Parameter estimation of Poisson generalized linear mixed models based on three different statistical principles : a simulation study

Generalized linear mixed models are flexible tools for modeling non-normal data and are useful for accommodating overdispersion in Poisson regression models with random effects. Their main difficulty resides in the parameter estimation because there is no analytic solution for the maximization of the marginal likelihood. Many methods have been proposed for this purpose and many of them are implemented in software packages. The purpose of this study is to compare the performance of three different statistical principles - marginal likelihood, extended likelihood, Bayesian analysis-via simulation studies. Real data on contact wrestling are used for illustration.

An Analysis of the Telecommunications Business in China by Linear Regression

In this paper, we study the influence of the National Telecom Business Volume by the data in 2008 that have been published in China Statistical Yearbook of Statistics. We illustrate the procedure of modeling “National Telecom Business Volume” on the following eight variables, GDP, Consumption Levels, Retail Sales of Social Consumer Goods Total Renovation Investment, the Local Telephone Exchange Capacity, Mobile Telephone Exchange Capacity, Mobile Phone End Users, and the Local Telephone End Users. The testing of heteroscedasticity and multicollinearity for model evaluation is included. We also consider AIC and BIC criterion to select independent variables, and conclude the result of the factors which are the optimal regression model for the amount of telecommunications business and the relation between independent variables and dependent variable. Based on the final results, we propose several recommendations about how to improve telecommunication services and promote the economic development.

Feasible estimation of generalized linear mixed models (GLMM) with weak dependency between groups

This paper presents a two-step pseudo likelihood estimation technique for generalized linear mixed models with the random effects being correlated between groups. The core idea is to deal with the intractable integrals in the likelihood function by multivariate Taylor's approximation. The accuracy of the estimation technique is assessed in a Monte-Carlo study. An application of it with a binary response variable is presented using a real data set on credit defaults from two Swedish banks. Thanks to the use of two-step estimation technique, the proposed algorithm outperforms conventional pseudo likelihood algorithms in terms of computational time.

Likelihood prediction for generalized linear mixed models under covariate uncertainty

This paper presents the techniques of likelihood prediction for the generalized linear mixed models. Methods of likelihood prediction is explained through a series of examples; from a classical one to more complicated ones. The examples show, in simple cases, that the likelihood prediction (LP) coincides with already known best frequentist practice such as the best linear unbiased predictor. The paper outlines a way to deal with the covariate uncertainty while producing predictive inference. Using a Poisson error-in-variable generalized linear model, it has been shown that in complicated cases LP produces better results than already know methods.

Inflammation, oxidative stress, glomerular filtration rate, and albuminuria in elderly men : a cross-sectional study

BACKGROUND: The role of inflammation and oxidative stress in mild renal impairment in the elderly is not well studied. Accordingly, we aimed at investigating the associations between estimated glomerular filtration rate (eGFR), albumin/creatinine ratio (ACR), and markers of different inflammatory pathways and oxidative stress in a community based cohort of elderly men. FINDINGS: Cystatin C-based GFR, ACR, and biomarkers of cytokine-mediated inflammation (interleukin-6, high-sensitivity C-reactive protein[CRP], serum amyloid A[SAA]), cyclooxygenase-mediated inflammation (urinary prostaglandin F2alpha [PGF2alpha]), and oxidative stress (urinary F2 isoprostanes) were assessed in the Uppsala Longitudinal Study of Adult Men(n = 647, mean age 77 years). RESULTS: In linear regression models adjusting for age, BMI, smoking, blood pressure, LDL-cholesterol, HDL-cholesterol, triglycerides, and treatment with statins, ACE-inhibitors, ASA, and anti-inflammatory agents, eGFR was inversely associated with CRP, interleukin-6, and SAA (beta-coefficient -0.13 to -0.19, p < 0.001 for all), and positively associated with urinary F2-isoprostanes (beta-coefficient 0.09, p = 0.02). In line with this, ACR was positively associated with CRP, interleukin-6, and SAA (beta- coefficient 0.09-0.12, p < 0.02 for all), and negatively associated with urinary F2-isoprostanes (beta-coefficient -0.12, p = 0.002). The associations were similar but with lower regression coefficients in a sub-sample with normal eGFR (>60 ml/min/1.73 m2, n = 514), with the exception that F2-isoprostane and SAA were no longer associated with eGFR. CONCLUSION: Our data indicate that cytokine-mediated inflammation is involved in the early stages of impaired kidney function in the elderly, but that cyclooxygenase-mediated inflammation does not play a role at this stage. The unexpected association between higher eGFR/lower albuminuria and increased F2-isoprostanes in urine merits further studies.

Testing linear cointegration against smooth-transition cointegration

This paper studies a smooth-transition (ST) type cointegration. The proposed ST cointegration allows for regime switching structure in a cointegrated system. It nests the linear cointegration developed by Engle and Granger (1987) and the threshold cointegration studied by Balke and Fomby (1997). We develop F-type tests to examine linear cointegration against ST cointegration in ST-type cointegrating regression models with or without time trends. The null asymptotic distributions of the tests are derived with stationary transition variables in ST cointegrating regression models. And it is shown that our tests have nonstandard limiting distributions expressed in terms of standard Brownian motion when regressors are pure random walks, while have standard asymptotic distributions when regressors contain random walks with nonzero drift. Finite-sample distributions of those tests are studied by Monto Carlo simulations. The small-sample performance of the tests states that our F-type tests have a better power when the system contains ST cointegration than when the system is linearly cointegrated. An empirical example for the purchasing power parity (PPP) data (monthly US dollar, Italy lira and dollar-lira exchange rate from 1973:01 to 1989:10) is illustrated by applying the testing procedures in this paper. It is found that there is no linear cointegration in the system, but there exits the ST-type cointegration in the PPP data.

Hglm: A package for fitting hierarchical generalized linear models

We present the hglm package for fitting hierarchical generalized linear models. It can be used for linear mixed models and generalized linear mixed models with random effects for a variety of links and a variety of distributions for both the outcomes and the random effects. Fixed effects can also be fitted in the dispersion part of the model.

Genetic heterogeneity of residual variance : estimation of variance components using double hierarchical generalized linear models

Background: The sensitivity to microenvironmental changes varies among animals and may be under genetic control. It is essential to take this element into account when aiming at breeding robust farm animals. Here, linear mixed models with genetic effects in the residual variance part of the model can be used. Such models have previously been fitted using EM and MCMC algorithms. Results: We propose the use of double hierarchical generalized linear models (DHGLM), where the squared residuals are assumed to be gamma distributed and the residual variance is fitted using a generalized linear model. The algorithm iterates between two sets of mixed model equations, one on the level of observations and one on the level of variances. The method was validated using simulations and also by re-analyzing a data set on pig litter size that was previously analyzed using a Bayesian approach. The pig litter size data contained 10,060 records from 4,149 sows. The DHGLM was implemented using the ASReml software and the algorithm converged within three minutes on a Linux server. The estimates were similar to those previously obtained using Bayesian methodology, especially the variance components in the residual variance part of the model. Conclusions: We have shown that variance components in the residual variance part of a linear mixed model can be estimated using a DHGLM approach. The method enables analyses of animal models with large numbers of observations. An important future development of the DHGLM methodology is to include the genetic correlation between the random effects in the mean and residual variance parts of the model as a parameter of the DHGLM.

A Note on Proxy Variables and Instrument Variable Regression

This is a note about proxy variables and instruments for identification of structural parameters in regression models. We have experienced that in the econometric textbooks these two issues are treated separately, although in practice these two concepts are very often combined. Usually, proxy variables are inserted in instrument variable regressions with the motivation they are exogenous. Implicitly meaning they are exogenous in a reduced form model and not in a structural model. Actually if these variables are exogenous they should be redundant in the structural model, e.g. IQ as a proxy for ability. Valid proxies reduce unexplained variation and increases the efficiency of the estimator of the structural parameter of interest. This is especially important in situations when the instrument is weak. With a simple example we demonstrate what is required of a proxy and an instrument when they are combined. It turns out that when a researcher has a valid instrument the requirements on the proxy variable is weaker than if no such instrument exists

Speed prediction for triggering vehicle activated signs

Accurate speed prediction is a crucial step in the development of a dynamic vehcile activated sign (VAS). A previous study showed that the optimal trigger speed of such signs will need to be pre-determined according to the nature of the site and to the traffic conditions. The objective of this paper is to find an accurate predictive model based on historical traffic speed data to derive the optimal trigger speed for such signs. Adaptive neuro fuzzy (ANFIS), classification and regression tree (CART) and random forest (RF) were developed to predict one step ahead speed during all times of the day. The developed models were evaluated and compared to the results obtained from artificial neural network (ANN), multiple linear regression (MLR) and naïve prediction using traffic speed data collected at four sites located in Sweden. The data were aggregated into two periods, a short term period (5-min) and a long term period (1-hour). The results of this study showed that using RF is a promising method for predicting mean speed in the two proposed periods.. It is concluded that in terms of performance and computational complexity, a simplistic input features to the predicitive model gave a marked increase in the response time of the model whilse still delivering a low prediction error.