Response surface method has been a commonly used statistical method for quality improvement. As the importance of short-term and low-cost product development becomes higher nowadays, conventional response surface designs may need too large number of experimental runs to be accepted. Recently, supersaturated response surface designs were constructed by using several columns of Hadamard matrices (two-level orthogonal arrays), which considerably reduce the number of experimental runs, and a stepwise regression based on -tests was applied to their data analysis. In this paper, a criterion is introduced for constructing supersaturated response surface designs, and a ridge regression is used for the data analysis of supersaturated response surface designs. Several comparisons through numerical simulations are also presented.
Rehabilitation is a medical intervention implemented mainly by therapists under the prescription orders of medical doctors in hospitals. It is difficult to standardize rehabilitation intervention processes because they largely depend on individual therapists rather than medicines or instruments, and there are few quantitative clinical indicators. In such situations, there are differences in intervention processes and outcomes between therapists and hospitals.
In this study, we aim to develop a method for standardization of rehabilitation intervention processes based on actual clinical data. In our method, we firstly prepare a standard intervention process that could include the differences between therapists and hospitals. Second, we prepare an investigation sheet, which is designed to record information on intervention, outcome, and patient background. Third, we accumulate actual clinical data on the standard intervention process. Fourth, we analyze the accumulated clinical data, based on the evaluation structure designed for the target rehabilitation intervention. Finally, we try to standardize the intervention processes based on the results of analysis among therapists and hospitals.
We applied our method to 87 total cases of dysphagia rehabilitation for cerebral stroke patients at three hospitals as the first cycle of standardization, and 130 cases as the second cycle. We thus designed a standard intervention process to record the clinical processes actually implemented in three hospitals. In addition, we obtained findings both on the effects of patient background and on effective intervention which supported the validity of our proposal.
High-dimensional data sets have been used extensively in recent years. However, their use is computationally expensive, and model features are difficult to capture. Thus, it is necessary to construct a simple and appropriate model. The least absolute shrinkage and selection operator (Lasso) can estimate several regression coefficients as exactly zero, making it possible to estimate a model and select variables at the same time. However, several problems exist. The decision procedure for the tuning parameter, which is the coefficient of the penalty term, is not established, and it is difficult to determine the value of the estimated model.
In this paper, we consider a model evaluation method and a selection method for the tuning parameter. We investigate selection methods for the most appropriate tuning parameter and model evaluation methods using the model evaluation indexes RSS, AIC, BIC, and Mallows’s Cp. Let several regression coefficients be zero and vary the number of zeroes. Then, we observe the performances of the evaluation indexes. Furthermore, we observe their performances when the values of the regression coefficients are close to zero and confirm them by simulation.
Panel data are a sort of multi-dimensional time-series data that consist of several sets of the observation unit as an identical community over time. Panel data include more information than time-series data or cross-section data. Using panel data, we are able to estimate more accurately, increase degrees of freedom, and avoid multi-collinearity.
In this paper, we consider a change point problem in panel data. Detection methods for change points in panel data have not been extensively proposed. This paper proposes a detection method for change points in panel data using the Mahalanobis–Taguchi (MT) method (Taguchi (2002)). As the MT method does not assume panel data or time-series data, we must extend the theory of the MT method. Furthermore, when the sample size is small, it is difficult to estimate the covariance matrix precisely (Miyakawa et al. (2007)). In this paper, the MT method is extended using Bayesian inference to resolve the above-mentioned difficulties. Conducting Monte Carlo simulations and a real data analysis, we show that our proposed method is useful.
Experimental design is a statistical technique used in the field of quality control. It is applied to determine the relationships between intended results and the factors considered to influence them. It is a fractional factorial design that is suitable when there are many factors considered to influence the result.
Recently, many supersaturated designs have been studied. These are experimental designs, which can be assigned more factors than the number of experiments. The technique is applied to reduce the number of influencing factors from the total set.
Previous studies focused on structure designs and their respective analyses. Each constitution method is evaluated absolutely particularly. Consequently, prior to this study, the proposed designs had not been systematically evaluated. This paper examines some previously proposed supersaturated designs with the use of several indices. It presents a selection guide that describes recommended constitution methods.