In the context of factor analysis, the most common estimation method for analysing discrete datais multiple step Diagonally Weighted Least Squares (DWLS). A novel estimation method is...Show moreIn the context of factor analysis, the most common estimation method for analysing discrete datais multiple step Diagonally Weighted Least Squares (DWLS). A novel estimation method is calledPairwise Maximum Likelihood (PML). PML calculates the product of bivariate likelihoods byonly using a single step. PML estimation was found effective for small datasets with few discretevariables. In this study, we investigate how PML performs with large datasets and different typesof data (e.g., discrete data, continuous data, and combinations thereof).We conducted two different simulation studies to compare the performance of PML to theDWLS estimation method in terms of accuracy and efficiency. We thereby examined differentexperimental conditions; model sizes (small, medium, large, and huge), sample sizes (200, 400, and800), and answer categories (two and four). In addition, we checked the robustness of PML byfitting a model without misspecifications (i.e., correctly specified model) and with misspecifications(i.e., misspecified model). ANOVAs were conducted to test whether the differences between PMLand DWLS depend on the aforementioned design factors. Regarding the performance of PMLand DWLS, our results indicate that the (relative) bias of both the parameter estimates and thestandard errors remain very small among the varying experimental conditions for the correctlyspecified model and slightly increases in conditions with a misspecified model. Overall, our findingsdemonstrate that PML performed slightly better compared to DWLS in terms bias of both theparameter estimates and the standard errors.Show less
Master thesis | Statistical Science for the Life and Behavioural Sciences (MSc)
open access
Random forests is generally known as an excellent classifier that is flexible in the types of data it is applied to. Despite this characteristic, it is also regarded as a ‘black box’ classifier:...Show moreRandom forests is generally known as an excellent classifier that is flexible in the types of data it is applied to. Despite this characteristic, it is also regarded as a ‘black box’ classifier: its ensembles comprise of hundreds of complex tree members. This is a major drawback for certain applications, where insight in the involvement of variables that account for certain outcomes is essential (e.g., medical diagnosis problems for identifying diseased individuals). There are however more recent methods that produce ensembles reduced in size by selecting the most important ensemble members. Some of these methods also yield ensemble members with simple structures to increase interpretation possibilities. Our selection of such methods comprises optimal trees ensemble (OTE), node harvest, and rule ensembles. These methods were assessed through a simulation study and an application to an MRI dataset on Alzheimer’s disease classification, to determine predictive performance and information recovery to estimate suitability for interpretational purposes. Random forests was taken as benchmark for predictive performance and baseline for improvement of interpretation. We focussed solely on binary classification. The benchmark random forests had generally good predictive performances and among the best variable importance recovery. It was still the superior classifier in high-dimensional settings. OTE often had similar predictive and variable importance recovery. It did however not have any advantage over random forests regarding suitability for interpretation. Node harvest had reasonable interaction recovery and good variable split point recovery, albeit at the cost of predictive and variable importance recovery performances. Rule ensembles proved to be a suitable alternative for random forests that produces models suitable for interpretation with comparable or better accuracy, but only when the dataset has clear signal. In noisy or high-dimensional settings, there still is no suitable, more interpretable tree ensemble alternative to random forests amongst the studied methods. Such settings still benefit from ensembles with numerous highly complex trees.Show less
