Using devices such as Jawbone Up, Nike FuelBand, and Fitbit it is now possible to collect a large amount of data about personal activity relatively inexpensively. These type of devices are part of the quantified self movement - a group of enthusiasts who take measurements about themselves regularly to improve their health, to find patterns in their behavior, or because they are tech geeks. One thing that people regularly do is quantify how much of a particular activity they do, but they rarely quantify how well they do it. The goal of this project is to use data from accelerometers on the belt, forearm, arm, and dumbbell of 6 participants as they perform barbell lifts correctly and incorrectly 5 different ways.

The training data for this project are available at:

https://d396qusza40orc.cloudfront.net/predmachlearn/pml-training.csv

The test data are available at:

https://d396qusza40orc.cloudfront.net/predmachlearn/pml-testing.csv

The goal of this project is to predict the manner in which subjects did the exercise. This is the "classe" variable in the training set. The model will use the other variables to predict with. This report describes:

• How the model is built
• Use of cross validation
• An estimate of expected out of sample error

The first step is to download the data, load it into R and prepare it for the modeling process.

All functions are loaded and static variables are assigned. Also in this section, the seed is set so the pseudo-random number generator operates in a consistent way for repeat-ability.

library(rpart.plot)
library(caret)
library(rpart)
library(rattle)
library(RColorBrewer)
library(randomForest)
library(e1071)

set.seed(1)

# You should download required files first

path <- paste(getwd(),"/","data", sep="")
train.file <- file.path(path, "pml-training.csv")
test.file <- file.path(path, "pml-testing.csv")

Process missing data (i.e., "NA", "#DIV/0!" and ""), and set them all to NA.

train.data.raw <- read.csv(train.file, na.strings=c("NA","#DIV/0!",""))
test.data.raw <- read.csv(test.file, na.strings=c("NA","#DIV/0!",""))

Columns that are not deeded for the model and columns that contain NAs are eliminated.

# Drop the first 7 columns as they're unnecessary for predicting.
train.data.clean1 <- train.data.raw[,8:length(colnames(train.data.raw))]
test.data.clean1 <- test.data.raw[,8:length(colnames(test.data.raw))]

# Drop colums with NAs
train.data.clean1 <- train.data.clean1[, colSums(is.na(train.data.clean1)) == 0] 
test.data.clean1 <- test.data.clean1[, colSums(is.na(test.data.clean1)) == 0] 

# Check for near zero variance predictors and drop them if necessary
nzv <- nearZeroVar(train.data.clean1,saveMetrics=TRUE)
zero.var.ind <- sum(nzv$nzv)

if ((zero.var.ind>0)) {
        train.data.clean1 <- train.data.clean1[,nzv$nzv==FALSE]
}

The training data is divided into two sets. This first is a training set with 70% of the data which is used to train the model. The second is a validation set used to assess model performance.

in.training <- createDataPartition(train.data.clean1$classe, p=0.70, list=F)
train.data.final <- train.data.clean1[in.training, ]
validate.data.final <- train.data.clean1[-in.training, ]

The training data-set is used to fit a Random Forest model because it automatically selects important variables and is robust to correlated covariates & outliers in general. 5-fold cross validation is used when applying the algorithm. A Random Forest algorithm is a way of averaging multiple deep decision trees, trained on different parts of the same data-set, with the goal of reducing the variance. This typically produces better performance at the expense of bias and interpret-ability. The Cross-validation technique assesses how the results of a statistical analysis will generalize to an independent data set. In 5-fold cross-validation, the original sample is randomly partitioned into 5 equal sized sub-samples. a single sample is retained for validation and the other sub-samples are used as training data. The process is repeated 5 times and the results from the folds are averaged.

control.parms <- trainControl(method="cv", 5)
rf.model <- train(classe ~ ., data=train.data.final, method="rf",
                 trControl=control.parms, ntree=251)
rf.model

The model fit using the training data is tested against the validation data. Predicted values for the validation data are then compared to the actual values. This allows forecasting the accuracy and overall out-of-sample error, which indicate how well the model will perform with other data.

rf.predict <- predict(rf.model, validate.data.final)
confusionMatrix(validate.data.final$classe, rf.predict)

accuracy <- postResample(rf.predict, validate.data.final$classe)
acc.out <- accuracy[1]

overall.ose <- 
        1 - as.numeric(confusionMatrix(validate.data.final$classe, rf.predict)
                       $overall[1])

The accuracy of this model is r acc.out and the Overall Out-of-Sample error is r overall.ose.

The model is applied to the test data to produce the results.

results <- predict(rf.model, 
                   test.data.clean1[, -length(names(test.data.clean1))])
results

treeModel <- rpart(classe ~ ., data=train.data.final, method="class")
fancyRpartPlot(treeModel)