Personality profiling has been utilised by companies for targeted advertising, political campaigns and public health campaigns. However, the accuracy and versatility of such models remains relatively unknown. Here we explore the extent to which peoples' online digital footprints can be used to profile their Myers-Briggs personality type. We analyse and compare four models: logistic regression, naive Bayes, support vector machines (SVMs) and random forests. We discover that a SVM model achieves the best accuracy of 20.95% for predicting a complete personality type. However, logistic regression models perform only marginally worse and are significantly faster to train and perform predictions. Moreover, we develop a statistical framework for assessing the importance of different sets of features in our models. We discover some features to be more informative than others in the Intuitive/Sensory (p = 0.032) and Thinking/Feeling (p = 0.019) models. Many labelled datasets present substantial class imbalances of personal characteristics on social media, including our own. We therefore highlight the need for attentive consideration when reporting model performance on such datasets and compare a number of methods to fix class-imbalance problems.