Logistic Regression on Titanic Data
Andriy Koval
Nov 26, 2019
This documents narrates the analysis of Titanic survival data.
Packages that will be used in this analysis:
# Attach these packages so their functions don't need to be qualified: http://r-pkgs.had.co.nz/namespace.html#search-path
library(magrittr) # enables piping : %>%
library(dplyr)
library(ggplot2)
library(titanic)
# Verify these packages are available on the machine, but their functions need to be qualified: http://r-pkgs.had.co.nz/namespace.html#search-path
requireNamespace("tidyr") # data manipulation
# requireNamespace("testit")# For asserting conditions meet expected patterns.
# requireNamespace("car") # For it's `recode()` function.Wrangling
Load
Import the data prepared by the./manipulation/0-greeter.R
| PassengerId | Survived | Pclass | Name | Sex | Age | SibSp | Parch | Ticket | Fare | Cabin | Embarked |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 0 | 3 | Braund, Mr. Owen Harris | male | 22 | 1 | 0 | A/5 21171 | 7.2500 | S | |
| 2 | 1 | 1 | Cumings, Mrs. John Bradley (Florence Briggs Thayer) | female | 38 | 1 | 0 | PC 17599 | 71.2833 | C85 | C |
| 3 | 1 | 3 | Heikkinen, Miss. Laina | female | 26 | 0 | 0 | STON/O2. 3101282 | 7.9250 | S | |
| 4 | 1 | 1 | Futrelle, Mrs. Jacques Heath (Lily May Peel) | female | 35 | 1 | 0 | 113803 | 53.1000 | C123 | S |
| 5 | 0 | 3 | Allen, Mr. William Henry | male | 35 | 0 | 0 | 373450 | 8.0500 | S | |
| 6 | 0 | 3 | Moran, Mr. James | male | NA | 0 | 0 | 330877 | 8.4583 | Q |
Observations: 891
Variables: 12
$ PassengerId <int> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, ...
$ Survived <int> 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1,...
$ Pclass <int> 3, 1, 3, 1, 3, 3, 1, 3, 3, 2, 3, 1, 3, 3, 3, 2, 3, 2, 3, 3, 2, 2, 3, 1, 3, 3, 3, 1, 3, 3, 1, 1,...
$ Name <chr> "Braund, Mr. Owen Harris", "Cumings, Mrs. John Bradley (Florence Briggs Thayer)", "Heikkinen, M...
$ Sex <chr> "male", "female", "female", "female", "male", "male", "male", "male", "female", "female", "fema...
$ Age <dbl> 22, 38, 26, 35, 35, NA, 54, 2, 27, 14, 4, 58, 20, 39, 14, 55, 2, NA, 31, NA, 35, 34, 15, 28, 8,...
$ SibSp <int> 1, 1, 0, 1, 0, 0, 0, 3, 0, 1, 1, 0, 0, 1, 0, 0, 4, 0, 1, 0, 0, 0, 0, 0, 3, 1, 0, 3, 0, 0, 0, 1,...
$ Parch <int> 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 1, 0, 0, 5, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 5, 0, 2, 0, 0, 0, 0,...
$ Ticket <chr> "A/5 21171", "PC 17599", "STON/O2. 3101282", "113803", "373450", "330877", "17463", "349909", "...
$ Fare <dbl> 7.2500, 71.2833, 7.9250, 53.1000, 8.0500, 8.4583, 51.8625, 21.0750, 11.1333, 30.0708, 16.7000, ...
$ Cabin <chr> "", "C85", "", "C123", "", "", "E46", "", "", "", "G6", "C103", "", "", "", "", "", "", "", "",...
$ Embarked <chr> "S", "C", "S", "S", "S", "Q", "S", "S", "S", "C", "S", "S", "S", "S", "S", "S", "Q", "S", "S", ...Inspect
To better understand the data set, let us inspect quantitative properties of each variable| variable | type | na | na_pct | unique | min | mean | max |
|---|---|---|---|---|---|---|---|
| PassengerId | int | 0 | 0.0 | 891 | 1.00 | 446.00 | 891.00 |
| Survived | int | 0 | 0.0 | 2 | 0.00 | 0.38 | 1.00 |
| Pclass | int | 0 | 0.0 | 3 | 1.00 | 2.31 | 3.00 |
| Name | chr | 0 | 0.0 | 891 | NA | NA | NA |
| Sex | chr | 0 | 0.0 | 2 | NA | NA | NA |
| Age | dbl | 177 | 19.9 | 89 | 0.42 | 29.70 | 80.00 |
| SibSp | int | 0 | 0.0 | 7 | 0.00 | 0.52 | 8.00 |
| Parch | int | 0 | 0.0 | 7 | 0.00 | 0.38 | 6.00 |
| Ticket | chr | 0 | 0.0 | 681 | NA | NA | NA |
| Fare | dbl | 0 | 0.0 | 248 | 0.00 | 32.20 | 512.33 |
| Cabin | chr | 0 | 0.0 | 148 | NA | NA | NA |
| Embarked | chr | 0 | 0.0 | 4 | NA | NA | NA |
Tweek
To prepare our data for modeling, let perform routine data transformations:
* 1. Convert column names to lowercase
* 2. Select and sort columns * 3. Rename columns
* 4. Covert strings to factors
* 5. Filter out missing values
Observations: 712
Variables: 8
$ survived <fct> Died, Survived, Survived, Survived, Died, Died, Died, Survived, Survived, Survived, Surv...
$ pclass <fct> Third, First, Third, First, Third, First, Third, Third, Second, Third, First, Third, Thi...
$ sex <fct> Men, Women, Women, Women, Men, Men, Men, Women, Women, Women, Women, Men, Men, Women, Wo...
$ age <dbl> 22, 38, 26, 35, 35, 54, 2, 27, 14, 4, 58, 20, 39, 14, 55, 2, 31, 35, 34, 15, 28, 8, 38, ...
$ n_siblings_spouses <int> 1, 1, 0, 1, 0, 0, 3, 0, 1, 1, 0, 0, 1, 0, 0, 4, 1, 0, 0, 0, 0, 3, 1, 3, 0, 0, 1, 1, 0, 2...
$ n_parents_children <int> 0, 0, 0, 0, 0, 0, 1, 2, 0, 1, 0, 0, 5, 0, 0, 1, 0, 0, 0, 0, 0, 1, 5, 2, 0, 0, 0, 0, 0, 0...
$ price_ticket <dbl> 7.2500, 71.2833, 7.9250, 53.1000, 8.0500, 51.8625, 21.0750, 11.1333, 30.0708, 16.7000, 2...
$ port_embarked <chr> "S", "C", "S", "S", "S", "S", "S", "S", "C", "S", "S", "S", "S", "S", "S", "Q", "S", "S"...Tabulating
Summary tables to help us see observed differenced broken down by levels of predictors
ds_modeling %>%
dplyr::group_by(survived, sex) %>%
dplyr::summarize(
n_people = n()
,mean_age = mean(age, na.rm = T)
)| survived | sex | n_people | mean_age |
|---|---|---|---|
| Died | Men | 360 | 31.61806 |
| Died | Women | 64 | 25.04688 |
| Survived | Men | 93 | 27.27602 |
| Survived | Women | 195 | 28.63077 |
Modeling
0 - Sex
Summary (m0)
Call:
stats::glm(formula = survived ~ sex, family = "binomial", data = ds_modeling)
Deviance Residuals:
Min 1Q Median 3Q Max
-1.6721 -0.6779 -0.6779 0.7534 1.7795
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -1.3535 0.1163 -11.64 <2e-16 ***
sexWomen 2.4676 0.1852 13.33 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 960.90 on 711 degrees of freedom
Residual deviance: 749.57 on 710 degrees of freedom
AIC: 753.57
Number of Fisher Scoring iterations: 4Graph (g0)
1 - Sex + Age
Summary (m1)
Call:
stats::glm(formula = survived ~ sex + age, family = "binomial",
data = ds_modeling)
Deviance Residuals:
Min 1Q Median 3Q Max
-1.7412 -0.6896 -0.6539 0.7572 1.9094
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -1.174251 0.222864 -5.269 1.37e-07 ***
sexWomen 2.453935 0.185570 13.224 < 2e-16 ***
age -0.005906 0.006339 -0.932 0.352
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 960.9 on 711 degrees of freedom
Residual deviance: 748.7 on 709 degrees of freedom
AIC: 754.7
Number of Fisher Scoring iterations: 4Graph (g1)
2 - Sex + Age + Class
Summary (m2)
Call:
stats::glm(formula = survived ~ sex + age + pclass, family = "binomial",
data = ds_modeling)
Deviance Residuals:
Min 1Q Median 3Q Max
-2.7274 -0.6795 -0.3958 0.6561 2.4657
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 1.255302 0.359875 3.488 0.000486 ***
sexWomen 2.513890 0.207614 12.108 < 2e-16 ***
age -0.037194 0.007669 -4.850 1.24e-06 ***
pclassSecond -1.301220 0.278173 -4.678 2.90e-06 ***
pclassThird -2.572385 0.281508 -9.138 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 960.90 on 711 degrees of freedom
Residual deviance: 646.69 on 707 degrees of freedom
AIC: 656.69
Number of Fisher Scoring iterations: 5Graph (g2)
3 - Sex + Age + Class + Port
Summary (m3)
Call:
stats::glm(formula = survived ~ sex + age + pclass + port_embarked,
family = "binomial", data = ds_modeling)
Deviance Residuals:
Min 1Q Median 3Q Max
-2.6464 -0.6808 -0.3979 0.6367 2.4715
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 1.521032 0.390591 3.894 9.85e-05 ***
sexWomen 2.515793 0.209293 12.020 < 2e-16 ***
age -0.036082 0.007715 -4.677 2.92e-06 ***
pclassSecond -1.144614 0.290678 -3.938 8.23e-05 ***
pclassThird -2.409565 0.291179 -8.275 < 2e-16 ***
port_embarkedQ -0.814190 0.567903 -1.434 0.1517
port_embarkedS -0.493651 0.266886 -1.850 0.0644 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 960.90 on 711 degrees of freedom
Residual deviance: 642.68 on 705 degrees of freedom
AIC: 656.68
Number of Fisher Scoring iterations: 5Graph (g3)
session information
For the sake of documentation and reproducibility, the current report was rendered in the following environment. Click the line below to expand.
Environment
R version 3.5.2 (2018-12-20)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows 10 x64 (build 17763)
Matrix products: default
locale:
[1] LC_COLLATE=English_United States.1252 LC_CTYPE=English_United States.1252 LC_MONETARY=English_United States.1252
[4] LC_NUMERIC=C LC_TIME=English_United States.1252
attached base packages:
[1] grid stats graphics grDevices utils datasets methods base
other attached packages:
[1] RColorBrewer_1.1-2 dichromat_2.0-0 titanic_0.1.0 ggplot2_3.1.1 dplyr_0.8.3 magrittr_1.5
[7] knitr_1.26
loaded via a namespace (and not attached):
[1] tidyselect_0.2.5 xfun_0.11 purrr_0.3.3 reshape2_1.4.3 colorspace_1.4-1 vctrs_0.2.0
[7] htmltools_0.4.0 yaml_2.2.0 utf8_1.1.4 rlang_0.4.1 pillar_1.4.2 later_1.0.0
[13] glue_1.3.1 withr_2.1.2 lifecycle_0.1.0 plyr_1.8.4 stringr_1.4.0 munsell_0.5.0
[19] gtable_0.3.0 explore_0.5.1 htmlwidgets_1.5.1 evaluate_0.14 memoise_1.1.0 labeling_0.3
[25] fastmap_1.0.1 httpuv_1.5.2 fansi_0.4.0 highr_0.8 Rcpp_1.0.3 xtable_1.8-4
[31] backports_1.1.5 scales_1.0.0 promises_1.1.0 DT_0.10 mime_0.7 gridExtra_2.3
[37] digest_0.6.22 stringi_1.4.3 shiny_1.4.0 cli_1.1.0 tools_3.5.2 lazyeval_0.2.2
[43] tibble_2.1.3 crayon_1.3.4 tidyr_1.0.0 pkgconfig_2.0.3 zeallot_0.1.0 ellipsis_0.3.0
[49] assertthat_0.2.1 rmarkdown_1.17 R6_2.4.1 compiler_3.5.2