Dimensionality Reduction in High-Dimensional Profile Analysis Using Scores

Profile analysis is a multivariate statistical method for comparing the mean vectors for different groups. It consists of three tests, they are the tests for parallelism, level and flatness. The results from each test give information about the behaviour of the groups and the variables in the groups. The test statistics used when there are more than two groups are likelihood-ratio tests. However, issues in the form indeterminate test statistics occur in the high-dimensional setting, that is when there are more variables than observations. This thesis investigates a method to approach this problem by reducing the dimensionality of the data using scores, that is linear combinations of the variables. Three different ways of choosing this score are compared: the eigendecomposition and two variations of the non-negative matrix factorization. The methods are compared using simulations for five different type of mean parameter settings. The results show that the eigendecomposition is the best technique for choosing the score, and that using more scores only slightly improves the results. Moreover, the results for the parallelism and the flatness tests are shown to be very good, but the results for the level hypothesis deviate from the expectation.