Load data

# load in the raw data
training_raw <- as.data.frame(fread(path('pml-training.csv'), na.strings = c('NA', '', '#DIV/0')) %>%
  mutate(classe = as.factor(classe)))
testing <- as.data.frame(fread(path('pml-testing.csv'), na.strings = c('NA', '', '#DIV/0')))

Partition into training and validation sets

inTrain <- createDataPartition(training_raw$classe, p = 0.7, list = FALSE)
training <- training_raw[inTrain,]
validation <- training_raw[-inTrain,]

Remove irrelevant variables and variables with >= 50% NAs

# remove the `V1` variable from all data
# and make classe a factor variable
training <- training %>%
  select(-V1)
validation <- validation %>%
  select(-V1)
testing <- testing %>%
  select(-V1)

# store problem numbers in testing data as a vector (will use later)
testingProblemIDs <- testing$problem_id

# then remove the `problem_id` variable
testing <- testing %>%
  select(-problem_id)

# remove variables with majority NA values from all sets
numRows <- nrow(training)
include <- NULL
for(ii in 1:ncol(training)){
  sumNAs <- sum(is.na(training[,ii]))/numRows
  if (sumNAs < 0.5) {
    include <- c(include, ii)
  } else {
  }
}

trainingSet <- training[,include]
validationSet <- validation[,include]
indicesForTest <- include[1:length(include)-1] # account for 1 less variable in testing data (classe)
testingSet <- testing[,indicesForTest]

Remove variables with near-zero-variance

nzv_training <- nearZeroVar(trainingSet, saveMetrics = FALSE)
trainingSet <- trainingSet[,-nzv_training]
nzv_validation <- nearZeroVar(validationSet, saveMetrics = FALSE)
validationSet <- validationSet[,-nzv_validation]
nzv_testing <- nearZeroVar(testingSet, saveMetrics = FALSE)
testingSet <- testingSet[,-nzv_testing]

# check that column names are still consistent across datasets
all(names(trainingSet) == names(validationSet))

## [1] TRUE

all(names(trainingSet)[1:length(testingSet)] == names(testingSet))

## [1] TRUE

Convert variable types

trainingSet <- trainingSet %>% mutate_if(is.character, as.factor)
validationSet <- validationSet %>% mutate_if(is.character, as.factor)
testingSet <- testingSet %>% mutate_if(is.character, as.factor)

Option 1: Decision tree

# fit the model 
mod_rpart <- train(classe ~ ., method = "rpart", data = trainingSet)

# show the decision tree
fancyRpartPlot(mod_rpart$finalModel)

# predict validation set values based on model fit
predict_rpart <- predict(mod_rpart, newdata = validationSet)
 
# compute accuracy of model in predicting validation set classe
confusionMatrix(predict_rpart, validationSet$classe)$overall[1]

##  Accuracy 
## 0.5542906

Option 2: Random forest

# fit the model 
mod_rf <- randomForest(classe ~ ., data = trainingSet)

# predict validation set values based on model fit
predict_rf <- predict(mod_rf, newdata = validationSet)
 
# compute accuracy of model in predicting validation set classe
confusionMatrix(predict_rf, validationSet$classe)$overall[1]

##  Accuracy 
## 0.9991504

Option 3: Boosting

# fit the model 
mod_gbm <- train(classe ~ ., method = "gbm", data = trainingSet, verbose = FALSE, 
                 trControl = trainControl(method = "cv", number = 8)) # added training control options, otherwise too computationally intensive for my machine

# predict validation set values based on model fit
predict_gbm <- predict(mod_gbm, newdata = validationSet)
 
# compute accuracy of model in predicting validation set classe
confusionMatrix(predict_gbm, validationSet$classe)$overall[1]

##  Accuracy 
## 0.9971113

Option 4: Linear discriminant

# fit the model 
mod_lda <- train(classe ~ ., method = "lda", data = trainingSet)

# predict validation set values based on model fit
predict_lda <- predict(mod_lda, newdata = validationSet)
 
# compute accuracy of model in predicting validation set classe
confusionMatrix(predict_lda, validationSet$classe)$overall[1]

## Accuracy 
## 0.864401

Most accurate prediction method

Of all methods used, the random forest method yielded the highest accuracy in terms of predictions of the validation set. It is worth noting that the boosting method yielded an accuracy value that was only very slightly lower, whereas the linear discriminant and decision tree methods were less accurate. The percent expected out-of-sample error for the random forest method is calculated below:

accuracy_rf <- confusionMatrix(predict_rf, validationSet$classe)$overall[1]
expected_error <- 100 - accuracy_rf*100
expected_error 

##   Accuracy 
## 0.08496177

Most important predictor variables according to the random forest method

Using the random forest method method, the following 5 variables were most useful for prediction:

indices <- order(varImp(mod_rf))[1:5]
names(testingSet)[indices]

## [1] "raw_timestamp_part_2" "gyros_arm_z"          "gyros_dumbbell_z"    
## [4] "gyros_forearm_x"      "gyros_forearm_z"

Predictions of test set values

Using this method, I obtain the following predictions from the original testing data:

# ensure that training set and testing set data have matching factor levels

levels(testingSet$user_name) <- levels(trainingSet$user_name)
levels(testingSet$cvtd_timestamp) <- levels(trainingSet$cvtd_timestamp)

predictedVals <- predict(mod_rf, newdata = testingSet)
kable(data.frame(testingProblemIDs, predictedVals), format = 'html') %>%
  kable_styling('striped', full_width = FALSE)