Three topics are investigated in this dissertation with each one focusing on one type of GLMs. Topic I considers GLMs with factorial effects and one continuous covariate. Factors can have interactions among each other and there is no restriction on the possible values of the continuous covariate. The locally D-optimal design structures for such models are identified and results for obtaining smaller optimal designs using orthogonal arrays (OAs) are presented. Topic II considers GLMs with multiple covariates under the assumptions that all but one covariate are bounded within specified intervals and interaction effects among those bounded covariates may also exist. An explicit formula for D-optimal designs is derived and OA-based smaller D-optimal designs for models with one or two two-factor interactions are also constructed. Topic III considers multiple-covariate logistic models. All covariates are nonnegative and there is no interaction among them. Two types of D-optimal design structures are identified and their global D-optimality is proved using the celebrated equivalence theorem.
to stimuli presented to subjects in a scanner. It is important to conduct statistical
inference on such time series fMRI data obtained. It is also important to select optimal designs for practical experiments. Design selection under autoregressive models
have not been thoroughly discussed before. This paper derives general information
matrices for orthogonal designs under autoregressive model with an arbitrary number
of correlation coefficients. We further provide the minimum trace of orthogonal circulant designs under AR(1) model, which is used as a criterion to compare practical
designs such as M-sequence designs and circulant (almost) orthogonal array designs.
We also explore optimal designs under AR(2) model. In practice, types of stimuli can
be more than one, but in this paper we only consider the simplest situation with only
one type of stimuli.
Study Region: 43 rivers in Spain with measurement stations for air and water temperatures.
Study Focus: River water temperatures influence aquatic ecosystem dynamics. This work aims to develop transferable river temperature forecasting models, which are not confined to sites with historical measurements of air and water temperatures. For that purpose, we estimate nonlinear mixed models (NLMM), which are based on site-specific time-series models and account for seasonality and S-shaped air-to-water temperature associations. A detailed evaluation of the short-term forecasting performance of both NLMM and site-specific models is undertaken. Measurements from 31 measurement sites were used to estimate model parameters whereas data from 12 additional sites were used solely for the evaluation of NLMM.
New Hydrological Insights for the Region: Mixed models achieve levels of accuracy analogous to linear site-specific time-series regressions. Nonlinear site-specific models attain 1-day ahead forecasting accuracy close to 1 °C in terms of mean absolute error (MAE) and root mean square error (RMSE). Our results may facilitate adaptive management of freshwater resources in Spain in accordance with European water policy directives.