| General Linear Models, the foundation for most statistical analyses, are extensively used in applied and social research. The regression model developed for a clinical trial survey assessed the factors contributing to movement-related fear for subjects with Fibromyalgia (FM). In addition, non-linear regression models were formulated to analyze and infer how likely a person with FM has being employed, and has being out of control of their balance. Bayesian methodologies using three different likelihoods; namely Student-t with Uniform priors, Gaussian with Uniform priors, and Gaussian with a combination of Jeffreys' and Gaussian priors were compared with regression model derived from the FM data. Use of the prior information demonstrated that the Bayesian solution reduces uncertainty in the estimations, moreover estimates could be obtained from very less amount of data with prior information in clinical trial data. Even with a much higher standard deviation we demonstrated that a high uncertain prior would result in better estimates. In all these processes, some fragments of real data are always missing due to various reasons. Multiple Imputation (MI) methodology was used to impute the missing values of FM data that had 10%, 20%, 30%, 40% and 50% missing data to make the models more precise and reliable. The development of the MI method is discussed for the data set having log-normal behavior which are different from the traditional method assuming multivariate normal distributions. |
