Recurrent events experienced by individual units or systems occur in many fields. The main target of this thesis is to develop formal tests for certain features of recurrent event processes, and to discuss their properties. In particular, carryover effects and time trends are considered. The former is related to clustering of events together in time, and the latter refers to a tendency for the rate of event occurrence to change over time in some systematic way. Score tests are developed for models incorporating carryover effects or time trends. The tests considered are easily interpreted and based on simple models but have good robustness properties against a range of carryover and trend alternatives. Asymptotic properties of test statistics are discussed when the number of processes approaches infinity as well as when one process is under observation for a long time. In applications involving multiple systems or individuals, heterogeneity is often apparent, and there is a need for tests developed for such cases. Allowance for heterogeneity is, therefore, considered. Methods are applied to data sets from industry and medicine. The results are supported by simulation studies.

Recurrent events experienced by individual units or systems occur in many fields. The main target of this thesis is to develop formal tests for certain features of recurrent event processes, and to discuss their properties. In particular, carryover effects and time trends are considered. The former is related to clustering of events together in time, and the latter refers to a tendency for the rate of event occurrence to change over time in some systematic way. Score tests are developed for models incorporating carryover effects or time trends. The tests considered are easily interpreted and based on simple models but have good robustness properties against a range of carryover and trend alternatives. Asymptotic properties of test statistics are discussed when the number of processes approaches infinity as well as when one process is under observation for a long time. In applications involving multiple systems or individuals, heterogeneity is often apparent, and there is a need for tests developed for such cases. Allowance for heterogeneity is, therefore, considered. Methods are applied to data sets from industry and medicine. The results are supported by simulation studies.

Linear assets are complex industrial systems that extend from one geographical region to another. Given the criticality of the industrial activities linked to them, it is vital to accurately estimate the systems' reliability. However, this task can be complex as the operational, maintenance and design conditions vary largely along linear asset thereby causing heterogeneity thus complicating the reliability analysis. This leads to inadequacy of the traditional single-parameter reliability approach that uses time as the only predictor variable. This thesis job reviews the existing methods to include explanatory factors into the analysis as covariates. Then, a workflow process is proposed to describe the sequence of steps and decisions needed to carry out the appropriate analysis. The presented flowcharts show how to deal with challenges that are often present in the industrial field. Approaches for dealing with multicollinearity, categorical and continuous covariates, time-dependent covariates, and repairable systems are treated in this work. Subsequently, a case study of railway track is presented as a repairable system with several covariates and failure times as provided by the Swedish Transport Administration. Two different models based on proportional hazard models i.e. the AG (Andersen-Gill) and the PWP(Prentice–Williams–Peterson) methods were run to estimate the regression parameters. Some other functions associated with reliability are obtained from the models such as the cumulative hazard rate and the probability of non-occurrence of the next recurrent event.  In addition, to check the goodness of fit from the obtained models, the Cox-Snell residuals are estimated and used to verify if the estimated parameters fit the data. This procedure is done using a graphical method. From the goodness of fit test, it can be concluded that the PWP model performs better than the AG model. However, the fit is not good enough thus other model validation residual-based techniques are suggested as future work to investigate the reason for the discrepancy. Finally, some actions to deal with multicollinearity are recommended, including using a frailty model and the possibility of reformulating the covariates.

Growth mixture modeling (GMM) is a useful tool for examining both between- and within-persons change over time and uncovering unobserved heterogeneity in growth trajectories. Importantly, the correct extraction of latent classes and parameter recovery can be dependent upon the type of covariates used. Time-varying covariates (TVCs) can influence class membership but are scarcely included in GMMs as predictors. Other times, TVCs are incorrectly modeled as time-invariant covariates (TICs). Additionally, problematic results can occur with the use of maximum likelihood (ML) estimation in GMMs, including convergence issues and sub-optimal maxima. In such cases, Bayesian estimation may prove to be a useful solution. The present Monte Carlo simulation study aimed to assess class enumeration accuracy and parameter recovery of GMMs with a TVC, particularly when a TVC has been incorrectly specified as a TIC. Both ML estimation and Bayesian estimation were examined. Results indicated that class enumeration indices perform less favorably in the case of TVC misspecification, particularly absolute class enumeration indices. Additionally, in the case of TVC misspecification, parameter bias was found to be greater than the generally accepted cutoff of 10%, particularly for variance estimates. It is recommended that researchers continue to use a variety of class enumeration indices during class enumeration, particularly relative indices. Additionally, researchers should take caution when interpreting variance parameter estimates when the GMM contains a misspecified TVC.

Statistics show that hate crimes continue to occur in United States, inciting fear and intimidation in minority communities (Petrosino, 1999; Torres, 1999; Saucier et al., 2006; Nolan et al., 2002; Jacobs & Potter, 1997). Although hate crime legislation has been passed, very little research has assessed what impact it has. This is particularly true for jury decision making. The aim of this study was to examine the main effects of type of crime (hate versus non-hate), offender-victim racial composition (African-American/Caucasian), and the interaction between these two variables on ratings of guilt likelihood, deserved punishment, and sentence recommendations after controlling for offender dangerousness, witness credibility, and hate motivation. The first hypothesis assumed that differences in guilt and hate crime adjudications would emerge across the experimental conditions. The second hypothesis indicated that dangerousness, and hate motivation would exert significant influence on deserved punishment and sentence recommendations; while witness credibility would exert influence on guilt adjudication. The third and fourth hypothesis stated that there would be no main effects of type of crime (hate versus non-hate) and offender-victim racial composition (African-American/Caucasian) on ratings of guilt likelihood, deserved punishment, and sentence recommendations. The fifth hypothesis suggested that there would be interaction effects between type of crime and offender-victim racial composition on ratings of guilt likelihood, deserved punishment, and recommended sentence after controlling for dangerousness, hate motivation, and witness credibility. Results indicated that there were no main effects for type of crime, offender-victim racial composition, or the interaction between these two variables on ratings of guilt likelihood, deserved punishment, and sentence recommendations. There was a significant interaction effect on ratings of guilt likelihood for aggravated battery; however this interaction disappeared after controlling for offender dangerousness, witness credibility, and hate motivation. Dangerousness and hate motivation appeared to exert influence on the study outcomes. Overall, the findings were not congruent with prior research. It appeared that the covarying factors seemed to exert significant influence on the study outcomes; thus further study is warranted.

Small area estimation is an arena that has seen rapid development in the past 50 years, due to its widespread applicability in government projects, marketing research and many other areas. However, it is often difficult to obtain error-free data for this purpose. In this dissertation, each project describes a model used for small area estimation in which the covariates are measured with error. We applied different methods of bias correction to improve the estimates of the parameter of interest in the small areas. There is a variety of methods available for bias correction of estimates in the presence of measurement error. We applied the simulation extrapolation (SIMEX), ordinary corrected scores and Monte Carlo corrected scores methods of bias correction in the Fay-Herriot model, and investigated the performance of the bias-corrected estimators. The performance of the estimators in the presence of non-normal measurement error and of the SIMEX estimator in the presence of non-additive measurement error was also studied. For each of these situations, we presented simulation studies to observe the performance of the proposed correction procedures. In addition, we applied our proposed methodology to analyze a real life, nontrivial data set and present the results. We showed that the Lohr-Ybarra estimator is slightly inefficient and that applying methods of bias correction like SIMEX, corrected scores or Monte Carlo corrected scores (MCCS) increases the efficiency of the small area estimates. In particular, we showed that the simulation based bias correction methods like SIMEX and MCCS provide a greater gain in efficiency. We also showed that the SIMEX method of bias correction is robust with respect to departures from normality or additivity of measurement error. We showed that the MCCS method is robust with respect to departure from normality of measurement error.

Higher stocking density under seasonal-rotation grazing is expected to increase plant abundance because expanded animal distribution and reduced selective grazing on forage species will reduce the spatial variation and competitive advantage of non-forage species compared to yearlong grazing. Rangeland scientists struggle with how long rangeland experiments must continue in order to detect grazing treatment effects, particularly in semi-arid ecosystems with slow responses and high spatio-temporal variability. My first study investigated grazing system effects on plant abundance (cover and density) over the short-term (12yrs) or long-term (22 or 34yrs) after accounting for covariates (mesquite and precipitation gradients). My second study assessed how grazing systems affected spatial variation in grass abundance over 22 or 34 years after accounting for precipitation gradient. The first study was a course resolution approach, looking at grazing impacts on plant abundance. The second study was a finer resolution assessment of the underlying assumption that rotational grazing systems reduce selective grazing. Using split-plot analysis of variance, with year as the split, changes in mean plant abundance and variance in grass abundance were compared between two grazing systems (yearlong vs. seasonal rotation), after accounting for covariate(s). Variance of grass abundance among sample locations within an experimental pasture was the measure of spatial variability and was expected to increase with selective grazing. Grazing systems did not influence plant abundance or spatial variation of grasses. The absence of grazing effect may be due to overriding influences of grazing intensity, large pasture sizes, temporal variation in precipitation, and few replicates. Specific to spatial variation, the absence of grazing system effect may be due to discrepancies in transect representation across ecological sites and spatial variation of grasses occurring at scales different than the 30-m transect size. Like earlier research, my studies failed to substantiate the fundamental premise for implementing rotational grazing systems. This exposes challenges that confront rangeland scientists when implementing grazing studies in spatio-temporally heterogeneous ecosystems. I recommend that research shift from comparing rigid schedule-driven grazing systems to more adaptive management approach where there are comparisons between different levels or different designs of flexible systems.

Capture-recapture (CRC) models use two or more samples, or lists, to estimate the size of a population. In the canonical example, a researcher captures, marks, and releases several samples of fish in a lake. When the fish that are captured more than once are few compared to the total number that are captured, one suspects that the lake contains many more uncaptured fish. This basic intuition motivates CRC models in fields as diverse as epidemiology, entomology, and computer science. We use simulations to study the performance of conventional log-linear models for CRC. Specifically we evaluate model selection criteria, model averaging, an asymptotic variance formula, and several small-sample data adjustments. Next, we argue that interpretable models are essential for credible inference, since sets of models that fit the data equally well can imply vastly different estimates of the population size. A secondary analysis of data on survivors of the World Trade Center attacks illustrates this issue. Our main chapter develops local log-linear models. Heterogeneous populations tend to bias conventional log-linear models. Post-stratification can reduce the effects of heterogeneity by using covariates, such as the age or size of each observed unit, to partition the data into relatively homogeneous post-strata. One can fit a model to each post-stratum and aggregate the resulting estimates across post-strata. We extend post-stratification to its logical extreme by selecting a local log-linear model for each observed point in the covariate space, while smoothing to achieve stability. Local log-linear models serve a dual purpose. Besides estimating the population size, they estimate the rate of missingness as a function of covariates. Simulations demonstrate the superiority of local log-linear models for estimating local rates of missingness for special cases in which the generating model varies over the covariate space. We apply the method to estimate bird species richness in continental North America and to estimate the prevalence of multiple sclerosis in a region of France.

Esta tese tem como objetivo a modelagem da degradação de correias em transportadores utilizados em mineração, como função do tempo e de outras covariáveis independentes que fazem parte do processo de mineração e que influenciam no desgaste das mesmas. Para a realização do trabalho, utilizou-se um método dividido em duas etapas: (i) abordagem qualitativa (estudo teórico do tópico degradação de correias e coleta de dados através da técnica de Grupo Focado – GF), para definição de variáveis influentes no desgaste, e (ii) abordagem quantitativa, para obtenção do modelo de degradação das correias, sendo utilizada, no estudo em questão, uma regressão linear múltipla. Como resultado foi possível identificar através da literatura, assim como via GF, que as variáveis ciclo da correia, comprimento e largura da correia, queda do material, limpador de correias (raspadores), taxa de alimentação, granulometria, composto e velocidade da correia impactariam potencialmente na degradação de correias. Já com o uso da regressão múltipla, constatou-se que as mesmas realmente são significativas e influentes, corroborando os dados obtidos via GF. De posse dos modelos de degradação obtidos para cada correia, foi possível elaborar uma proposta de sistemática de gestão da degradação de correias, baseada na comparação da evolução do desgaste real com o previsto, de modo a se detectar possíveis desvios e permitir a elaboração de ações de correção, visando minimizar a degradação acelerada e maximizar a vida útil das correias. Conseguiu-se estimar um ganho financeiro potencial de cerca de R$ 1.132.000,00 por ano, a partir da comparação entre a vida útil calculada pelos modelos de degradação e a vida estimada pela área de manutenção do complexo. / This thesis aims at modelling of the conveyor’s belt degradation used in mining as a function of time and other independent covariate that are part of the mining process and have influence in their wearing. To carry out the research we implemented a method divided in two stages: (i) a qualitative approach (theoretical study of conveyor belts degradation and data collection through Focused Groups – FG) for definition of factors that are influential in the wearing of belts, and (ii) a quantitative approach for obtaining a belts’ degradation model through multiple linear regression. It was possible to identify in the literature and through FG that variables such as belt cycle, belt length and width, material fall, belt cleaner, feed rate, particle size, compound and belt speed could potentially impact on the degradation of belts. Using multiple regression such variables were found to be statistically significant, corroborating the data obtained from FG. With the degradation models obtained for each conveyor belt it was possible to propose a method for the maintenance management of conveyor belts. The method was based on the comparison of real wear versus predicted wear in order to detect possible deviations and to allow the development of correction actions that aim at minimizing accelerated degradation and maximizing the belt’s lifetime. A potential financial gain of approximately R$ 1.132.000,00 per year was estimated comparing the lifetime obtained using the degradation models and the life estimated by the maintenance area of the complex.

Esta tese tem como objetivo a modelagem da degradação de correias em transportadores utilizados em mineração, como função do tempo e de outras covariáveis independentes que fazem parte do processo de mineração e que influenciam no desgaste das mesmas. Para a realização do trabalho, utilizou-se um método dividido em duas etapas: (i) abordagem qualitativa (estudo teórico do tópico degradação de correias e coleta de dados através da técnica de Grupo Focado – GF), para definição de variáveis influentes no desgaste, e (ii) abordagem quantitativa, para obtenção do modelo de degradação das correias, sendo utilizada, no estudo em questão, uma regressão linear múltipla. Como resultado foi possível identificar através da literatura, assim como via GF, que as variáveis ciclo da correia, comprimento e largura da correia, queda do material, limpador de correias (raspadores), taxa de alimentação, granulometria, composto e velocidade da correia impactariam potencialmente na degradação de correias. Já com o uso da regressão múltipla, constatou-se que as mesmas realmente são significativas e influentes, corroborando os dados obtidos via GF. De posse dos modelos de degradação obtidos para cada correia, foi possível elaborar uma proposta de sistemática de gestão da degradação de correias, baseada na comparação da evolução do desgaste real com o previsto, de modo a se detectar possíveis desvios e permitir a elaboração de ações de correção, visando minimizar a degradação acelerada e maximizar a vida útil das correias. Conseguiu-se estimar um ganho financeiro potencial de cerca de R$ 1.132.000,00 por ano, a partir da comparação entre a vida útil calculada pelos modelos de degradação e a vida estimada pela área de manutenção do complexo. / This thesis aims at modelling of the conveyor’s belt degradation used in mining as a function of time and other independent covariate that are part of the mining process and have influence in their wearing. To carry out the research we implemented a method divided in two stages: (i) a qualitative approach (theoretical study of conveyor belts degradation and data collection through Focused Groups – FG) for definition of factors that are influential in the wearing of belts, and (ii) a quantitative approach for obtaining a belts’ degradation model through multiple linear regression. It was possible to identify in the literature and through FG that variables such as belt cycle, belt length and width, material fall, belt cleaner, feed rate, particle size, compound and belt speed could potentially impact on the degradation of belts. Using multiple regression such variables were found to be statistically significant, corroborating the data obtained from FG. With the degradation models obtained for each conveyor belt it was possible to propose a method for the maintenance management of conveyor belts. The method was based on the comparison of real wear versus predicted wear in order to detect possible deviations and to allow the development of correction actions that aim at minimizing accelerated degradation and maximizing the belt’s lifetime. A potential financial gain of approximately R$ 1.132.000,00 per year was estimated comparing the lifetime obtained using the degradation models and the life estimated by the maintenance area of the complex.