On estimation and influence diagnostics for zero-inflated negative binomial regression models

The zero-inflated negative binomial model is used to account for overdispersion detected in data that are initially analyzed under the zero-Inflated Poisson model A frequentist analysis a jackknife estimator and a non-parametric bootstrap for parameter estimation of zero-inflated negative binomial regression models are considered In addition an EM-type algorithm is developed for performing maximum likelihood estimation Then the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes and some ways to perform global influence analysis are derived In order to study departures from the error assumption as well as the presence of outliers residual analysis based on the standardized Pearson residuals is discussed The relevance of the approach is illustrated with a real data set where It is shown that zero-inflated negative binomial regression models seems to fit the data better than the Poisson counterpart (C) 2010 Elsevier B V All rights reserved

Media bias and central bank response. Evidence from the nominal exchange rate behavior in Colombia

Since 1991 Colombia has had a market-determined Peso - US Dollar Nominal Exchange Rate (NER), after more than 20 years of controlled and multiple exchange rates. The behavior (revaluation / devaluation) of the NER is constantly reported in news, editorials and op-eds of major newspapers of the nation with particular attention to revaluation. The uneven reporting of revaluation episodes can be explained by the existence of an interest group particulary affected by revaluation, looking to increase awareness and sympathy for help from public institutions. Using the number of news and op-eds from a major Colombian newspaper, it is shown that there is an over-reporting of revaluation episodes in contrast to devaluation ones. Secondly, using text analysis upon the content of the news, it is also shown that the words devaluation and revaluation are far apart in the distribution of words within the news; and revaluation is highly correlated with words related to: public institutions, exporters and the need of assistance. Finally it is also shown that the probability of the central bank buying US dollars to lessen revaluation effects increases with the number of news; even though the central bank allegedly intervenes in the exchange rate market only to tame volatility or accumulate international reserves.

Tooth loss in Brazilian middle-aged adults: multilevel effects

Objective. To examine the link between tooth loss and multilevel factors in a national sample of middle-aged adults in Brazil. Material and methods. Analyses were based on the 2003 cross-sectional national epidemiological survey of the oral health of the Brazilian population, which covered 13 431 individuals (age 35-44 years). Multistage cluster sampling was used. The dependent variable was tooth loss and the independent variables were classified according to the individual or contextual level. A multilevel negative binomial regression model was adopted. Results. The average tooth loss was 14 (standard deviation 9.5) teeth. Half of the individuals had lost 12 teeth. The contextual variables showed independent effects on tooth loss. It was found that having 9 years or more of schooling was associated with protection against tooth loss (means ratio range 0.68-0.76). Not having visited the dentist and not having visited in the last >= 3 years accounted for increases of 33.5% and 21.3%, respectively, in the risk of tooth loss (P < 0.05). The increase in tooth extraction ratio showed a strong contextual effect on increased risk of tooth loss, besides changing the effect of protective variables. Conclusions. Tooth loss in middle-aged adults has important associations with social determinants of health. This study points to the importance of the social context as the main cause of oral health injuries suffered by most middle-aged Brazilian adults.

Post-merger innovative performance in the renewable energy sector

Due to global warming and shrinking fossil fuel resources, politics as well as society urge for a reduction of green house gas (GHG) emissions. This leads to a re-orientation towards a renewable energy sector. In this context, innovation and new technologies are key success factors. Moreover, the renewable energy sector has entered a consolidation stage, where corporate investors and mergers and acquisitions (M&A) gain in importance. Although both M&A and innovation in the renewable energy sector are important corporate strategies, the link between those two aspects has not been examined before. The present thesis examines the research question how M&A influence the acquirer’s post-merger innovative performance in the renewable energy sector. Based on a framework of relevant literature, three hypotheses are defined. First, the relation between non-technology oriented M&A and post-merger innovative performance is discussed. Second, the impact of absolute acquired knowledge on postmerger innovativeness is examined. Third, the target-acquirer relatedness is discussed. A panel data set of 117 firms collected over a period of six years has been analyzed via a random effects negative binomial regression model and a time lag of one year. The results support a non-significant, negative impact of non-technology M&A on postmerger innovative performance. The applied model did not support a positive and significant impact of absolute acquired knowledge on post-merger innovative performance. Lastly, the results suggest a reverse relation than postulated by Hypothesis 3. Targets from the same industry significantly and negatively influence the acquirers’ innovativeness.

Questionnaire-based study to assess the association between management practices and mastitis within tie-stall and free-stall dairy housing systems in Switzerland.

BACKGROUND Prophylactic measures are key components of dairy herd mastitis control programs, but some are only relevant in specific housing systems. To assess the association between management practices and mastitis incidence, data collected in 2011 by a survey among 979 randomly selected Swiss dairy farms, and information from the regular test day recordings from 680 of these farms was analyzed. RESULTS The median incidence of farmer-reported clinical mastitis (ICM) was 11.6 (mean 14.7) cases per 100 cows per year. The median annual proportion of milk samples with a composite somatic cell count (PSCC) above 200,000 cells/ml was 16.1 (mean 17.3) %. A multivariable negative binomial regression model was fitted for each of the mastitis indicators for farms with tie-stall and free-stall housing systems separately to study the effect of other (than housing system) management practices on the ICM and PSCC events (above 200,000 cells/ml). The results differed substantially by housing system and outcome. In tie-stall systems, clinical mastitis incidence was mainly affected by region (mountainous production zone; incidence rate ratio (IRR) = 0.73), the dairy herd replacement system (1.27) and farmers age (0.81). The proportion of high SCC was mainly associated with dry cow udder controls (IRR = 0.67), clean bedding material at calving (IRR = 1.72), using total merit values to select bulls (IRR = 1.57) and body condition scoring (IRR = 0.74). In free-stall systems, the IRR for clinical mastitis was mainly associated with stall climate/temperature (IRR = 1.65), comfort mats as resting surface (IRR = 0.75) and when no feed analysis was carried out (IRR = 1.18). The proportion of high SSC was only associated with hand and arm cleaning after calving (IRR = 0.81) and beef producing value to select bulls (IRR = 0.66). CONCLUSIONS There were substantial differences in identified risk factors in the four models. Some of the factors were in agreement with the reported literature while others were not. This highlights the multifactorial nature of the disease and the differences in the risks for both mastitis manifestations. Attempting to understand these multifactorial associations for mastitis within larger management groups continues to play an important role in mastitis control programs.

Disparities in medical expenditure and utilization among hypertensive men and women in the U.S.: Cross-section and lifetime analysis

Objectives. To investigate procedural gender equity by assessing predisposing, enabling and need predictors of gender differences in annual medical expenditures and utilization among hypertensive individuals in the U.S. Also, to estimate and compare lifetime medical expenditures among hypertensive men and women in the U.S. ^ Data source. 2001-2004 the Medical Expenditure Panel Survey (MEPS);1986-2000 National Health Interview Survey (NHIS) and National Health Interview Survey linked to mortality in the National Death Index through 2002 (2002 NHIS-NDI). ^ Study design. We estimated total medical expenditure using four equations regression model, specific medical expenditures using two equations regression model and utilization using negative binomial regression model. Procedural equity was assessed by applying the Aday et al. theoretical framework. Expenditures were estimated in 2004 dollars. We estimated hypertension-attributable medical expenditure and utilization among men and women. ^ To estimate lifetime expenditures from ages 20 to 85+, we estimated medical expenditures with cross-sectional data and survival with prospective data. The four equations regression model were used to estimate average annual medical expenditures defined as sum of inpatient stay, emergency room visits, outpatient visits, office based visits, and prescription drugs expenditures. Life tables were used to estimate the distribution of life time medical expenditures for hypertensive men and women at different age and factors such as disease incidence, medical technology and health care cost were assumed to be fixed. Both total and hypertension attributable expenditures among men and women were estimated. ^ Data collection. We used the 2001-2004 MEPS household component and medical condition files; the NHIS person and condition files from 1986-1996 and 1997-2000 sample adult files were used; and the 1986-2000 NHIS that were linked to mortality in the 2002 NHIS-NDI. ^ Principal findings. Hypertensive men had significantly less utilization for most measures after controlling predisposing, enabling and need factors than hypertensive women. Similarly, hypertensive men had less prescription drug (-9.3%), office based (-7.2%) and total medical (-4.5%) expenditures than hypertensive women. However, men had more hypertension-attributable medical expenditures and utilization than women. ^ Expected total lifetime expenditure for average life table individuals at age 20, was $188,300 for hypertensive men and $254,910 for hypertensive women. But the lifetime expenditure that could be attributed to hypertension was $88,033 for men and $40,960 for women. ^ Conclusion. Hypertensive women had more utilization and expenditure for most measures than hypertensive men, possibly indicating procedural inequity. However, relatively higher hypertension-attributable health care of men shows more utilization of resources to treat hypertension related diseases among men than women. Similar results were reported in lifetime analyses.^ Key words: gender, medical expenditures, utilization, hypertension-attributable, lifetime expenditure ^

The negative binomial-beta Weibull regression model to predict the cure of prostate cancer

In this article, for the first time, we propose the negative binomial-beta Weibull (BW) regression model for studying the recurrence of prostate cancer and to predict the cure fraction for patients with clinically localized prostate cancer treated by open radical prostatectomy. The cure model considers that a fraction of the survivors are cured of the disease. The survival function for the population of patients can be modeled by a cure parametric model using the BW distribution. We derive an explicit expansion for the moments of the recurrence time distribution for the uncured individuals. The proposed distribution can be used to model survival data when the hazard rate function is increasing, decreasing, unimodal and bathtub shaped. Another advantage is that the proposed model includes as special sub-models some of the well-known cure rate models discussed in the literature. We derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes. We analyze a real data set for localized prostate cancer patients after open radical prostatectomy.

Robust Estimates of the Negative Binomial Model

We consider robust parametric procedures for univariate discrete distributions, focusing on the negative binomial model. The procedures are based on three steps: ?First, a very robust, but possibly inefficient, estimate of the model parameters is computed. ?Second, this initial model is used to identify outliers, which are then removed from the sample. ?Third, a corrected maximum likelihood estimator is computed with the remaining observations. The final estimate inherits the breakdown point (bdp) of the initial one and its efficiency can be significantly higher. Analogous procedures were proposed in [1], [2], [5] for the continuous case. A comparison of the asymptotic bias of various estimates under point contamination points out the minimum Neyman's chi-squared disparity estimate as a good choice for the initial step. Various minimum disparity estimators were explored by Lindsay [4], who showed that the minimum Neyman's chi-squared estimate has a 50% bdp under point contamination; in addition, it is asymptotically fully efficient at the model. However, the finite sample efficiency of this estimate under the uncontaminated negative binomial model is usually much lower than 100% and the bias can be strong. We show that its performance can then be greatly improved using the three step procedure outlined above. In addition, we compare the final estimate with the procedure described in

A Note on Bayesian Estimation for the Negative-Binomial Model

2000 Mathematics Subject Classification: 62F15.

Genetic parameters for production traits of dairy Gyr (Bos indicus) x Holstein cattle estimated with a random regression model

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A Nonstationary Negative Binomial Time Series with Time-Dependent Covariates: Enterococcus Counts in Boston Harbor

Boston Harbor has had a history of poor water quality, including contamination by enteric pathogens. We conduct a statistical analysis of data collected by the Massachusetts Water Resources Authority (MWRA) between 1996 and 2002 to evaluate the effects of court-mandated improvements in sewage treatment. Motivated by the ineffectiveness of standard Poisson mixture models and their zero-inflated counterparts, we propose a new negative binomial model for time series of Enterococcus counts in Boston Harbor, where nonstationarity and autocorrelation are modeled using a nonparametric smooth function of time in the predictor. Without further restrictions, this function is not identifiable in the presence of time-dependent covariates; consequently we use a basis orthogonal to the space spanned by the covariates and use penalized quasi-likelihood (PQL) for estimation. We conclude that Enterococcus counts were greatly reduced near the Nut Island Treatment Plant (NITP) outfalls following the transfer of wastewaters from NITP to the Deer Island Treatment Plant (DITP) and that the transfer of wastewaters from Boston Harbor to the offshore diffusers in Massachusetts Bay reduced the Enterococcus counts near the DITP outfalls.

An empirical model to estimate the demand for primary care in urban settings

Objective. To measure the demand for primary care and its associated factors by building and estimating a demand model of primary care in urban settings.^ Data source. Secondary data from 2005 California Health Interview Survey (CHIS 2005), a population-based random-digit dial telephone survey, conducted by the UCLA Center for Health Policy Research in collaboration with the California Department of Health Services, and the Public Health Institute between July 2005 and April 2006.^ Study design. A literature review was done to specify the demand model by identifying relevant predictors and indicators. CHIS 2005 data was utilized for demand estimation.^ Analytical methods. The probit regression was used to estimate the use/non-use equation and the negative binomial regression was applied to the utilization equation with the non-negative integer dependent variable.^ Results. The model included two equations in which the use/non-use equation explained the probability of making a doctor visit in the past twelve months, and the utilization equation estimated the demand for primary conditional on at least one visit. Among independent variables, wage rate and income did not affect the primary care demand whereas age had a negative effect on demand. People with college and graduate educational level were associated with 1.03 (p < 0.05) and 1.58 (p < 0.01) more visits, respectively, compared to those with no formal education. Insurance was significantly and positively related to the demand for primary care (p < 0.01). Need for care variables exhibited positive effects on demand (p < 0.01). Existence of chronic disease was associated with 0.63 more visits, disability status was associated with 1.05 more visits, and people with poor health status had 4.24 more visits than those with excellent health status. ^ Conclusions. The average probability of visiting doctors in the past twelve months was 85% and the average number of visits was 3.45. The study emphasized the importance of need variables in explaining healthcare utilization, as well as the impact of insurance, employment and education on demand. The two-equation model of decision-making, and the probit and negative binomial regression methods, was a useful approach to demand estimation for primary care in urban settings.^

The use of Poisson regression in the sociological study of suicide

This paper explains how Poisson regression can be used in studies in which the dependent variable describes the number of occurrences of some rare event such as suicide. After pointing out why ordinary linear regression is inappropriate for treating dependent variables of this sort, we go on to present the basic Poisson regression model and show how it fits in the broad class of generalized linear models. Then we turn to discussing a major problem of Poisson regression known as overdispersion and suggest possible solutions, including the correction of standard errors and negative binomial regression. The paper ends with a detailed empirical example, drawn from our own research on suicide.

Development of safety performance functions for empirical Bayes estimation of crash reduction factors

Crash reduction factors (CRFs) are used to estimate the potential number of traffic crashes expected to be prevented from investment in safety improvement projects. The method used to develop CRFs in Florida has been based on the commonly used before-and-after approach. This approach suffers from a widely recognized problem known as regression-to-the-mean (RTM). The Empirical Bayes (EB) method has been introduced as a means to addressing the RTM problem. This method requires the information from both the treatment and reference sites in order to predict the expected number of crashes had the safety improvement projects at the treatment sites not been implemented. The information from the reference sites is estimated from a safety performance function (SPF), which is a mathematical relationship that links crashes to traffic exposure. The objective of this dissertation was to develop the SPFs for different functional classes of the Florida State Highway System. Crash data from years 2001 through 2003 along with traffic and geometric data were used in the SPF model development. SPFs for both rural and urban roadway categories were developed. The modeling data used were based on one-mile segments that contain homogeneous traffic and geometric conditions within each segment. Segments involving intersections were excluded. The scatter plots of data show that the relationships between crashes and traffic exposure are nonlinear, that crashes increase with traffic exposure in an increasing rate. Four regression models, namely, Poisson (PRM), Negative Binomial (NBRM), zero-inflated Poisson (ZIP), and zero-inflated Negative Binomial (ZINB), were fitted to the one-mile segment records for individual roadway categories. The best model was selected for each category based on a combination of the Likelihood Ratio test, the Vuong statistical test, and the Akaike's Information Criterion (AIC). The NBRM model was found to be appropriate for only one category and the ZINB model was found to be more appropriate for six other categories. The overall results show that the Negative Binomial distribution model generally provides a better fit for the data than the Poisson distribution model. In addition, the ZINB model was found to give the best fit when the count data exhibit excess zeros and over-dispersion for most of the roadway categories. While model validation shows that most data points fall within the 95% prediction intervals of the models developed, the Pearson goodness-of-fit measure does not show statistical significance. This is expected as traffic volume is only one of the many factors contributing to the overall crash experience, and that the SPFs are to be applied in conjunction with Accident Modification Factors (AMFs) to further account for the safety impacts of major geometric features before arriving at the final crash prediction. However, with improved traffic and crash data quality, the crash prediction power of SPF models may be further improved.