library(pacman)
p_load(titanic, tidyverse, janitor, naniar, DataExplorer, tidymodels, discrim)

Load the data from the titanic R package. Note that the titanic_train dataset contains the labels for Survived aND THE titanic_test dataset does not contain the labels. So we will build our machine learning model using the titanic_train dataset and then make a final classification for the titanic_test dataset. This is how kaggle competitions are done.

I like to clean names so the variables all have names with lowercase letters and underscores.

titanic_train <- titanic_train %>% clean_names()

head(titanic_train)

It is always a good idea to check for duplicate records/examples/rows in your dataset.

get_dupes(titanic_train)
No variable names specified - using all columns.

No duplicate combinations found of: passenger_id, survived, pclass, name, sex, age, sib_sp, parch, ticket, ... and 3 other variables

Drop the unique identifiers: passenger_id, name, and ticket. Also drop cabin because it has a high missing rate.

titanic_train2 <- titanic_train %>% select(-passenger_id, -name, -ticket, -cabin) %>%
  mutate(
    survived = as_factor(survived),
    pclass = as_factor(pclass),
    sex = as_factor(sex),
    embarked = as_factor(embarked)
  )

head(titanic_train2)
titanic_test <- titanic_test %>% clean_names()

head(titanic_test)

It is always a good idea to check for duplicate records/examples/rows in your dataset.

get_dupes(titanic_test)
No variable names specified - using all columns.

No duplicate combinations found of: passenger_id, pclass, name, sex, age, sib_sp, parch, ticket, fare, ... and 2 other variables
titanic_test2 <- titanic_test %>% select(-passenger_id, -name, -ticket, -cabin) %>%
  mutate(
    pclass = as_factor(pclass),
    sex = as_factor(sex),
    embarked = as_factor(embarked)
  )

head(titanic_test2)
NA

Start by investigating the missing values and completeness of the features in the data. Note that the age variable contains some missing values.

vis_miss(titanic_train2)

gg_miss_var(titanic_train2)

gg_miss_var(titanic_train2, show_pct = TRUE)

create_report(titanic_train2, y = "survived", output_file = "report.html", output_dir = getwd())

Now try the ML algorithms.

Model 0:

Summarize the y-variable. Null Model.

titanic_train2 %>% group_by(survived) %>%
  summarize(n = n()) %>%
  mutate(freq = n / sum(n))

Make the first split with 80% of the data being in the training data set.

titanic_train2_split <- initial_split(titanic_train2, prop = 0.8)
titanic_train2_split
<Analysis/Assess/Total>
<713/178/891>

Training data.

titanic_train2_split %>%
  training() 

Create the recipe for applying the preprocessing. Note the use of step_nzv(), which removes any columns that have very low variability, and the use of the step_meanimpute() function, which fills in the cells that are missing with the mean of the column.

Apply the recipe, so the age variable should be complete after the imputation.

titanic_train2_testing <- titanic_train2_recipe %>%
  bake(testing(titanic_train2_split)) 

titanic_train2_testing
titanic_train2_training <- juice(titanic_train2_recipe)

titanic_train2_training

Model 0: null

null_model(mode = "classification")
Model Specification (classification)
titanic_train2_null <- null_model() %>%
  set_mode("classification") %>%
  fit(survived ~ ., data = titanic_train2_training)
Engine set to `parsnip`.
predict(titanic_train2_null, titanic_train2_training)
titanic_train2_null %>%
  predict(titanic_train2_testing) %>%
  bind_cols(titanic_train2_testing) 
titanic_train2_null %>%
  predict(titanic_train2_testing) %>%
  bind_cols(titanic_train2_testing) %>%
  metrics(truth = survived, estimate = .pred_class)
titanic_train2_null %>%
  predict(titanic_train2_testing) %>%
  bind_cols(titanic_train2_testing) %>%
  conf_mat(truth = survived, estimate = .pred_class)
          Truth
Prediction   0   1
         0 109  69
         1   0   0
titanic_train2_null %>%
  predict(titanic_train2_testing, type = "prob") %>%
  bind_cols(titanic_train2_testing) %>%
  roc_curve(survived, .pred_0) %>%
  autoplot() 

Model 4: GLM

Setup the model.

titanic_train2_glm <- logistic_reg(penalty = 0.001, mixture = 0.5) %>% 
  set_engine("glmnet") %>%
  set_mode("classification") %>%
  fit(survived ~ ., data = titanic_train2_training)
predict(titanic_train2_glm, titanic_train2_training)
titanic_train2_glm %>%
  predict(titanic_train2_testing) %>%
  bind_cols(titanic_train2_testing) 
titanic_train2_glm %>%
  predict(titanic_train2_testing) %>%
  bind_cols(titanic_train2_testing) %>%
  metrics(truth = survived, estimate = .pred_class)
titanic_train2_glm %>%
  predict(titanic_train2_testing) %>%
  bind_cols(titanic_train2_testing) %>%
  conf_mat(truth = survived, estimate = .pred_class)
          Truth
Prediction   0   1
         0 104  48
         1   5  21
titanic_train2_glm %>%
  predict(titanic_train2_testing, type = "prob") %>%
  bind_cols(titanic_train2_testing) %>%
  roc_curve(survived, .pred_0) %>%
  autoplot()

titanic_train2_glm %>%
  predict(titanic_train2_testing, type = "prob") %>%
  bind_cols(titanic_train2_testing) %>%
  roc_auc(survived, .pred_0) 

Model 5: Naive Bayes

Setup the model.

titanic_train2_nb <- naive_Bayes(Laplace = 1) %>% 
  set_engine("klaR") %>%
  set_mode("classification") %>%
  fit(survived ~ ., data = titanic_train2_training)
predict(titanic_train2_nb, titanic_train2_training)
Numerical 0 probability for all classes with observation 348
titanic_train2_nb %>%
  predict(titanic_train2_testing) %>%
  bind_cols(titanic_train2_testing) 
titanic_train2_nb %>%
  predict(titanic_train2_testing) %>%
  bind_cols(titanic_train2_testing) %>%
  metrics(truth = survived, estimate = .pred_class)
titanic_train2_nb %>%
  predict(titanic_train2_testing) %>%
  bind_cols(titanic_train2_testing) %>%
  conf_mat(truth = survived, estimate = .pred_class)
          Truth
Prediction  0  1
         0 81 40
         1 28 29

titanic_train2_nb %>%
  predict(titanic_train2_testing, type = "prob") %>%
  bind_cols(titanic_train2_testing) %>%
  roc_auc(survived, .pred_0) 
titanic_train2_nb %>%
  predict(titanic_train2_testing, type = "prob") %>%
  bind_cols(titanic_train2_testing) %>%
  ggplot() +
  geom_density(aes(x = .pred_1, fill = survived), 
               alpha = 0.5)
---
title: "Stat 652: Midterm: Model 4, Model 5"
author: "Prof. Eric A. Suess"
output:
  html_notebook: default
  word_document: default
  pdf_document: default
---



```{r}
library(pacman)
p_load(titanic, tidyverse, janitor, naniar, DataExplorer, tidymodels, discrim)
```

Load the data from the titanic R package.  Note that the *titanic_train* dataset contains the labels for Survived aND THE *titanic_test* dataset does not contain the labels.  So we will build our machine learning model using the *titanic_train* dataset and then make a final classification for the *titanic_test* dataset.  This is how kaggle competitions are done.

I like to clean names so the variables all have names with lowercase letters and underscores.

```{r}
titanic_train <- titanic_train %>% clean_names()

head(titanic_train)
```

It is always a good idea to check for duplicate records/examples/rows in your dataset.

```{r}
get_dupes(titanic_train)
```

Drop the unique identifiers: *passenger_id*, *name*, and *ticket*.  Also drop *cabin* because it has a high missing rate.

```{r}
titanic_train2 <- titanic_train %>% select(-passenger_id, -name, -ticket, -cabin) %>%
  mutate(
    survived = as_factor(survived),
    pclass = as_factor(pclass),
    sex = as_factor(sex),
    embarked = as_factor(embarked)
  )

head(titanic_train2)
```

```{r}
titanic_test <- titanic_test %>% clean_names()

head(titanic_test)
```

It is always a good idea to check for duplicate records/examples/rows in your dataset.

```{r}
get_dupes(titanic_test)
```

```{r}
titanic_test2 <- titanic_test %>% select(-passenger_id, -name, -ticket, -cabin) %>%
  mutate(
    pclass = as_factor(pclass),
    sex = as_factor(sex),
    embarked = as_factor(embarked)
  )

head(titanic_test2)

```


Start by investigating the missing values and completeness of the features in the data.  Note that the *age* variable contains some missing values.

```{r}
vis_miss(titanic_train2)
gg_miss_var(titanic_train2)
gg_miss_var(titanic_train2, show_pct = TRUE)
```

```{r eval = FALSE}
create_report(titanic_train2, y = "survived", output_file = "report.html", output_dir = getwd())
```

Now try the ML algorithms.


## Model 0:

Summarize the y-variable.  Null Model.

```{r}
titanic_train2 %>% group_by(survived) %>%
  summarize(n = n()) %>%
  mutate(freq = n / sum(n))
```

Make the first split with 80% of the data being in the training data set.

```{r}
titanic_train2_split <- initial_split(titanic_train2, prop = 0.8)
titanic_train2_split
```

Training data.

```{r}
titanic_train2_split %>%
  training() 
```

Create the recipe for applying the preprocessing.  Note the use of step_nzv(), which removes any columns that have very low variability, and the use of the step_meanimpute() function, which fills in the cells that are missing with the mean of the column.

```{r}
titanic_train2_recipe <- training(titanic_train2_split) %>%
  recipe(survived ~ .) %>%
  step_rm(pclass, sex, embarked) %>% 
  step_nzv(all_predictors()) %>%
  step_meanimpute(age) %>%
  prep()

summary(titanic_train2_recipe)

tidy(titanic_train2_recipe)
```

Apply the recipe, so the *age* variable should be complete after the imputation.

```{r}
titanic_train2_testing <- titanic_train2_recipe %>%
  bake(testing(titanic_train2_split)) 

titanic_train2_testing
```

```{r}
titanic_train2_training <- juice(titanic_train2_recipe)

titanic_train2_training
```

### Model 0: null


```{r}
null_model(mode = "classification")

titanic_train2_null <- null_model() %>%
  set_mode("classification") %>%
  fit(survived ~ ., data = titanic_train2_training)

```

```{r}
predict(titanic_train2_null, titanic_train2_training)
```

```{r}
titanic_train2_null %>%
  predict(titanic_train2_testing) %>%
  bind_cols(titanic_train2_testing) 
```


```{r}
titanic_train2_null %>%
  predict(titanic_train2_testing) %>%
  bind_cols(titanic_train2_testing) %>%
  metrics(truth = survived, estimate = .pred_class)
```



```{r}
titanic_train2_null %>%
  predict(titanic_train2_testing) %>%
  bind_cols(titanic_train2_testing) %>%
  conf_mat(truth = survived, estimate = .pred_class)
```

```{r}
titanic_train2_null %>%
  predict(titanic_train2_testing, type = "prob") %>%
  bind_cols(titanic_train2_testing) %>%
  roc_curve(survived, .pred_0) %>%
  autoplot() 
```



### Model 4: GLM

Setup the model.

```{r}
titanic_train2_glm <- logistic_reg(penalty = 0.001, mixture = 0.5) %>% 
  set_engine("glmnet") %>%
  set_mode("classification") %>%
  fit(survived ~ ., data = titanic_train2_training)

```



```{r}
predict(titanic_train2_glm, titanic_train2_training)
```

```{r}
titanic_train2_glm %>%
  predict(titanic_train2_testing) %>%
  bind_cols(titanic_train2_testing) 
```


```{r}
titanic_train2_glm %>%
  predict(titanic_train2_testing) %>%
  bind_cols(titanic_train2_testing) %>%
  metrics(truth = survived, estimate = .pred_class)
```



```{r}
titanic_train2_glm %>%
  predict(titanic_train2_testing) %>%
  bind_cols(titanic_train2_testing) %>%
  conf_mat(truth = survived, estimate = .pred_class)
```

```{r}
titanic_train2_glm %>%
  predict(titanic_train2_testing, type = "prob") %>%
  bind_cols(titanic_train2_testing) %>%
  roc_curve(survived, .pred_0) %>%
  autoplot()
```

```{r}
titanic_train2_glm %>%
  predict(titanic_train2_testing, type = "prob") %>%
  bind_cols(titanic_train2_testing) %>%
  roc_auc(survived, .pred_0) 
```

```{r}
titanic_train2_glm %>%
  predict(titanic_train2_testing, type = "prob") %>%
  bind_cols(titanic_train2_testing) %>%
  ggplot() +
  geom_density(aes(x = .pred_1, fill = survived), 
               alpha = 0.5)
```

### Model 5: Naive Bayes

Setup the model.

```{r}
titanic_train2_nb <- naive_Bayes(Laplace = 1) %>% 
  set_engine("klaR") %>%
  set_mode("classification") %>%
  fit(survived ~ ., data = titanic_train2_training)

```



```{r}
predict(titanic_train2_nb, titanic_train2_training)
```

```{r}
titanic_train2_nb %>%
  predict(titanic_train2_testing) %>%
  bind_cols(titanic_train2_testing) 
```


```{r}
titanic_train2_nb %>%
  predict(titanic_train2_testing) %>%
  bind_cols(titanic_train2_testing) %>%
  metrics(truth = survived, estimate = .pred_class)
```



```{r}
titanic_train2_nb %>%
  predict(titanic_train2_testing) %>%
  bind_cols(titanic_train2_testing) %>%
  conf_mat(truth = survived, estimate = .pred_class)
```

```{r}
titanic_train2_nb %>%
  predict(titanic_train2_testing, type = "prob") %>%
  bind_cols(titanic_train2_testing) %>%
  roc_curve(survived, .pred_0) %>%
  autoplot() 
```

```{r}
titanic_train2_nb %>%
  predict(titanic_train2_testing, type = "prob") %>%
  bind_cols(titanic_train2_testing) %>%
  roc_auc(survived, .pred_0) 
```


```{r}
titanic_train2_nb %>%
  predict(titanic_train2_testing, type = "prob") %>%
  bind_cols(titanic_train2_testing) %>%
  ggplot() +
  geom_density(aes(x = .pred_1, fill = survived), 
               alpha = 0.5)
```



