Joshua Cook June 9, 2020
TidyTuesday link: https://github.com/rfordatascience/tidytuesday/blob/master/data/2020/2020-01-14/readme.md
knitr::opts_chunk$set(echo = TRUE,
comment = "#>",
cache = TRUE,
dpi = 300)
library(mustashe)
library(glue)
library(magrittr)
library(rstanarm)
library(bayestestR)
library(see)
library(MASS)
library(tidyverse)
library(conflicted)
conflict_prefer("filter", "dplyr")
conflict_prefer("select", "dplyr")
theme_set(theme_minimal())passwords <- read_csv(
"https://raw.githubusercontent.com/rfordatascience/tidytuesday/master/data/2020/2020-01-14/passwords.csv"
) %>%
janitor::clean_names() %>%
filter(!is.na(password)) %>%
select(-font_size) %>%
filter(strength <= 10)#> Parsed with column specification:
#> cols(
#> rank = col_double(),
#> password = col_character(),
#> category = col_character(),
#> value = col_double(),
#> time_unit = col_character(),
#> offline_crack_sec = col_double(),
#> rank_alt = col_double(),
#> strength = col_double(),
#> font_size = col_double()
#> )
time_table <- tribble(
~ time_unit, ~ in_sec,
"years", 60*60*24*365,
"months", 60*60*24*30.42,
"weeks", 60*60*24*7,
"days", 60*60*24,
"hours", 60*60,
"minutes", 60,
"seconds", 1
)
passwords %<>%
mutate(password_len = str_length(password)) %>%
left_join(time_table, by = "time_unit") %>%
mutate(guess_crack_sec = value * in_sec) %>%
select(-c(in_sec, value, time_unit))passwords %>%
count(category, sort = TRUE)#> # A tibble: 10 x 2
#> category n
#> <chr> <int>
#> 1 name 183
#> 2 cool-macho 79
#> 3 simple-alphanumeric 61
#> 4 fluffy 44
#> 5 sport 37
#> 6 nerdy-pop 30
#> 7 animal 29
#> 8 password-related 15
#> 9 food 11
#> 10 rebellious-rude 11
set.seed(0)
categories <- sort(unique(passwords$category))
category_pal <- randomcoloR::distinctColorPalette(length(categories))
names(category_pal) <- categories
passwords %>%
ggplot(aes(log(guess_crack_sec))) +
geom_density(aes(color = category, fill = category), size = 1.2, alpha = 0.2) +
scale_color_manual(values = category_pal) +
scale_fill_manual(values = category_pal) +
theme(legend.position = "top") +
labs(x = "time to guess the password (log(sec))",
y = "density",
title = "Time taken to guess the passwords of different categories")
passwords %>%
ggplot(aes(x = log(guess_crack_sec), y = log(offline_crack_sec))) +
geom_point()
passwords %>%
ggplot(aes(x = factor(password_len), y = log(guess_crack_sec))) +
geom_boxplot(width = 0.5)
passwords %<>%
mutate(num_alpha = str_count(password, "[:alpha:]"),
num_digit = str_count(password, "[:digit:]"))passwords %>%
select(password, strength, password_len, num_alpha, num_digit) %>%
pivot_longer(-c(password, strength)) %>%
ggplot(aes(x = name, y = value, color = strength)) +
geom_point(alpha = 0.5) +
geom_line(aes(group = password), alpha = 0.3) +
scale_color_gradient(low = "purple", high = "orange") +
theme(axis.text.x = element_text(angle = 35, hjust = 1))
scale2 <- function(x, na.rm = FALSE) {
(x - mean(x, na.rm = na.rm)) / sd(x, na.rm)
}
m1_data <- passwords %>%
select(strength, password_len, num_alpha, num_digit) %>%
mutate(password_len = scale2(password_len),
num_alpha = scale2(num_alpha),
num_digit = scale2(num_digit))m1 <- lm(
strength ~ .^2,
data = m1_data
)
m1_step <- stepAIC(m1, direction = "both", trace = 0)summary(m1)#>
#> Call:
#> lm(formula = strength ~ .^2, data = m1_data)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -8.5050 -0.8464 0.3246 1.1536 6.2074
#>
#> Coefficients: (2 not defined because of singularities)
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 6.6059505 0.0911029 72.511 <2e-16 ***
#> password_len -0.0128339 0.0925889 -0.139 0.890
#> num_alpha 1.6427485 0.0925505 17.750 <2e-16 ***
#> num_digit NA NA NA NA
#> password_len:num_alpha 0.0006545 0.0979508 0.007 0.995
#> password_len:num_digit 0.0059876 0.1004507 0.060 0.952
#> num_alpha:num_digit NA NA NA NA
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 1.635 on 480 degrees of freedom
#> Multiple R-squared: 0.5019, Adjusted R-squared: 0.4978
#> F-statistic: 120.9 on 4 and 480 DF, p-value: < 2.2e-16
summary(m1_step)#>
#> Call:
#> lm(formula = strength ~ password_len + num_digit, data = m1_data)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -8.5085 -0.8457 0.3229 1.1543 6.1832
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 6.60619 0.07411 89.14 <2e-16 ***
#> password_len 0.87495 0.07420 11.79 <2e-16 ***
#> num_digit -1.36241 0.07420 -18.36 <2e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 1.632 on 482 degrees of freedom
#> Multiple R-squared: 0.5019, Adjusted R-squared: 0.4999
#> F-statistic: 242.9 on 2 and 482 DF, p-value: < 2.2e-16
anova(m1, m1_step)#> Analysis of Variance Table
#>
#> Model 1: strength ~ (password_len + num_alpha + num_digit)^2
#> Model 2: strength ~ password_len + num_digit
#> Res.Df RSS Df Sum of Sq F Pr(>F)
#> 1 480 1283.9
#> 2 482 1283.9 -2 -0.022948 0.0043 0.9957
AIC(m1, m1_step)#> df AIC
#> m1 6 1860.527
#> m1_step 4 1856.536
library(caret)
library(glmnet)
m_elastic <- train(
strength ~ .^2,
data = m1_data,
method = "glmnet",
trControl = trainControl("cv", number = 10),
tuneLength = 10
)m_elastic$results %>%
ggplot(aes(alpha, RMSE)) +
geom_point(aes(color = lambda)) +
geom_line(aes(color = lambda, group = factor(lambda))) +
scale_color_gradient(low = "purple", high = "orange") +
labs(x = "alpha", y = "RMSE", color = "lambda",
title = "Tuning parameters for elastic net")
m_elastic$bestTune#> alpha lambda
#> 76 1 0.04964918
coef(m_elastic$finalModel, m_elastic$bestTune$lambda)#> 7 x 1 sparse Matrix of class "dgCMatrix"
#> 1
#> (Intercept) 6.606186
#> password_len .
#> num_alpha 1.585278
#> num_digit .
#> password_len:num_alpha .
#> password_len:num_digit .
#> num_alpha:num_digit .
m1_stan <- stan_glm(
strength ~ num_alpha + num_digit,
data = m1_data,
family = gaussian(link = "identity"),
prior = normal(location = 0, scale = 1),
prior_intercept = normal(location = 5, scale = 1),
cores = 1,
seed = 0
)#>
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summary(m1_stan)#>
#> Model Info:
#> function: stan_glm
#> family: gaussian [identity]
#> formula: strength ~ num_alpha + num_digit
#> algorithm: sampling
#> sample: 4000 (posterior sample size)
#> priors: see help('prior_summary')
#> observations: 485
#> predictors: 3
#>
#> Estimates:
#> mean sd 10% 50% 90%
#> (Intercept) 6.6 0.1 6.5 6.6 6.7
#> num_alpha 1.6 0.1 1.4 1.6 1.8
#> num_digit 0.0 0.1 -0.2 0.0 0.2
#> sigma 1.6 0.1 1.6 1.6 1.7
#>
#> Fit Diagnostics:
#> mean sd 10% 50% 90%
#> mean_PPD 6.6 0.1 6.5 6.6 6.7
#>
#> The mean_ppd is the sample average posterior predictive distribution of the outcome variable (for details see help('summary.stanreg')).
#>
#> MCMC diagnostics
#> mcse Rhat n_eff
#> (Intercept) 0.0 1.0 3258
#> num_alpha 0.0 1.0 2233
#> num_digit 0.0 1.0 2288
#> sigma 0.0 1.0 3218
#> mean_PPD 0.0 1.0 3624
#> log-posterior 0.0 1.0 1593
#>
#> For each parameter, mcse is Monte Carlo standard error, n_eff is a crude measure of effective sample size, and Rhat is the potential scale reduction factor on split chains (at convergence Rhat=1).
describe_posterior(m1_stan)#> Possible multicollinearity between num_digit and num_alpha (r = 0.85). This might lead to inappropriate results. See 'Details' in '?rope'.
#> # Description of Posterior Distributions
#>
#> Parameter | Median | 89% CI | pd | 89% ROPE | % in ROPE | Rhat | ESS
#> -----------------------------------------------------------------------------------------------
#> (Intercept) | 6.602 | [ 6.487, 6.730] | 1.000 | [-0.231, 0.231] | 0.000 | 1.000 | 3258.098
#> num_alpha | 1.613 | [ 1.386, 1.846] | 1.000 | [-0.231, 0.231] | 0.000 | 1.000 | 2232.847
#> num_digit | -0.022 | [-0.267, 0.190] | 0.565 | [-0.231, 0.231] | 96.855 | 1.002 | 2287.809
plot(point_estimate(m1_stan), show_intercept = TRUE, priors = TRUE)
plot(point_estimate(m1_stan), show_intercept = TRUE, priors = FALSE)
plot(hdi(m1_stan), show_intercept = TRUE)
m2_stan <- stan_glm(
strength ~ password_len,
data = m1_data,
family = gaussian(link = "identity"),
prior = normal(location = 0, scale = 3),
prior_intercept = normal(location = 5, scale = 3),
cores = 1,
seed = 0
)#>
#> SAMPLING FOR MODEL 'continuous' NOW (CHAIN 1).
#> Chain 1:
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describe_posterior(m2_stan)#> # Description of Posterior Distributions
#>
#> Parameter | Median | 89% CI | pd | 89% ROPE | % in ROPE | Rhat | ESS
#> --------------------------------------------------------------------------------------------
#> (Intercept) | 6.605 | [6.456, 6.753] | 1 | [-0.231, 0.231] | 0 | 1.000 | 4345.994
#> password_len | 0.902 | [0.752, 1.050] | 1 | [-0.231, 0.231] | 0 | 1.000 | 4621.807
plot(point_estimate(m2_stan), show_intercept = TRUE, priors = TRUE)
plot(point_estimate(m2_stan), show_intercept = TRUE, priors = FALSE)
plot(hdi(m2_stan), show_intercept = TRUE)
m2_data <- passwords %>%
mutate(password_len = scale2(password_len),
char_password = str_detect(password, "[:alpha:]")) %>%
select(strength, category, password_len, char_password)
m2_data#> # A tibble: 485 x 4
#> strength category password_len char_password
#> <dbl> <chr> <dbl> <lgl>
#> 1 8 password-related 1.73 TRUE
#> 2 4 simple-alphanumeric -0.172 FALSE
#> 3 4 simple-alphanumeric 1.73 FALSE
#> 4 4 simple-alphanumeric -2.07 FALSE
#> 5 8 simple-alphanumeric -0.172 TRUE
#> 6 4 simple-alphanumeric -1.12 FALSE
#> 7 8 animal -0.172 TRUE
#> 8 4 sport 1.73 TRUE
#> 9 7 sport 1.73 TRUE
#> 10 8 password-related 0.778 TRUE
#> # … with 475 more rows