, En Route, and Take-off run phases, as well as during Overcast skies or at Dusk, are more likely to yield a negative effect. Faster speeds make the risk slightly less, while at higher altitudes, the risk is slightly up. The results clearly address the research question by explaining whether negative outcomes are more and less likely with certain conditions.

The model works relatively well, matching better than a model with no predictors and calculating a high AUC for prediction shows that it is a reasonably good model. But plenty of the rows were missing values, as well as some important factors, such as aircraft type, bird species, or number of birds hit that weren’t included. For the future this model can be enhanced with addition of interaction among variables, increase of predictors or with special method for large datasets. Studies could also examine patterns over time or in other places, to better understand and prevent risky wildlife strikes.

References

https://sscc.wisc.edu/sscc/pubs/dwr/06_logical.html?utm_source=chatgpt.com