Statnote 25: Stepwise multiple regression

An investigator may also wish to select a small subset of the X variables which give the best prediction of the Y variable. In this case, the question is how many variables should the regression equation include? One method would be to calculate the regression of Y on every subset of the X variables and choose the subset that gives the smallest mean square deviation from the regression. Most investigators, however, prefer to use a ‘stepwise multiple regression’ procedure. There are two forms of this analysis called the ‘step-up’ (or ‘forward’) method and the ‘step-down’ (or ‘backward’) method. This Statnote illustrates the use of stepwise multiple regression with reference to the scenario introduced in Statnote 24, viz., the influence of climatic variables on the growth of the crustose lichen Rhizocarpon geographicum (L.)DC.

Grouping and the pitch of a mistuned fundamental component:effects of applying simultaneous multiple mistunings to the other harmonics

Mistuning a harmonic produces an exaggerated change in its pitch. This occurs because the component becomes inconsistent with the regular pattern that causes the other harmonics (constituting the spectral frame) to integrate perceptually. These pitch shifts were measured when the fundamental (F0) component of a complex tone (nominal F0 frequency = 200 Hz) was mistuned by +8% and -8%. The pitch-shift gradient was defined as the difference between these values and its magnitude was used as a measure of frame integration. An independent and random perturbation (spectral jitter) was applied simultaneously to most or all of the frame components. The gradient magnitude declined gradually as the degree of jitter increased from 0% to ±40% of F0. The component adjacent to the mistuned target made the largest contribution to the gradient, but more distant components also contributed. The stimuli were passed through an auditory model, and the exponential height of the F0-period peak in the averaged summary autocorrelation function correlated well with the gradient magnitude. The fit improved when the weighting on more distant channels was attenuated by a factor of three per octave. The results are consistent with a grouping mechanism that computes a weighted average of periodicity strength across several components. © 2006 Elsevier B.V. All rights reserved.

Advanced handover procedure for cellular communication systems

Third Generation cellular communication systems are expected to support mixed cell architecture in which picocells, microcells and macrocells are used to achieve full coverage and increase the spectral capacity. Supporting higher numbers of mobile terminals and the use of smaller cells will result in an increase in the number of handovers, and consequently an increase in the time delays required to perform these handovers. Higher time delays will generate call interruptions and forced terminations, particularly for time sensitive applications like real-time multimedia and data services. Currently in the Global System for Mobile communications (GSM), the handover procedure is initiated and performed by the fixed part of the Public Land Mobile Network (PLMN). The mobile terminal is only capable of detecting candidate base stations suitable for the handover; it is the role of the network to interrogate a candidate base station for a free channel. Handover signalling is exchanged via the fixed network and the time delay required to perform the handover is greatly affected by the levels of teletraffic handled by the network. In this thesis, a new handover strategy is developed to reduce the total time delay for handovers in a microcellular system. The handover signalling is diverted from the fixed network to the air interface to prevent extra delays due to teletraffic congestion, and to allow the mobile terminal to exchange signalling directly with the candidate base station. The new strategy utilises Packet Reservation Multiple Access (PRMA) technique as a mechanism to transfer the control of the handover procedure from the fixed network to the mobile terminal. Simulation results are presented to show a dramatic reduction in the handover delay as compared to those obtained using fixed channel allocation and dynamic channel allocation schemes.

Data analysis methods in optometry Part 7: multiple linear regression

Multiple regression analysis is a complex statistical method with many potential uses. It has also become one of the most abused of all statistical procedures since anyone with a data base and suitable software can carry it out. An investigator should always have a clear hypothesis in mind before carrying out such a procedure and knowledge of the limitations of each aspect of the analysis. In addition, multiple regression is probably best used in an exploratory context, identifying variables that might profitably be examined by more detailed studies. Where there are many variables potentially influencing Y, they are likely to be intercorrelated and to account for relatively small amounts of the variance. Any analysis in which R squared is less than 50% should be suspect as probably not indicating the presence of significant variables. A further problem relates to sample size. It is often stated that the number of subjects or patients must be at least 5-10 times the number of variables included in the study.5 This advice should be taken only as a rough guide but it does indicate that the variables included should be selected with great care as inclusion of an obviously unimportant variable may have a significant impact on the sample size required.

A biological-inspired support frame for an artificial cornea

Bilateral corneal blindness represents a quarter of the total blind, world-wide. The artificial cornea in assorted forms, was developed to replace opaque non-functional corneas and to return sight in otherwise hopeless cases that were not amenable to corneal grafts; believed to be 2% of corneal blind. Despite technological advances in materials design and tissue engineering no artificial cornea has provided absolute, long-term success. Formidable problems exist, due to a combination of unpredictable wound healing and unmanageable pathology. To have a solid guarantee of reliable success an artificial cornea must possess three attributes: an optical window to replace the opaque cornea; a strong, long term union to surrounding ocular tissue; and the ability to induce desired host responses. A unique artificial cornea possesses all three functional attributes- the Osteo-odonto-keratoprosthesis (OOKP). The OOKP has a high success rate and can survive for up to twenty years, but it is complicated both in structure and in surgical procedure; it is expensive and not universally available. The aim of this project was to develop a synthetic substitute for the OOKP, based upon key features of the tooth and bone structure. In doing so, surgical complexity and biological complications would be reduced. Analysis of the biological effectiveness of the OOKP showed that the structure of bone was the most crucial component for implant retention. An experimental semi-rigid hydroxyapatite framework was fabricated with a complex bone-like architecture, which could be fused to the optical window. The first method for making such a framework, was pressing and sintering of hydroxyapatite powders; however, it was not possible to fabricate a void architecture with the correct sizes and uniformity of pores. Ceramers were synthesised using alternative pore forming methods, providing for improved mechanical properties and stronger attachment to the plastic optical window. Naturally occurring skeletal structures closely match the structural features of all forms of natural bone. Synthetic casts were fabricated using the replamineform process, of desirable natural artifacts, such as coral and sponges. The final method of construction by-passed ceramic fabrication in favour of pre-formed coral derivatives and focused on methods for polymer infiltration, adhesion and fabrication. Prototypes were constructed and evaluated; a fully penetrative synthetic OOKP analogue was fabricated according to the dimensions of the OOKP. Fabrication of the cornea shaped OOKP synthetic analogue was also attempted.

Determining planar multiple sound-soft obstacles from scattered acoustic fields

An inverse problem is considered where the structure of multiple sound-soft planar obstacles is to be determined given the direction of the incoming acoustic field and knowledge of the corresponding total field on a curve located outside the obstacles. A local uniqueness result is given for this inverse problem suggesting that the reconstruction can be achieved by a single incident wave. A numerical procedure based on the concept of the topological derivative of an associated cost functional is used to produce images of the obstacles. No a priori assumption about the number of obstacles present is needed. Numerical results are included showing that accurate reconstructions can be obtained and that the proposed method is capable of finding both the shapes and the number of obstacles with one or a few incident waves.