On the Existence and Uniqueness of the Maximum Likelihood Estimators of Normal and Lognormal Population Parameters with Grouped Data

Lognormal distribution has abundant applications in various fields. In literature, most inferences on the two parameters of the lognormal distribution are based on Type-I censored sample data. However, exact measurements are not always attainable especially when the observation is below or above the detection limits, and only the numbers of measurements falling into predetermined intervals can be recorded instead. This is the so-called grouped data. In this paper, we will show the existence and uniqueness of the maximum likelihood estimators of the two parameters of the underlying lognormal distribution with Type-I censored data and grouped data. The proof was first established under the case of normal distribution and extended to the lognormal distribution through invariance property. The results are applied to estimate the median and mean of the lognormal population.

A Generalized Log-Normal Model for Grouped Survival Data

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

THE LOG-BURR XII REGRESSION MODEL FOR GROUPED SURVIVAL DATA

The log-Burr XII regression model for grouped survival data is evaluated in the presence of many ties. The methodology for grouped survival data is based on life tables, where the times are grouped in k intervals, and we fit discrete lifetime regression models to the data. The model parameters are estimated by maximum likelihood and jackknife methods. To detect influential observations in the proposed model, diagnostic measures based on case deletion, so-called global influence, and influence measures based on small perturbations in the data or in the model, referred to as local influence, are used. In addition to these measures, the total local influence and influential estimates are also used. We conduct Monte Carlo simulation studies to assess the finite sample behavior of the maximum likelihood estimators of the proposed model for grouped survival. A real data set is analyzed using a regression model for grouped data.

Choosing between Cox proportional hazards and logistic models for interval-censored data via bootstrap

This work develops a new methodology in order to discriminate models for interval-censored data based on bootstrap residual simulation by observing the deviance difference from one model in relation to another, according to Hinde (1992). Generally, this sort of data can generate a large number of tied observations and, in this case, survival time can be regarded as discrete. Therefore, the Cox proportional hazards model for grouped data (Prentice & Gloeckler, 1978) and the logistic model (Lawless, 1982) can befitted by means of generalized linear models. Whitehead (1989) considered censoring to be an indicative variable with a binomial distribution and fitted the Cox proportional hazards model using complementary log-log as a link function. In addition, a logistic model can be fitted using logit as a link function. The proposed methodology arises as an alternative to the score tests developed by Colosimo et al. (2000), where such models can be obtained for discrete binary data as particular cases from the Aranda-Ordaz distribution asymmetric family. These tests are thus developed with a basis on link functions to generate such a fit. The example that motivates this study was the dataset from an experiment carried out on a flax cultivar planted on four substrata susceptible to the pathogen Fusarium oxysoprum. The response variable, which is the time until blighting, was observed in intervals during 52 days. The results were compared with the model fit and the AIC values.

Suomalaisen alkuperäiskarjan liha – kuluttajien osto- ja maksuhalukkuus

Tutkielman tavoitteena on selvittää suomalaisen alkuperäiskarjan lihan potentiaalista kysyntää. Alkuperäiskarjan lihan erikoistuotemarkkinat voivat auttaa pitämään uhanalaiset, kotimaiset karjarodut tuotantokäytössä. Näin ollen erikoistuotemarkkinat voivat auttaa arvokkaiden suomalaisten eläingeenivarojen säilyttämisessä. Koska alkuperäiskarjan lihan tuotannon kannattavuus riippuu lihasta saatavasta lisähinnasta, tutkimuksen tavoitteena on myös tutkia, millainen kuluttajien maksuhalukkuus alkuperäiskarjan lihasta on verrattuna tavanomaiseen lihaan. Tutkimusaineisto kerättiin Maa- ja elintarviketalouden tutkimuskeskuksen ja Kuluttajatutkimuskeskuksen suunnittelemalla kyselytutkimuksella keväällä 2010. Tutkimuksessa käytettiin ehdollisen käyttäytymisen ja ehdollisen arvottamisen menetelmiä ja sen otoskoko on 1623. Kuluttajien ostohalukkuutta ja siihen vaikuttavia tekijöitä tutkittiin sekä binäärisen että ordinaalisen regression malleilla. Kuluttajien maksuhalukkuutta alkuperäiskarjan lihasta ja siihen vaikuttavia tekijöitä tutkittiin grouped data -mallin avulla. Malleissa käytettiin selittävinä muuttujina sosioekonomisten muuttujien lisäksi kuluttajien asenteita ja käyttäytymistä kuvaavia muuttujia. Tutkielman tulosten mukaan jopa 86 % vastaajista ostaisi alkuperäiskarjan lihaa, jos sitä olisi tarjolla kaupoissa. Ostohalukkuutta lisää muun muassa, jos vastaajalla on alle 18-vuotiaita lapsia ja vastaaja arvostaa lähellä tuotettua, paikallista ruokaa sekä ympäristöystävällisyyttä. Miehet ostaisivat alkuperäiskarjan lihaa todennäköisemmin kuin naiset. Suurin osa vastaajista ostaisi alkuperäiskarjan lihaa, jos se olisi samanhintaista kuin tavanomainen liha, mutta noin neljäsosa (23,5 %) vastaajista olisi valmis maksamaan alkuperäiskarjan lihasta korkeampaa hintaa kuin tavanomaisesta lihasta. Maksuhalukkuuteen vaikuttivat positiivisesti muun muassa kuuluminen ympäristöjärjestöön ja korkea tulotaso. Negatiivisesti vaikutti puolestaan esimerkiksi se, että vastaaja on nainen. Keskimääräinen maksuhalukkuus alkuperäiskarjan lihasta oli 6,25 % korkeampi kuin tavanomaisesta lihasta. Maksuhalukkuus alkuperäiskarjan lihasta oli selvästi yhteydessä siihen, kuinka usein vastaaja olisi halukas ostamaan sitä. Maksuhalukkuus oli korkein niillä vastaajilla, jotka haluaisivat ostaa lihaa säännöllisesti.

The distribution of autobiographical memories across the lifespan.

Words were used to cue autobiographical memories from 20- and 70-year-old subjects. Both groups showed a decrease in memories from the childhood years and a power-function retention function for their most recent 10 years. Older subjects also had an increase in the number of memories from the ages 10 to 30. These results held for individual subjects as well as grouped data and held when either 124 or 921 memories were cued. Reaction times to produce memories were constant across decades except for childhood where they were longer.

Depression and mortality: Artifact of measurement and analysis?

Background: Previous research demonstrates various associations between depression, cardiovascular disease (CVD) incidence and mortality, possibly as a result of the different methodologies used to measure depression and analyse relationships. This analysis investigated the association between depression, CVD incidence (CVDI) and mortality from CVD (MCVD), smoking related conditions (MSRC), and all causes (MALL), in a sample data set, where depression was measured using items from a validated questionnaire and using items derived from the factor analysis of a larger questionnaire, and analyses were conducted based on continuous data and grouped data.

Methods: Data from the PRIME Study (N=9798 men) on depression and 10-year CVD incidence and mortality were analysed using Cox proportional hazards models.

Results: Using continuous data, both measures of depression resulted in the emergence of positive associations between depression and mortality (MCVD, MSRC, MALL). Using grouped data, however, associations between a validated measure of depression and MCVD, and between a measure of depression derived from factor analysis and all measures of mortality were lost.

Limitations: Low levels of depression, low numbers of individuals with high depression and low numbers of outcome events may limit these analyses, but levels are usual for the population studied.

Conclusions: These data demonstrate a possible association between depression and mortality but detecting this association is dependent on the measurement used and method of analysis. Different findings based on methodology present clear problems for the elucidation and determination of relationships. The differences here argue for the use of validated scales where possible and suggest against over-reduction via factor analysis and grouping.

Cognitive Behavior Therapy for Obsessive-Compulsive Behavior in Children with Autism Spectrum Disorder: A Comparison of Hierarchical Linear Modelling and Visual Analysis

Behavioral researchers commonly use single subject designs to evaluate the effects of a given treatment. Several different methods of data analysis are used, each with their own set of methodological strengths and limitations. Visual inspection is commonly used as a method of analyzing data which assesses the variability, level, and trend both within and between conditions (Cooper, Heron, & Heward, 2007). In an attempt to quantify treatment outcomes, researchers developed two methods for analysing data called Percentage of Non-overlapping Data Points (PND) and Percentage of Data Points Exceeding the Median (PEM). The purpose of the present study is to compare and contrast the use of Hierarchical Linear Modelling (HLM), PND and PEM in single subject research. The present study used 39 behaviours, across 17 participants to compare treatment outcomes of a group cognitive behavioural therapy program, using PND, PEM, and HLM on three response classes of Obsessive Compulsive Behaviour in children with Autism Spectrum Disorder. Findings suggest that PEM and HLM complement each other and both add invaluable information to the overall treatment results. Future research should consider using both PEM and HLM when analysing single subject designs, specifically grouped data with variability.

The distribution of male wages in Brazil

This paper examines the evolution of wage inequality in Brazil in the 1980s and 1990s . It tries to investigate the role played by changing economic returns to education and to experience over this period together with the evolution of within-group inequality. It applies a quantile regression approach on grouped data to the Brazilian case. Results using repeated cross-sections of a Brazilian annual household survey indicate that : i) Male wage dispersion remained basically constant overall in the 1980's and 1990' s but has increased substantially within education and age groups. ii) Returns to experience increased significantly over this period, with the rise concentrated on the iliterate/primary school group iii) Returns to college education have risen over time, whereas return to intermediate and high-school education have fallen iv) The apparent rise in within-group inequality seems to be the result of a fall in real wages, since the difference in wage leveIs has dec1ined substantially over the period, especially within the high-educated sample. v) Returns to experience rise with education. vi) Returns to education rise over the life-cycle. vii) Wage inequality increases over the life-cycle. The next step i~ this research will try to conciliate all these stylised facts.

Estimação em modelos de tempo de falha acelerado para dados de sobrevivência correlacionados

We presented in this work two methods of estimation for accelerated failure time models with random e_ects to process grouped survival data. The _rst method, which is implemented in software SAS, by NLMIXED procedure, uses an adapted Gauss-Hermite quadrature to determine marginalized likelihood. The second method, implemented in the free software R, is based on the method of penalized likelihood to estimate the parameters of the model. In the _rst case we describe the main theoretical aspects and, in the second, we briey presented the approach adopted with a simulation study to investigate the performance of the method. We realized implement the models using actual data on the time of operation of oil wells from the Potiguar Basin (RN / CE).

Estimação de parâmetros genéticos para resistência à infecção por IMNV em camarões Litopenaeus vannamei por meio de análise de sobrevivência

The main specie of marine shrimp raised at Brazil and in the world is Litopenaeus vannamei, which had arrived in Brazil in the `80s. However, the entry of infectious myonecrosis virus (IMNV), causing the infectious myonecrosis disease in marine shrimps, brought economic losses to the national shrimp farming, with up to 70% of mortality in the shrimp production. In this way, the objective was to evaluate the survival of shrimps Litopenaeus vannamei infected with IMNV using the non parametric estimator of Kaplan-Meier and a model of frailty for grouped data. It were conducted three tests of viral challenges lasting 20 days each, at different periods of the year, keeping the parameters of pH, temperature, oxygen and ammonia monitored daily. It was evaluated 60 full-sib families of L. vannamei infected by IMNV in each viral challenge. The confirmation of the infection by IMNV was performed using the technique of PCR in real time through Sybr Green dye. Using the Kaplan-Meier estimator it was possible to detect significant differences (p <0.0001) between the survival curves of families and tanks and also in the joint analysis between viral challenges. It were estimated in each challenge, genetic parameters such as genetic value of family, it`s respective rate risk (frailty), and heritability in the logarithmic scale through the frailty model for grouped data. The heritability estimates were respectively 0.59; 0.36; and 0.59 in the viral challenges 1; 2; and 3, and it was also possible to identify families that have lower and higher rates of risk for the disease. These results can be used for selecting families more resistant to the IMNV infection and to include characteristic of disease resistance in L. vannamei into the genetic improvement programs

Algumas distribuições de probalidade para idosos grupados e censurados

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Modelos para dados grupados e sensurados aplicados à área biológica: comparação usando fator de Bayes

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Perspective transformation: Women in long-term recovery from alcohol abuse

Objective. The purpose of this study was to determine the meaning of personal transformation for twenty women in long term, stable recovery from alcohol abuse; to identify themes or patterns of this recovery, and; to determine the extent to which they experienced the phenomenon of perspective transformation. ^ Method. Volunteers were recruited by advertisement, word of mouth, and through a closed circuit web based broadcast. A descriptive, exploratory study, which analyzed perspective transformation from the standpoint of five action phases, was conducted. Data was collected using in-depth personal interviews and questionnaires. Subjects' responses were analyzed by qualitative methods. Triangulation was performed on the grouped data comparing the interviews to the data produced by the questionnaires. Quantitative analysis of questionnaire items explored behavioral changes experienced before and after alcoholism recovery. ^ Results. Five phases of recovery were identified. Phase I which involved recognition that alcohol was a problem and change might be possible took several years during which 3 major transitions occurred: (1) from often being alienated to having relationships with family and friends; (2) from daily upheavals to eventually a more peaceful existence, and; (3) from denial that alcohol was a problem to acceptance and willingness to change. Recovery was often seen in a spiritual context, which also required ongoing support. During Phase II there was an assessment of self, others, and the environment which revealed a pattern of intense unhappiness and negative feelings toward self and others with a disregard for cultural norms. Phase III revealed a period of desperation as life became unmanageable, but gradual willingness to accept support and guidance and a desire to improve self and help others. This led to improvement of existing role performance and the willingness to try out new roles. In Phase IV there was a pattern of personal growth which included: the establishment of boundaries, setting priorities, a willingness to place others' needs above their own, acceptance of responsibility, and learning to cope without alcohol, often with the use of tools learned in AA. During Phase V, many experienced knowledge of frailties but growing respect for self and others, with an improved ability to function in giving relationships. Implications for Prevention and Recovery: Early education concerning addiction and recovery may play a crucial role in prevention and early recovery, as it did for children of women in this study. Recovery requires persistent effort and organized support. ^

Risk assessment of the spanish national railway system

The principal risks in the railway industry are mainly associated with collisions, derailments and level crossing accidents. An understanding of the nature of previous accidents on the railway network is required to identify potential causes and develop safety systems and deploy safety procedures. Risk assessment is a process for determining the risk magnitude to assist with decision-making. We propose a three-step methodology to predict the mean number of fatalities in railway accidents. The first is to predict the mean number of accidents by analyzing generalized linear models and selecting the one that best fits to the available historical data on the basis of goodness-offit statistics. The second is to compute the mean number of fatalities per accident and the third is to estimate the mean number of fatalities. The methodology is illustrated on the Spanish railway system. Statistical models accounting for annual and grouped data for the 1992-2009 time period have been analyzed. After identifying the models for broad and narrow gauges, we predicted mean number of accidents and the number of fatalities for the 2010-18 time period.