Quadratic Exponential Model Research Articles

Testing for state dependence in the fixed-effects ordered logit model

We propose a test for state dependence in the fixed-effects ordered logit, based on the Quadratic Exponential model. The test can be applied to models where persistence lies either in the latent or observed response variable.

Analysis of familial aggregation using recurrence risk for complex survey data

Familial or family aggregation of a disease is important for studying possible genetic etiology of a disease. A popular and useful measure of family aggregation is recurrence risk. Household health surveys with (family) network sampling, which surveyed individuals report about disease status of themselves and specified relatives, have been shown to be useful for estimating prevalence of diseases and more recently for estimating recurrence risk of disease using nonparametric classical survey methods. Because these surveys have complex sample designs with sample weighting for differential sample selection rates, this paper extends the composite-likelihood estimation and hypothesis of parameters of the quadratic exponential model (QEM) for simple random samples to data from these complex sample designs. In addition, the QEM is extended to simultaneously estimate and test parameters and recurrence risk for multiple family relationships, for comparing recurrence risk across family-level covariates (e.g. race) and utilizing propensity score weighting to adjust for confounding by individual-level covariates (e.g. age). Simulations are used to study the finite sample properties of the parameter estimation, variance estimation and level and power of hypothesis testing based on derived Wald and Quasi-Score tests for these extended QEMs. Finally, our methods are illustrated using the 1976 National Health Interview Survey diabetes data set.

Recursive Computation of the Conditional Probability Function of the Quadratic Exponential Model for Binary Panel Data

Recursive Computation of the Conditional Probability Function of the Quadratic Exponential Model for Binary Panel Data

A Quadratic–Exponential Model of Variogram Based on Knowing the Maximal Variability: Application to a Rainfall Time Series

Variogram models are a valuable tool used to analyze the variability of a time series; such variability usually entails a spherical or exponential behavior, and so, models based on such functions are commonly used to fit and explain a time series. Variograms have a quasi-periodic structure for rainfall cases, and some extra steps are required to analyze their entire behavior. In this work, we detailed a procedure for a complete analysis of rainfall time series, from the construction of the experimental variogram to curve fitting with well-known spherical and exponential models, and finally proposed a novel model: quadratic–exponential. Our model was developed based on the analysis of 6 out of 30 rainfall stations from our case study: the Río Bravo–San Juan basin, and was constructed from the exponential model while introducing a quadratic behavior near to the origin and taking into account the fact that the maximal variability of the process is known. Considering a sample with diverse Hurst exponents, the stations were selected. The results obtained show robustness in our proposed model, reaching a good fit with and without the nugget effect for different Hurst exponents. This contrasts to previous models, which show good outcomes only without the nugget effect.

Evaluation of diffusion kurtosis imaging in stratification of nonalcoholic fatty liver disease and early diagnosis of nonalcoholic steatohepatitis in a rabbit model

PurposeTo examine the feasibility of MR diffusion kurtosis imaging (DKI) for characterizing nonalcoholic fatty liver disease (NAFLD) and diagnosing nonalcoholic steatohepatitis (NASH). MethodsThirty-two rabbits on high fat diet with different severities of NAFLD were imaged at 3 T MR including diffusion weighted imaging (DWI) and DKI using b values of 0, 400, 800 s/mm2 with 15 diffusion directions at each b value. Apparent diffusion coefficient (ADC) was derived from the linear exponential DWI model. Mean diffusion (MD) and mean kurtosis (MK) were derived from the quadratic exponential model of DKI. Correlations between MR parameters and hepatic pathology determined by the NAFLD activity scoring system were analyzed by Spearman rank correlation analysis. Receiver operating characteristic analyses were applied to determine the cutoff values of MD, MK as well as ADC in distinguishing NASH from non-NASH. The diagnostic efficacies of MD and MK in detecting NASH were compared with that of ADC. ResultsValues for ADC and MD significantly decreased as the severity of NAFLD increased (ρ = −0.529, −0.904, respectively; P < 0.05). MK values significantly increased as the severity of NAFLD increased (ρ = 0.761; P < 0.05). In addition, both MD and MK values were significantly different between borderline NASH and NASH groups (MD: 1.729 ± 0.144 vs. 1.458 ± 0.240[×10−3 mm2/s]; MK: 1.096 ± 0.079 vs. 1.237 ± 0.180; P < 0.05). Moreover, there was a significantly higher area under the curve (AUC) for both MD (0.955) and MK (0.905), as compared to ADC (0.736). ConclusionDiffusion kurtosis imaging was feasible for stratifying NAFLD, and more accurately discriminated NASH from non-NASH when compared with DWI.

Cquad: An R and Stata Package for Conditional Maximum Likelihood Estimation of Dynamic Binary Panel Data Models

We illustrate the R package cquad for conditional maximum likelihood estimation of the quadratic exponential (QE) model proposed by Bartolucci and Nigro (2010) for the analysis of binary panel data. The package also allows us to estimate certain modified versions of the QE model, which are based on alternative parametrizations, and it includes a function for the pseudo-conditional likelihood estimation of the dynamic logit model, as proposed by Bartolucci and Nigro (2012). We also illustrate a reduced version of this package that is available in Stata. The use of the main functions of this package is based on examples using labor market data.

Testing for state dependence in binary panel data with individual covariates by a modified quadratic exponential model

ABSTRACTWe propose a test for state dependence in binary panel data with individual covariates. For this aim, we rely on a quadratic exponential model in which the association between the response variables is accounted for in a different way with respect to more standard formulations. The level of association is measured by a single parameter that may be estimated by a Conditional Maximum Likelihood (CML) approach. Under the dynamic logit model, the conditional estimator of this parameter converges to zero when the hypothesis of absence of state dependence is true. Therefore, it is possible to implement a t-test for this hypothesis which may be very simply performed and attains the nominal significance level under several structures of the individual covariates. Through an extensive simulation study, we find that our test has good finite sample properties and it is more robust to the presence of (autocorrelated) covariates in the model specification in comparison with other existing testing procedures for state dependence. The proposed approach is illustrated by two empirical applications: the first is based on data coming from the Panel Study of Income Dynamics and concerns employment and fertility; the second is based on the Health and Retirement Study and concerns the self reported health status.

Ultrafiltration of municipal wastewater: study on fouling models and fouling mechanisms

Ultrafiltration (UF) with hollow fiber membranes is a proven membrane technique that can achieve high water quality standards as a tertiary treatment in municipal wastewater treatment plants. However, UF has a major drawback, membrane fouling, which causes losses of productivity and increases operation costs. Thus, the aim of this work is to model membrane fouling in the UF of a secondary treatment effluent. The tests were carried out with a model wastewater solution that consisted of bovine serum albumin and dextran. Three different transmembrane pressures and three different crossflow velocities were tested. Several fouling models available in the literature, and new models proposed, were fitted to permeate flux decline experimental data. The models studied by other authors and considered in this study were: Hermia’s models (complete, intermediate, standard pore blocking and gel layer) and Belfort’s model. The new models proposed in this work were: modified Belfort’s model, quadratic exponential model, logarithmic inversed model, double exponential model and tangent inversed model. The fitting accuracy of the models was determined in terms of the R-squared and standard deviation. The results showed that the model that had the higher fitting accuracy was the logarithmic inversed model. Among the Hermia’s models, the model that had the higher fitting accuracy was the intermediate pore blocking model. Therefore, the predominant fouling mechanism was determined and it was the intermediate pore blocking model.

Pseudo conditional maximum likelihood estimation of the dynamic logit model for binary panel data

We show how the dynamic logit model for binary panel data may be approximated by a quadratic exponential model. Under the approximating model, simple sufficient statistics exist for the subject-specific parameters introduced to capture the unobserved heterogeneity between subjects. The latter must be distinguished from the state dependence which is accounted for by including the lagged response variable among the regressors. By conditioning on the sufficient statistics, we derive a pseudo conditional likelihood estimator of the structural parameters of the dynamic logit model, which is simple to compute. Asymptotic properties of this estimator are studied in detail. Simulation results show that the estimator is competitive in terms of efficiency with estimators recently proposed in the econometric literature.

Pseudo Conditional Maximum Likelihood Estimation of the Dynamic Logit Model for Binary Panel Data

We show how the dynamic logit model for binary panel data may be approximated by a quadratic exponential model. Under the approximating model, simple sufficient statistics exist for the subject-specific parameters introduced to capture the unobserved heterogeneity between subjects. The latter must be distinguished from the state dependence which is accounted for by including the lagged response variable among the regressors. By conditioning on the sufficient statistics, we derive a pseudo conditional likelihood estimator for the structural parameters of the dynamic logit model which is very simple to compute. Asymptotic properties of this estimator are derived. Simulation results show that the estimator is competitive in terms of efficiency with estimators very recently proposed in the econometric literature. We also show how the approach may be exploited to construct a Wald-type test for state dependence.

Analysis of Familial Aggregation in the Presence of Varying Family Sizes

Summary Family studies are frequently undertaken as the first step in the search for genetic and/or environmental determinants of disease. Significant familial aggregation of disease is suggestive of a genetic aetiology for the disease and may lead to more focused genetic analysis. Of course, it may also be due to shared environmental factors. Many methods have been proposed in the literature for the analysis of family studies. One model that is appealing for the simplicity of its computation and the conditional interpretation of its parameters is the quadratic exponential model. However, a limiting factor in its application is that it is not reproducible, meaning that all families must be of the same size. To increase the applicability of this model, we propose a hybrid approach in which analysis is based on the assumption of the quadratic exponential model for a selected family size and combines a missing data approach for smaller families with a marginalization approach for larger families. We apply our approach to a family study of colorectal cancer that was sponsored by the Cancer Genetics Network of the National Institutes of Health. We investigate the properties of our approach in simulation studies. Our approach applies more generally to clustered binary data.

Growth indices ans productivity in sugarcane

A knowledge about the temporal development of agronomic variables in sugarcane is a very important aspect for the development of crop yield prediction models using remote sensing, and further studies are still needed. This paper describes the temporal evolution of sugarcane biophysical parameters, such as total biomass, leaf area index, number of plants per meter, and productivity. During two seasons, a commercial field in Araras/SP, planted with variety SP80-1842, on the 4th and 5th cuts, was monitored on eight different dates, and data were obtained for 2 m of sugarcane in three crop rows at 18 sampling points. Linear and multiple regression analyses were used to study growth analysis and to correlate agronomic variables (leaf area index and number of plants per meter) with biomass and productivity. Gompertz model, a sigmoidal curve, was the best adjustment curve for total biomass and yield in relation to days after cutting (r² = 0.8987 and r² = 0.9682, respectively); number of plants and leaf area index showed best fit with a cubic exponential model and a quadratic exponential model, respectively. Total biomass and cane productivity were well correlated with LAI in the first two stages of the sugarcane cycle using linear regression. At the end of the cycle, total biomass and cane productivity were more related to number of plants, and lower r² values than in other stages were obtained by the models.

Power calculations for familial aggregation studies.

Family studies are frequently undertaken as the first step in the search for genetic determinants of disease. Significant familial aggregation of disease is suggestive of a genetic etiology for the disease, and may lead to more focused genetic analyses. Many methods have been proposed in the literature for the analysis of family studies. One model that is appealing for its simplicity of computation and the conditional interpretation of its parameters is the quadratic exponential model (e.g., Zhao and Prentice [1990] Biometrika 77:642-648; Betensky and Whittemore [1996] Appl. Stat. 45:422-429; Hudson et al. [2001a] Am. J. Epidemiol. 153:500-514). However, a limiting factor in its application, as well as that of the other proposed methods, is that power and sample size calculations have not been derived. These calculations are essential for investigators who are designing family studies. Here we derive analytic approximations for power for testing for familial aggregation, for both randomly sampled and nonrandomly sampled families. We also present simulation studies of power for both single- and two-disease cases, both under random and nonrandom sampling.

Trends in urbanization and patterns of land use in the Asian mega cities Jakarta, Bangkok, and Metro Manila

Asian mega cities have experienced rapid population growth and continue to grow. Urbanization in those areas is proceeding differently from the patterns of city growth experienced in Western countries. Understanding the characteristics of Asian urbanization will be indispensable for the establishment of a local landscape planning system. In this study, we used the Clark linear exponential model and the Newling quadratic exponential model to compare the spatial distribution of population densities in three Southeast Asian mega cities: Jakarta, Bangkok, and Metro Manila. We analyzed land-use patterns in each of the three cities by examining the mixture of urban and agricultural land use. The Clark and Newling models showed that the three cities were at different stages of urbanization. Jakarta had entered the suburbanization stage, Metro Manila was still at an early stage of urbanization, and Bangkok was at an intermediate stage between Jakarta and Metro Manila. Analysis of spatial patterns revealed areas of mixed land use within and around the city region in the three cities and that these areas of mixed land use would shift outward as urbanization proceeds. These findings indicate that planning concepts need to respect the vernacular landscape of each Asian mega cities as well as its stage of urbanization.

Multivariate logistic regression for familial aggregation of two disorders. I. Development of models and methods.

The question of whether two disorders cluster together, or coaggregate, within families often arises. This paper considers how to analyze familial aggregation of two disorders and presents two multivariate logistic regression methods that model both disorder outcomes simultaneously. The first, a proband predictive model, predicts a relative's outcomes (the presence or absence of each of the two disorders) by using the proband's disorder status. The second, a family predictive model derived from the quadratic exponential model, predicts a family member's outcomes by using all of the remaining family members' disorder statuses. The models are more realistic, flexible, and powerful than univariate models. Methods for estimation and testing account for the correlation of outcomes among family members and can be implemented by using commercial software.

An Analysis of Correlated Multivariate Binary Data: Application to Familial Cancers of the Ovary and Breast

SUMMARY The association between ovarian and breast cancer, both within and between family members, is examined using pooled data from five case-control studies. The occurrences of these diseases in sisters and mothers are analysed using a quadratic exponential model, which is an extension of the model of Zhao and Prentice for correlated univariate data. An advantage of this model is that the associations between pairs of diseases and pairs of relatives, which are of primary importance, are related to simple functions of its parameters. Also, the model applies to non-randomly sampled data, such as the case-control data, because it completely specifies the joint distribution of responses. A major weakness is that it is not immediately applicable to studies of families of different sizes. None-the-less, we find it to be useful under certain conditions, such as rare diseases. Our analysis of the data suggests that the risk of ovarian cancer is highly dependent on maternal history.

Exponential mixtures and quadratic exponential families

SUMMARY Conditions are derived under which quadratic and polynomial exponential models can be generated as mixtures of linear exponential models. The conditions are highly restrictive for continuous sample spaces, but less restrictive in the discrete case. Some properties of binary quadratic exponential models are explored with a view towards finding models that have properties suitable for epidemiological applications.

A generalized estimating equations approach to fitting major gene models in segregation analysis of continuous phenotypes

This paper discusses the application of estimating equations methods based on a quadratic exponential model [Prentice and Zhao, 1991] as a potential competitor with full likelihood approaches to estimating the effect of major genes in a segregation analysis [Elston, 1981] of continuous phenotypes, in the single allele problem. We show that while the estimating equations methods based on the quadratic exponential family cannot be used by themselves to estimate all parameters of interest, an iterative two-stage approach can be used, in which the population allele frequency is first considered to be a known parameter, which permits the estimating equations method to estimate the remaining parameters. At the second stage a "pseudo-profile" loglikelihood based only on the founders is used to estimate the allele frequency. After each maximization of the pseudo-profile loglikelihood at the second stage, the parameters in the first stage are reestimated using a new value of the allele frequency, and a new value of the second stage pseudo-profile loglikelihood is obtained. We used simulated pedigree data for illustrations.

Estimating Equations for Parameters in Means and Covariances of Multivariate Discrete and Continuous Responses

Generalized estimating equations are introduced in an ad hoc fashion for the covariance matrix of a multivariate response. These equations are to be solved jointly with score equations from a generalized linear model for mean parameters. A class of quadratic exponential models is used to develop joint estimating equations for mean and covariance parameters in a more systematic fashion, and proposals for the use of such equations are developed. Comments on the relative merits of the ad hoc and model-based approaches to estimation are given and a regression illustration with a bivariate response is provided.

Correlated Binary Regression Using a Quadratic Exponential Model

Correlated Binary Regression Using a Quadratic Exponential Model