Manganese model complexes, relevant to the oxygen-evolving complex (OEC) in photosynthesis, were studied with Mn K-edge X-ray absorption near-edge spectroscopy (XANES), Mn Kb X-ray emission spectroscopy (XES), and vibrational spectroscopy. A more detailed understanding was obtained of the influence of nuclearity, overall structure, oxidation state, and ligand environment of the Mn atoms on the spectra from these methods. This refined understanding is necessary for improving the interpretation of spectra of the OEC. Mn XANES and Kb XES were used to study a di-(mu)-oxo and a mono-(mu)-oxo di-nuclear Mn compound in the (III,III), (III,IV), and (IV,IV) oxidation states. XANES spectra show energy shifts of 0.8 - 2.2 eV for 1-electron oxidation-state changes and 0.4 - 1.8 eV for ligand-environment changes. The shifts observed for Mn XES spectra were approximately 0.21 eV for oxidation state-changes and only approximately 0.04 eV for ligand-environment changes. This indicates that Mn Kb XES is more sensitive to the oxidation state and less sensitive to the ligand environment of the Mn atoms than XANES. These complimentary methods provide information about the oxidation state and the ligand environment of Mn atoms in model compounds and biological systems. A versatile spectroelectrochemical apparatus was designed to aid the interpretation of IR spectra of Mn compounds in different oxidation states. The design, based on an attenuated total reflection device, permits the study of a wide spectral range: 16,700 (600 nm) - 225 0 cm-1 and 1900 - 250 cm-1. A data collection protocol was introduced to deal with electrochemically non-reversible background signals. IR spectra of an adamantane-like tetra-nuclear Mn compound in two different oxidation states were obtained and analyzed by normal-mode analysis. Bridging Mn-O vibrational modes were identified by isotopic exchange (16O AE18O) in the 750 - 650 cm-1 and 520 - 460 cm-1 ranges for the MnIV4 and MnIIIMnIV3 species. These vibrational modes are in the same spectral range as modes that have been observed for the OEC. Using S4 symmetry for the MnIV4 species and Cs symmetry for the MnIIIMnIV3 species, stretching force constants of 2.45 mdyn/Angstrom, and 3.10 mdyn/Angstrom were extracted for the MnIII-O and MnIV-O bridging bonds, respectively.

This dissertation is organized into two studies investigating common modeling issues that occur when including a covariate in a latent class analysis (LCA) model. When estimating a conditional LCA model, applied researchers must make decisions about the estimation strategy (one-step vs. three-step), the handling of incomplete covariate data, and specification of covariate relationships. Study 1 examined the performance of different methods for handling incomplete covariate data when using a three-step approach to estimation. The simulation results found that Bayesian estimation with informative normal priors correctly centered on the regression coefficient population values produced the most consistent and accurate regression coefficient estimates, regardless of the covariate distribution, strength, and missing data pattern. However, informative priors centered on the wrong population values produced some of the most biased regression coefficients. In most modeling conditions, full information maximum likelihood (FIML) and multiple imputation (MI) still worked well. When estimating a conditional LCA model, applied researchers must also make decisions about how to specify the covariate relations with the LCA measurement model. Specifically, applied researcher must decide if the covariate only has an indirect effect on the observed indicators via the latent class variable or if the covariate is related to one or more of the observed indicator variables. The goal of Study 2 was to explore the utility of using small-variance priors to help evaluate covariate relationships. Specifically, small- variance normal priors centered on zero were specified for the direct effects between the covariate and the latent class indicators for a series of population models with varying covariate relationships. Results from the Study 2 simulation indicate small-variance priors can be a useful tool for detecting covariate misspecifications, depending on the number of direct effects, sample size, and class sizes. Overall, findings from Study 1 and Study 2 highlight how Bayesian estimation can be especially helpful for handling common modeling issues in conditional LCA models.