Estimation of Parameters in Random Effect Models with Incidence Matrix Uncertainty

Random effect models have been widely applied in many fields of research. However, models with uncertain design matrices for random effects have been little investigated before. In some applications with such problems, an expectation method has been used for simplicity. This method does not include the extra information of uncertainty in the design matrix is not included. The closed solution for this problem is generally difficult to attain. We therefore propose an two-step algorithm for estimating the parameters, especially the variance components in the model. The implementation is based on Monte Carlo approximation and a Newton-Raphson-based EM algorithm. As an example, a simulated genetics dataset was analyzed. The results showed that the proportion of the total variance explained by the random effects was accurately estimated, which was highly underestimated by the expectation method. By introducing heuristic search and optimization methods, the algorithm can possibly be developed to infer the 'model-based' best design matrix and the corresponding best estimates.

A Poisson mixed model with nonnormal random effect distribution

In this paper, we propose a random intercept Poisson model in which the random effect is assumed to follow a generalized log-gamma (GLG) distribution. This random effect accommodates (or captures) the overdispersion in the counts and induces within-cluster correlation. We derive the first two moments for the marginal distribution as well as the intraclass correlation. Even though numerical integration methods are, in general, required for deriving the marginal models, we obtain the multivariate negative binomial model from a particular parameter setting of the hierarchical model. An iterative process is derived for obtaining the maximum likelihood estimates for the parameters in the multivariate negative binomial model. Residual analysis is proposed and two applications with real data are given for illustration. (C) 2011 Elsevier B.V. All rights reserved.

Parameterized Link Functions in Generalized Linear Random Effect Models: a Case Study on Breast Cancer Treatment

In non-linear random effects some attention has been very recently devoted to the analysis ofsuitable transformation of the response variables separately (Taylor 1996) or not (Oberg and Davidian 2000) from the transformations of the covariates and, as far as we know, no investigation has been carried out on the choice of link function in such models. In our study we consider the use of a random effect model when a parameterized family of links (Aranda-Ordaz 1981, Prentice 1996, Pregibon 1980, Stukel 1988 and Czado 1997) is introduced. We point out the advantages and the drawbacks associated with the choice of this data-driven kind of modeling. Difficulties in the interpretation of regression parameters, and therefore in understanding the influence of covariates, as well as problems related to loss of efficiency of estimates and overfitting, are discussed. A case study on radiotherapy usage in breast cancer treatment is discussed.

Predicting random level and seasonality of hotel prices. A structural equation growth curve approach

This article examines the effect on price of different characteristics of holiday hotels in the sun-and-beach segment, under the hedonic function perspective. Monthly prices of the majority of hotels in the Spanish continental Mediterranean coast are gathered from May to October 1999 from the tour operator catalogues. Hedonic functions are specified as random-effect models and parametrized as structural equation models with two latent variables, a random peak season price and a random width of seasonal fluctuations. Characteristics of the hotel and the region where they are located are used as predictors of both latent variables. Besides hotel category, region, distance to the beach, availability of parking place and room equipment have an effect on peak price and also on seasonality. 3- star hotels have the highest seasonality and hotels located in the southern regions the lowest, which could be explained by a warmer climate in autumn

The Effect of Four-Lane to Three-Lane Conversion on the Number of Crashes and Crash Rates in Iowa Roads, June 2005

We analyze crash data collected by the Iowa Department of Transportation using Bayesian methods. The data set includes monthly crash numbers, estimated monthly traffic volumes, site length and other information collected at 30 paired sites in Iowa over more than 20 years during which an intervention experiment was set up. The intervention consisted in transforming 15 undivided road segments from four-lane to three lanes, while an additional 15 segments, thought to be comparable in terms of traffic safety-related characteristics were not converted. The main objective of this work is to find out whether the intervention reduces the number of crashes and the crash rates at the treated sites. We fitted a hierarchical Poisson regression model with a change-point to the number of monthly crashes per mile at each of the sites. Explanatory variables in the model included estimated monthly traffic volume, time, an indicator for intervention reflecting whether the site was a “treatment” or a “control” site, and various interactions. We accounted for seasonal effects in the number of crashes at a site by including smooth trigonometric functions with three different periods to reflect the four seasons of the year. A change-point at the month and year in which the intervention was completed for treated sites was also included. The number of crashes at a site can be thought to follow a Poisson distribution. To estimate the association between crashes and the explanatory variables, we used a log link function and added a random effect to account for overdispersion and for autocorrelation among observations obtained at the same site. We used proper but non-informative priors for all parameters in the model, and carried out all calculations using Markov chain Monte Carlo methods implemented in WinBUGS. We evaluated the effect of the four to three-lane conversion by comparing the expected number of crashes per year per mile during the years preceding the conversion and following the conversion for treatment and control sites. We estimated this difference using the observed traffic volumes at each site and also on a per 100,000,000 vehicles. We also conducted a prospective analysis to forecast the expected number of crashes per mile at each site in the study one year, three years and five years following the four to three-lane conversion. Posterior predictive distributions of the number of crashes, the crash rate and the percent reduction in crashes per mile were obtained for each site for the months of January and June one, three and five years after completion of the intervention. The model appears to fit the data well. We found that in most sites, the intervention was effective and reduced the number of crashes. Overall, and for the observed traffic volumes, the reduction in the expected number of crashes per year and mile at converted sites was 32.3% (31.4% to 33.5% with 95% probability) while at the control sites, the reduction was estimated to be 7.1% (5.7% to 8.2% with 95% probability). When the reduction in the expected number of crashes per year, mile and 100,000,000 AADT was computed, the estimates were 44.3% (43.9% to 44.6%) and 25.5% (24.6% to 26.0%) for converted and control sites, respectively. In both cases, the difference in the percent reduction in the expected number of crashes during the years following the conversion was significantly larger at converted sites than at control sites, even though the number of crashes appears to decline over time at all sites. Results indicate that the reduction in the expected number of sites per mile has a steeper negative slope at converted than at control sites. Consistent with this, the forecasted reduction in the number of crashes per year and mile during the years after completion of the conversion at converted sites is more pronounced than at control sites. Seasonal effects on the number of crashes have been well-documented. In this dataset, we found that, as expected, the expected number of monthly crashes per mile tends to be higher during winter months than during the rest of the year. Perhaps more interestingly, we found that there is an interaction between the four to three-lane conversion and season; the reduction in the number of crashes appears to be more pronounced during months, when the weather is nice than during other times of the year, even though a reduction was estimated for the entire year. Thus, it appears that the four to three-lane conversion, while effective year-round, is particularly effective in reducing the expected number of crashes in nice weather.

On the performance of small-area estimators: Fixed vs. random area parameters

Most methods for small-area estimation are based on composite estimators derived from design- or model-based methods. A composite estimator is a linear combination of a direct and an indirect estimator with weights that usually depend on unknown parameters which need to be estimated. Although model-based small-area estimators are usually based on random-effects models, the assumption of fixed effects is at face value more appropriate.Model-based estimators are justified by the assumption of random (interchangeable) area effects; in practice, however, areas are not interchangeable. In the present paper we empirically assess the quality of several small-area estimators in the setting in which the area effects are treated as fixed. We consider two settings: one that draws samples from a theoretical population, and another that draws samples from an empirical population of a labor force register maintained by the National Institute of Social Security (NISS) of Catalonia. We distinguish two types of composite estimators: a) those that use weights that involve area specific estimates of bias and variance; and, b) those that use weights that involve a common variance and a common squared bias estimate for all the areas. We assess their precision and discuss alternatives to optimizing composite estimation in applications.

The effect on prices of the attributes of holiday hotels: a hedonic prices approach

This article examines the effect on price of different characteristics of holiday hotels in the sun-and-beach segment. The effect on price is estimated under the hedonic function perspective by means of random effect models, known also as mixed or panel models. Some 82,000 prices were gathered between 1991 and 1998 from tour operator catalogues. The study reveals huge price differences between 4-star hotels and the rest, coupled with practically no difference between 1-star and 2-star hotels. Other attributes with a significant effect on price are town, hotel size, distance to the beach and availability of parking place. The results can assist hotel managers in shaping pricing and investment strategies

Predicting random level and seasonality of hotel prices. A structural equation growth curve approach

This article examines the effect on price of different characteristics of holiday hotels in the sun-and-beach segment, under the hedonic function perspective. Monthly prices of the majority of hotels in the Spanish continental Mediterranean coast are gathered from May to October 1999 from the tour operator catalogues. Hedonic functions are specified as random-effect models and parametrized as structural equation models with two latent variables, a random peak season price and a random width of seasonal fluctuations. Characteristics of the hotel and the region where they are located are used as predictors of both latent variables. Besides hotel category, region, distance to the beach, availability of parking place and room equipment have an effect on peak price and also on seasonality. 3- star hotels have the highest seasonality and hotels located in the southern regions the lowest, which could be explained by a warmer climate in autumn

The effect of adhesive and flowable composite on postoperative sensitivity: 2-Week results

Objective: To measure 2-week postoperative sensitivity in Class II composite restorations placed with a self-etching adhesive (Clearfil SE Bond) or a total-etch adhesive (Prime&Bond NT) with or without a flowable composite as cervical increment. Method and materials: Upon approval by the University of Guarulhos Committee on Human Subjects, 100 restorations were inserted in 46 patients who required Class II restorations in their molars and premolars. Enamel and dentin walls were conditioned with a self-etching primer (for Clearfil SE Bond) or etched with 34% phosphoric acid (for Prime&Bond NT). A 1- to 2-mm-thick increment of a flowable composite (Filtek Flow) was used in the proximal box in 50% of the restorations of each adhesive. Preparations were restored with a packable composite (Surefil). The restorations were evaluated preoperatively and 2 weeks postoperatively for sensitivity to cold, air, and masticatory forces using a visual analog scale. Marginal integrity of the accessible margins was also evaluated. Statistical analysis used a mixed linear model with subject as a random effect. Results: Ninety-eight teeth from 44 subjects were observed at 2 weeks. The type of adhesive and use of flowable composite had no significant effects or interaction for any of the four outcomes of interest, ie, change from baseline to 2 weeks in sensitivity and response time for the cold or air stimulus. For the air stimulus, the overall average change from baseline was not significant for either sensitivity or response time. For the cold stimulus, the overall average change from baseline was significant for both sensitivity and response time. No case of sensitivity to masticatory forces was observed. Conclusion: No differences in postoperative sensitivity were observed between a self-etch adhesive and a total-etch adhesive at 2 weeks. The use of flowable composite did not decrease postoperative sensitivity.

The sleeper effect: Artifact or phenomenon—A brief comment on Bell et al. (2013)

OBJECTIVE: Bell, Marcus, and Goodlad (2013) recently conducted a meta-analysis of randomized controlled additive trials and found that adding an additional component to an existing treatment vis-à-vis the existing treatment produced larger effect sizes on targeted outcomes at 6-months follow-up than at termination, an effect they labeled as a sleeper effect. One of the limitations with Bell et al.'s detection of the sleeper effect was that they did not conduct a statistical test of the size of the effect at follow-up versus termination. METHOD: To statistically test if the differences of effect sizes between the additive conditions and the control conditions at follow-up differed from those at termination, we used a restricted maximum-likelihood random-effect model with known variances to conduct a multilevel longitudinal meta-analysis (k = 30). RESULTS: Although the small effects at termination detected by Bell et al. were replicated (ds = 0.17-0.23), none of the analyses of growth from termination to follow-up produced statistically significant effects (ds < 0.08; p > .20), and when asymmetry was considered using trim-and-fill procedure or the studies after 2000 were analyzed, magnitude of the sleeper effect was negligible (d = 0.00). CONCLUSION: There is no empirical evidence to support the sleeper effect.

Analysis Of The Fluorescence Of Body Fluids On Different Surfaces And Times.

The use of screening techniques, such as an alternative light source (ALS), is important for finding biological evidence at a crime scene. The objective of this study was to evaluate whether biological fluid (blood, semen, saliva, and urine) deposited on different surfaces changes as a function of the age of the sample. Stains were illuminated with a Megamaxx™ ALS System and photographed with a Canon EOS Utility™ camera. Adobe Photoshop™ was utilized to prepare photographs for analysis, and then ImageJ™ was used to record the brightness values of pixels in the images. Data were submitted to analysis of variance using a generalized linear mixed model with two fixed effects (surface and fluid). Time was treated as a random effect (through repeated measures) with a first-order autoregressive covariance structure. Means of significant effects were compared by the Tukey test. The fluorescence of the analyzed biological material varied depending on the age of the sample. Fluorescence was lower when the samples were moist. Fluorescence remained constant when the sample was dry, up to the maximum period analyzed (60 days), independent of the substrate on which the fluid was deposited, showing the novelty of this study. Therefore, the forensic expert can detect biological fluids at the crime scene using an ALS even several days after a crime has occurred.

Sources of variation of energy and nutrient intake among adolescents in São Paulo, Brazil

The aim of the current study was to describe the sources of variation of energy and nutrient intake and to calculate the number of repetitions of diet measurements to estimate usual intake in adolescents from São Paulo, Brazil. Data was collected using 24-hour dietary recalls (24hR) in 273 adolescents between 2007 and 2008. Individuals completed a repeat 24hR around two months later. The sources of variation were estimated using the random effect model. Variance ratios (within-person to between-person variance ratio) and the number of repetitions of 24hR to estimate usual intake were calculated. The principal source of variation was due to within-person variance. The contribution of day of week and month of year was less than 8%. Variations ranged from 1.15 for calcium to 7.31 for vitamin E. The number of 24hR repeats required to estimate usual intake varied according to nutrient and gender, numbering 15 for males and 8 for females.

Fontes de variação da ingestão de energia e nutrientes entre adolescentes do Município de São Paulo, Brasil

Este estudo propôs-se a descrever as fontes de variação da ingestão de energia e nutrientes e calcular o número de dias necessários para a estimativa da ingestão habitual em adolescentes do Município de São Paulo, Brasil. Foi aplicado um recordatório alimentar de 24 horas (R24h) em 273 adolescentes, durante os anos de 2007 e 2008, e posteriormente cada indivíduo foi convidado a responder a outro R24h. Foram estimadas as fontes de variação da ingestão utilizando-se modelo de efeitos aleatórios. A variância intrapessoal foi o componente de variância que mais contribuiu para a variabilidade da ingestão de energia e nutrientes, ao passo que a contribuição do dia da semana e mês do ano foi pequena (< 8por cento ) para a variabilidade total da ingestão. As razões de variância variaram de 1,15 para o cálcio a 7,31 para a vitamina E. O número de R24h necessário para estimar a ingestão habitual variou de acordo com o nutriente: em torno de 15 para o sexo masculino e 8 para o feminino

Double generalized linear model for tissue culture proportion data: a Bayesian perspective

Joint generalized linear models and double generalized linear models (DGLMs) were designed to model outcomes for which the variability can be explained using factors and/or covariates. When such factors operate, the usual normal regression models, which inherently exhibit constant variance, will under-represent variation in the data and hence may lead to erroneous inferences. For count and proportion data, such noise factors can generate a so-called overdispersion effect, and the use of binomial and Poisson models underestimates the variability and, consequently, incorrectly indicate significant effects. In this manuscript, we propose a DGLM from a Bayesian perspective, focusing on the case of proportion data, where the overdispersion can be modeled using a random effect that depends on some noise factors. The posterior joint density function was sampled using Monte Carlo Markov Chain algorithms, allowing inferences over the model parameters. An application to a data set on apple tissue culture is presented, for which it is shown that the Bayesian approach is quite feasible, even when limited prior information is available, thereby generating valuable insight for the researcher about its experimental results.