Likelihood ratio tests for variance components in linear mixed models

Although the asymptotic distributions of the likelihood ratio for testing hypotheses of null variance components in linear mixed models derived by Stram and Lee [1994. Variance components testing in longitudinal mixed effects model. Biometrics 50, 1171-1177] are valid, their proof is based on the work of Self and Liang [1987. Asymptotic properties of maximum likelihood estimators and likelihood tests under nonstandard conditions. J. Amer. Statist. Assoc. 82, 605-610] which requires identically distributed random variables, an assumption not always valid in longitudinal data problems. We use the less restrictive results of Vu and Zhou [1997. Generalization of likelihood ratio tests under nonstandard conditions. Ann. Statist. 25, 897-916] to prove that the proposed mixture of chi-squared distributions is the actual asymptotic distribution of such likelihood ratios used as test statistics for null variance components in models with one or two random effects. We also consider a limited simulation study to evaluate the appropriateness of the asymptotic distribution of such likelihood ratios in moderately sized samples. (C) 2008 Elsevier B.V. All rights reserved.

Skovgaard`s adjustment to likelihood ratio tests in exponential family nonlinear models

Likelihood ratio tests can be substantially size distorted in small- and moderate-sized samples. In this paper, we apply Skovgaard`s [Skovgaard, I.M., 2001. Likelihood asymptotics. Scandinavian journal of Statistics 28, 3-321] adjusted likelihood ratio statistic to exponential family nonlinear models. We show that the adjustment term has a simple compact form that can be easily implemented from standard statistical software. The adjusted statistic is approximately distributed as X(2) with high degree of accuracy. It is applicable in wide generality since it allows both the parameter of interest and the nuisance parameter to be vector-valued. Unlike the modified profile likelihood ratio statistic obtained from Cox and Reid [Cox, D.R., Reid, N., 1987. Parameter orthogonality and approximate conditional inference. journal of the Royal Statistical Society B49, 1-39], the adjusted statistic proposed here does not require an orthogonal parameterization. Numerical comparison of likelihood-based tests of varying dispersion favors the test we propose and a Bartlett-corrected version of the modified profile likelihood ratio test recently obtained by Cysneiros and Ferrari [Cysneiros, A.H.M.A., Ferrari, S.L.P., 2006. An improved likelihood ratio test for varying dispersion in exponential family nonlinear models. Statistics and Probability Letters 76 (3), 255-265]. (C) 2008 Elsevier B.V. All rights reserved.

Modifications and Alternatives to the Tests of Levene and Brown & Forsythe for Equality of Variances and Means

The usual tests to compare variances and means (e. g. Bartlett`s test and F-test) assume that the sample comes from a normal distribution. In addition, the test for equality of means requires the assumption of homogeneity of variances. In some situation those assumptions are not satisfied, hence we may face problems like excessive size and low power. In this paper, we describe two tests, namely the Levene`s test for equality of variances, which is robust under nonnormality; and the Brown and Forsythe`s test for equality of means. We also present some modifications of the Levene`s test and Brown and Forsythe`s test, proposed by different authors. We analyzed and applied one modified form of Brown and Forsythe`s test to a real data set. This test is a robust alternative under nonnormality, heteroscedasticity and also when the data set has influential observations. The equality of variance can be well tested by Levene`s test with centering at the sample median.

Some restriction tests in a new class of regression models for proportions

The main purpose of this work is to study the behaviour of Skovgaard`s [Skovgaard, I.M., 2001. Likelihood asymptotics. Scandinavian journal of Statistics 28, 3-32] adjusted likelihood ratio statistic in testing simple hypothesis in a new class of regression models proposed here. The proposed class of regression models considers Dirichlet distributed observations, and the parameters that index the Dirichlet distributions are related to covariates and unknown regression coefficients. This class is useful for modelling data consisting of multivariate positive observations summing to one and generalizes the beta regression model described in Vasconcellos and Cribari-Neto [Vasconcellos, K.L.P., Cribari-Neto, F., 2005. Improved maximum likelihood estimation in a new class of beta regression models. Brazilian journal of Probability and Statistics 19,13-31]. We show that, for our model, Skovgaard`s adjusted likelihood ratio statistics have a simple compact form that can be easily implemented in standard statistical software. The adjusted statistic is approximately chi-squared distributed with a high degree of accuracy. Some numerical simulations show that the modified test is more reliable in finite samples than the usual likelihood ratio procedure. An empirical application is also presented and discussed. (C) 2009 Elsevier B.V. All rights reserved.

Local power of some tests in exponential family nonlinear models

In this paper we obtain asymptotic expansions up to order n(-1/2) for the nonnull distribution functions of the likelihood ratio, Wald, score and gradient test statistics in exponential family nonlinear models (Cordeiro and Paula, 1989), under a sequence of Pitman alternatives. The asymptotic distributions of all four statistics are obtained for testing a subset of regression parameters and for testing the dispersion parameter, thus generalising the results given in Cordeiro et al. (1994) and Ferrari et al. (1997). We also present Monte Carlo simulations in order to compare the finite-sample performance of these tests. (C) 2010 Elsevier B.V. All rights reserved.

In vitro tests to establish LC(50) and discriminating concentrations for fipronil against Rhipicephalus (Boophilus) microplus (Acari: Ixodidae) and their standardization

Laboratory test was carried out on larvae and adults of the cattle tick, Rhipicephalus (Boophilus) microplus, to determine fipronil toxicity. Adult immersion test (AIT, N = 26), larval immersion test (LIT, N = 71) and larval packet test (LPT, N = 41) were standardized using susceptible strain (Mozo). Dose-response curves were compared with a fipronil resistant strain. Four variables were analyzed from AIT results: mortality, weight of eggs on day 7 and on day 14, index of fertility, and index of fecundity. For larval test, dose mortality curves were analyzed. In spite of the high LC(50) variability, all variables determined for AIT were appropriate to discriminate both strains. AIT and LIT had more sensitivity than LPT, with larger resistance factors. It was used two times LC(99.9) as discriminating doses (DCs) following FAO suggestion. For mortality by AIT, LIT and LPT the DCs were estimated: 4.98 ppm, 7.64 ppm and 2365.8 ppm, respectively, for Mozo strain. DCs mortality values estimated for resistant strain by AIT, LIT and LPT were: 6.96 x 10(5) ppm, 343.26 ppm and 5.7 x 10(3) ppm, respectively and their respective resistant factors were: 202.4, 5.36 and 1.52. Protocols for AIT, LIT and LPT have been presented in this paper. (C) 2009 Elsevier B.V. All rights reserved.

Machine vision for the automatic classification of images acquired from Non-destructive tests

This project is based on Artificial Intelligence (A.I) and Digital Image processing (I.P) for automatic condition monitoring of sleepers in the railway track. Rail inspection is a very important task in railway maintenance for traffic safety issues and in preventing dangerous situations. Monitoring railway track infrastructure is an important aspect in which the periodical inspection of rail rolling plane is required.Up to the present days the inspection of the railroad is operated manually by trained personnel. A human operator walks along the railway track searching for sleeper anomalies. This monitoring way is not more acceptable for its slowness and subjectivity. Hence, it is desired to automate such intuitive human skills for the development of more robust and reliable testing methods. Images of wooden sleepers have been used as data for my project. The aim of this project is to present a vision based technique for inspecting railway sleepers (wooden planks under the railway track) by automatic interpretation of Non Destructive Test (NDT) data using A.I. techniques in determining the results of inspection.

Universal Experimental Measurement System «Sun-Walker» : Automotive measurement system for the evaluation of the solar irradiation distribution for the tests of the solar concentrated systems.

This Thesis project is a part of the research conducted in Solar industry. ABSOLICON Solar Concentrator AB has invented and started production of the prospective solar concentrated system Absolicon X10. The aims of this Thesis project are designing, assembling, calibrating and putting in operation the automatic measurement system intended to evaluate distribution of density of solar radiation in the focal line of the concentrated parabolic reflectors and to measure radiation from the artificial source of light being a calibration-testing tool.On the basis of the requirements of the company’s administration and needs of designing the concentrated reflectors the operation conditions for the Sun-Walker were formulated. As the first step, the complex design of the whole system was made and division on the parts was specified. After the preliminary conducted simulation of the functions and operation conditions of the all parts were formulated.As the next steps, the detailed design of all the parts was made. Most components were ordered from respective companies. Some of the mechanical components were made in the workshop of the company. All parts of the Sun-Walker were assembled and tested. The software part, which controls the Sun-Walker work and conducts measurements of solar irradiation, was created on the LabVIEW basis. To tune and test the software part, the special simulator was designed and assembled.When all parts were assembled in the complete system, the Sun-Walker was tested, calibrated and tuned.

Beneftis of modularity and module level tests

Many companies implement a modular architecture to support the need to create more variants with less effort. Although the modular architecture has many benefits, the tests to detect any defects become a major challenge. However, a modular architecture with defined functional elements seems beneficial to test at module level, so called MPV (Module Property Verification). This paper presents studies from 29 companies with the purpose of showing trends in the occurrence of defects and how these can support the MPV.

A home environment test battery for status assessment in patients with motor fluctuations

Background and aims Evaluating status in patients with motor fluctuations is complex and occasional observations/measurements do not give an adequate picture as to the time spent in different states. We developed a test battery to assess advanced Parkinson patients' status consisting of diary assessments and motor tests. This battery was constructed and implemented on a handheld computer with built-in mobile communication. In fluctuating patients, it should typically be used several times daily in the home environment, over periods of about one week. The aim of this battery is to provide status information in order to evaluate treatment effects in clinical practice and research, follow up treatments and disease progression and predict outcome to optimize treatment strategy. Methods Selection of diary questions was based on a previous study with Duodopa® (DIREQT). Tapping tests (with and without visual cueing) and a spiral drawing test were added. Rapid prototyping was used in development of the user interface. An evaluation with two pilot patients was performed before and after receiving new treatments for advanced disease (one received Duodopa® and one received DBS). Speed and proportion missed taps were calculated for the tapping tests and entropy of the radial drawing velocity was calculated for the spiral tests. Test variables were evaluated using non-parametric statistics. Results Post-treatment improvement was detected in both patients in many of the test variables. Conclusions Although validation work remains, preliminary results are promising and the test battery is currently being evaluated in a long-term health economics study with Duodopa® (DAPHNE).

A web application for follow-up of results from a mobile device test battery for parkinson’s disease patients

Background: A test battery consisting of self-assessments and motor tests (tapping and spiral drawing) was developed for a hand computer with touch screen in a telemedicine setting. Objectives: To develop and evaluate a web-based system that delivers decision support information to the treating clinical staff for assessing PD symptoms in their patients based on the test battery data. Methods: The test battery is currently being used in a clinical trial (DAPHNE, EudraCT No. 2005-002654-21) by sixty five patients with advanced Parkinson’s disease (PD) on 9991 test occasions (four tests per day during in all 362 week-long test periods) at nine clinics around Sweden. Test results are sent continuously from the hand unit over a mobile net to a central computer and processed with statistical methods. They are summarized into scores for different dimensions of the symptom state and an ‘overall test score’ reflecting the overall condition of the patient during a test period. The information in the web application is organized and presented graphically in a way that the general overview of the patient performance per test period is emphasized. Focus is on the overall test score, symptom dimensions and daily summaries. In a recent preliminary user evaluation, the web application was demonstrated to the fifteen study nurses who had used the test battery in the clinical trial. At least one patient per clinic was shown. Results: In general, the responses from nurses were positive. They claimed that the test results shown in the system were consistent with their own clinical observations. They could follow complications, changes and trends within their patients. Discussion: In conclusion, the system is able to summarise the various time series of motor test results and self-assessments during test periods and present them in a useful manner. Its main contribution is a novel and reliable way to capture and easily access symptom information from patients’ home environment. The convenient access to current symptom profile as well as symptom history provides a basis for individualized evaluation and adjustment of treatments.

Visualization of spirography-based objective measures in Parkinson's disease

Objective: To investigate whether advanced visualizations of spirography-based objective measures are useful in differentiating drug-related motor dysfunctions between Off and dyskinesia in Parkinson’s disease (PD). Background: During the course of a 3 year longitudinal clinical study, in total 65 patients (43 males and 22 females with mean age of 65) with advanced PD and 10 healthy elderly (HE) subjects (5 males and 5 females with mean age of 61) were assessed. Both patients and HE subjects performed repeated and time-stamped assessments of their objective health indicators using a test battery implemented on a telemetry touch screen handheld computer, in their home environment settings. Among other tasks, the subjects were asked to trace a pre-drawn Archimedes spiral using the dominant hand and repeat the test three times per test occasion. Methods: A web-based framework was developed to enable a visual exploration of relevant spirography-based kinematic features by clinicians so they can in turn evaluate the motor states of the patients i.e. Off and dyskinesia. The system uses different visualization techniques such as time series plots, animation, and interaction and organizes them into different views to aid clinicians in measuring spatial and time-dependent irregularities that could be associated with the motor states. Along with the animation view, the system displays two time series plots for representing drawing speed (blue line) and displacement from ideal trajectory (orange line). The views are coordinated and linked i.e. user interactions in one of the views will be reflected in other views. For instance, when the user points in one of the pixels in the spiral view, the circle size of the underlying pixel increases and a vertical line appears in the time series views to depict the corresponding position. In addition, in order to enable clinicians to observe erratic movements more clearly and thus improve the detection of irregularities, the system displays a color-map which gives an idea of the longevity of the spirography task. Figure 2 shows single randomly selected spirals drawn by a: A) patient who experienced dyskinesias, B) HE subject, and C) patient in Off state. Results: According to a domain expert (DN), the spirals drawn in the Off and dyskinesia motor states are characterized by different spatial and time features. For instance, the spiral shown in Fig. 2A was drawn by a patient who showed symptoms of dyskinesia; the drawing speed was relatively high (cf. blue-colored time series plot and the short timestamp scale in the x axis) and the spatial displacement was high (cf. orange-colored time series plot) associated with smooth deviations as a result of uncontrollable movements. The patient also exhibited low amount of hesitation which could be reflected both in the animation of the spiral as well as time series plots. In contrast, the patient who was in the Off state exhibited different kinematic features, as shown in Fig. 2C. In the case of spirals drawn by a HE subject, there was a great precision during the drawing process as well as unchanging levels of time-dependent features over the test trial, as seen in Fig. 2B. Conclusions: Visualizing spirography-based objective measures enables identification of trends and patterns of drug-related motor dysfunctions at the patient’s individual level. Dynamic access of visualized motor tests may be useful during the evaluation of drug-related complications such as under- and over-medications, providing decision support to clinicians during evaluation of treatment effects as well as improve the quality of life of patients and their caregivers. In future, we plan to evaluate the proposed approach by assessing within- and between-clinician variability in ratings in order to determine its actual usefulness and then use these ratings as target outcomes in supervised machine learning, similarly as it was previously done in the study performed by Memedi et al. (2013).

Self-reported symptoms and motor tests via telemetry in a 36-month levodopa-carbidopa intestinal gel infusion trial

Objective To investigate if a home environment test battery can be used to measure effects of Parkinson’s disease (PD) treatment intervention and disease progression. Background Seventy-seven patients diagnosed with advanced PD were recruited in an open longitudinal 36-month study at 10 clinics in Sweden and Norway; 40 of them were treated with levodopa-carbidopa intestinal gel (LCIG) and 37 patients were candidates for switching from oral PD treatment to LCIG. They utilized a mobile device test battery, consisting of self-assessments of symptoms and objective measures of motor function through a set of fine motor tests (tapping and spiral drawings), in their homes. Both the LCIG-naïve and LCIG-non-naïve patients used the test battery four times per day during week-long test periods. Methods Assessments The LCIG-naïve patients used the test battery at baseline (before LCIG), month 0 (first visit; at least 3 months after intraduodenal LCIG), and thereafter quarterly for the first year and biannually for the second and third years. The LCIG-non-naïve patients used the test battery from the first visit, i.e. month 0. Out of the 77 patients, only 65 utilized the test battery; 35 were LCIG-non-naïve and 30 LCIG-naïve. In 20 of the LCIG-naïve patients, assessments with the test battery were available during oral treatment and at least one test period after having started infusion treatment. Three LCIG-naïve patients did not use the test battery at baseline but had at least one test period of assessments thereafter. Hence, n=23 in the LCIG-naïve group. In total, symptom assessments in the full sample (including both patient groups) were collected during 379 test periods and 10079 test occasions. For 369 of these test periods, clinical assessments including UPDRS and PDQ-39 were performed in afternoons at the start of the test periods. The repeated measurements of the test battery were processed and summarized into scores representing patients’ symptom severities over a test period, using statistical methods. Six conceptual dimensions were defined; four subjectively-reported: ‘walking’, ‘satisfied’, ‘dyskinesia’, and ‘off’ and two objectively-measured: ‘tapping’ and ‘spiral’. In addition, an ‘overall test score’ (OTS) was defined to represent the global health condition of the patient during a test period. Statistical methods Change in the test battery scores over time, that is at baseline and follow-up test periods, was assessed with linear mixed-effects models with patient ID as a random effect and test period as a fixed effect of interest. The within-patient variability of OTS was assessed using intra-class correlation coefficient (ICC), for the two patient groups. Correlations between clinical rating scores and test battery scores were assessed using Spearman’s rank correlations (rho). Results In LCIG-naïve patients, mean OTS compared to baseline was significantly improved from the first test period on LCIG treatment until month 24. However, there were no significant changes in mean OTS scores of LCIG-non-naïve patients, except for worse mean OTS at month 36 (p<0.01, n=16). The mean scores of all subjectively-reported dimensions improved significantly throughout the course of the study, except ‘walking’ at month 36 (p=0.41, n=4). However, there were no significant differences in mean scores of objectively-measured dimensions between baseline and other test periods, except improved ‘tapping’ at month 6 and month 36, and ‘spiral’ at month 3 (p<0.05). The LCIG-naïve patients had a higher within-subject variability in their OTS scores (ICC=0.67) compared to LCIG-non-naïve patients (ICC=0.71). The OTS correlated adequately with total UPDRS (rho=0.59) and total PDQ-39 (rho=0.59). Conclusions In this 3-year follow-up study of advanced PD patients treated with LCIG we found that it is possible to monitor PD progression over time using a home environment test battery. The significant improvements in the mean OTS scores indicate that the test battery is able to measure functional improvement with LCIG sustained over at least 24 months.

A user guide to simple monitoring and sustainable operation of PV-diesel hybrid systems : Handbook for system users and operators

This report contains a suggestion for a simple monitoring and evaluation guideline for PV-diesel hybrid systems. It offers system users a way to better understand if their system is operated in a way that will make it last for a long time. It also gives suggestions on how to act if there are signs of unfavourable use or failure. The application of the guide requires little technical equipment, but daily manual measurements. For the most part, it can be managed by pen and paper, by people with no earlier experience of power systems.The guide is structured and expressed in a way that targets PV-diesel hybrid system users with no, or limited, earlier experience of power engineering. It is less detailed in terms of motivations for certain choices and limitations, but rich in details concerning calculations, evaluation procedures and maintenance routines. A more scientific description of the guide can be found in a related journal article.