Value-added models (VAMs) are used by many states to assess contributions of individual teachers and schools to students' academic growth. The generalized persistence VAM, one of the most flexible in the literature, estimates the ``value added'' by individual teachers to their students' current and future test scores by employing a mixed model with a longitudinal database of test scores. There is concern, however, that missing values that are common in the longitudinal student scores can bias value-added assessments, especially when the models serve as a basis for personnel decisions -- such as promoting or dismissing teachers -- as they are being used in some states. Certain types of missing data require that the VAM be modeled jointly with the missingness process in order to obtain unbiased parameter estimates. This dissertation studies two problems. First, the flexibility and multimembership random effects structure of the generalized persistence model lead to computational challenges that have limited the model's availability. To this point, no methods have been developed for scalable maximum likelihood estimation of the model. An EM algorithm to compute maximum likelihood estimates efficiently is developed, making use of the sparse structure of the random effects and error covariance matrices. The algorithm is implemented in the package GPvam in R statistical software. Illustrations of the gains in computational efficiency achieved by the estimation procedure are given. Furthermore, to address the presence of potentially nonignorable missing data, a flexible correlated random effects model is developed that extends the generalized persistence model to jointly model the test scores and the missingness process, allowing the process to depend on both students and teachers. The joint model gives the ability to test the sensitivity of the VAM to the presence of nonignorable missing data. Estimation of the model is challenging due to the non-hierarchical dependence structure and the resulting intractable high-dimensional integrals. Maximum likelihood estimation of the model is performed using an EM algorithm with fully exponential Laplace approximations for the E step. The methods are illustrated with data from university calculus classes and with data from standardized test scores from an urban school district.

This dissertation transforms a set of system complexity reduction problems to feature selection problems. Three systems are considered: classification based on association rules, network structure learning, and time series classification. Furthermore, two variable importance measures are proposed to reduce the feature selection bias in tree models. Associative classifiers can achieve high accuracy, but the combination of many rules is difficult to interpret. Rule condition subset selection (RCSS) methods for associative classification are considered. RCSS aims to prune the rule conditions into a subset via feature selection. The subset then can be summarized into rule-based classifiers. Experiments show that classifiers after RCSS can substantially improve the classification interpretability without loss of accuracy. An ensemble feature selection method is proposed to learn Markov blankets for either discrete or continuous networks (without linear, Gaussian assumptions). The method is compared to a Bayesian local structure learning algorithm and to alternative feature selection methods in the causal structure learning problem. Feature selection is also used to enhance the interpretability of time series classification. Existing time series classification algorithms (such as nearest-neighbor with dynamic time warping measures) are accurate but difficult to interpret. This research leverages the time-ordering of the data to extract features, and generates an effective and efficient classifier referred to as a time series forest (TSF). The computational complexity of TSF is only linear in the length of time series, and interpretable features can be extracted. These features can be further reduced, and summarized for even better interpretability. Lastly, two variable importance measures are proposed to reduce the feature selection bias in tree-based ensemble models. It is well known that bias can occur when predictor attributes have different numbers of values. Two methods are proposed to solve the bias problem. One uses an out-of-bag sampling method called OOBForest, and the other, based on the new concept of a partial permutation test, is called a pForest. Experimental results show the existing methods are not always reliable for multi-valued predictors, while the proposed methods have advantages.