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We consider varying coefficient models, which are an extension of the classical linear regression models in the sense that the regression coefficients are replaced by functions in certain variables (for example time), the covariates are also allowed to depend on other variables. Varying coefficient models are popular in longitudinal data and panel data studies, and have been applied in fields such as finance and health sciences. We consider longitudinal data and estimate the coefficient functions by the flexible B-spline technique. An important question in a varying coefficient model is whether an estimated coefficient function is statistically different from a constant (or zero). We develop testing procedures based on the estimated B-spline coefficients by making use of nice properties of a B-spline basis. Our method allows longitudinal data where repeated measurements for an individual can be correlated. We obtain the asymptotic null distribution of the test statistic. The power of the proposed testing procedures are illustrated on simulated data where we highlight the importance of including the correlation structure of the response variable and on real data. ; M. Ahkim's research was supported by the Special Research Fund (BOF) of Universiteit Antwerpen [grant number 42FA070300FFB5994]. A. Verhasselt gratefully acknowledge support from the IAP Research Network P7/06 of the Belgian State (Belgian Science Policy) and the FWO [grant number 1.5.137.13N]. The infrastructure of the VSC-Flemish Supercomputer Center, funded by the Hercules Foundation and the Flemish Government-department EWI, was used for the simulations.

AbstractThis study examines the varying coefficient model in tail index regression. The varying coefficient model is an efficient semiparametric model that avoids the curse of dimensionality when including large covariates in the model. In fact, the varying coefficient model is useful in mean, quantile, and other regressions. The tail index regression is not an exception. However, the varying coefficient model is flexible, but leaner and simpler models are preferred for applications. Therefore, it is important to evaluate whether the estimated coefficient function varies significantly with covariates. If the effect of the non-linearity of the model is weak, the varying coefficient structure is reduced to a simpler model, such as a constant or zero. Accordingly, the hypothesis test for model assessment in the varying coefficient model has been discussed in mean and quantile regression. However, there are no results in tail index regression. In this study, we investigate the asymptotic properties of an estimator and provide a hypothesis testing method for varying coefficient models for tail index regression.

We propose a new periodic autoregressive model for seasonally observed time series, where the number of seasons can potentially be very large. The main novelty is that we collect the periodic coefficients in a second‐level stochastic model. This leads to a random‐coefficient periodic autoregression with a substantial reduction in the number of parameters to be estimated. We discuss representation, parameter estimation, and inference. An illustration for monthly growth rates of US industrial production shows the merits of the new model specification.

The ordinary least squares (OLS) estimator gives biased coefficient estimates if coefficients are not constant for all cases but vary systematically with the explanatory variables. This article discusses several different ways to estimate models with systematically and randomly varying coefficients using estimated generalized least squares and maximum likelihood procedures. A Monte Carlo simulation of the different methods is presented to illustrate their use and to contrast their results to the biased results obtained with ordinary least squares. Several applications of the methods are discussed and one is presented in detail. The conclusion is that, in situations with variables coefficients, these methods offer relatively easy means for overcoming the problems.

We estimated benzene risk using a novel framework of risk assessment that employed the measurement of radiation dose equivalents to benzene metabolites and a PBPK model. The highest risks for 1 μg/m3and 3.2 mg/m3life time exposure of benzene estimated with a linear regression were 5.4 × 10−7and 1.3 × 10−3, respectively. Even though these estimates were based onin vitrochromosome aberration test data, they were about one‐sixth to one‐fourteenth that from other studies and represent a fairly good estimate by using radiation equivalent coefficient as an "internal standard."

AbstractA common causal identification strategy in political science is selection on observables. This strategy assumes one observes a set of covariates that is, after statistical adjustment, sufficient to make treatment status as-if random. Under adjustment methods such as matching or inverse probability weighting, coefficients for control variables are treated as nuisance parameters and are not directly estimated. This is in direct contrast to regression approaches where estimated parameters are obtained for all covariates. Analysts often find it tempting to give a causal interpretation to all the parameters in such regression models—indeed, such interpretations are often central to the proposed research design. In this paper, we ask when we can justify interpreting two or more coefficients in a regression model as causal parameters. We demonstrate that analysts must appeal to causal identification assumptions to give estimates causal interpretations. Under selection on observables, this task is complicated by the fact that more than one causal effect might be identified. We show how causal graphs provide a framework for clearly delineating which effects are presumed to be identified and thus merit a causal interpretation, and which are not. We conclude with a set of recommendations for how researchers should interpret estimates from regression models when causal inference is the goal.

Abstract
This article examines the influence of interviewers on the estimation of regression coefficients from survey data. First, we present theoretical considerations with a focus on measurement errors and nonresponse errors due to interviewers. Then, we show via simulation which of several nonresponse and measurement error scenarios has the biggest impact on the estimate of a slope parameter from a simple linear regression model. When response propensity depends on the dependent variable in a linear regression model, bias in the estimated slope parameter is introduced. We find no evidence that interviewer effects on the response propensity have a large impact on the estimated regression parameters. We do find, however, that interviewer effects on the predictor variable of interest explain a large portion of the bias in the estimated regression parameter. Simulation studies suggest that standard measurement error adjustments using the reliability ratio (i.e., the ratio of the measurement-error-free variance to the observed variance with measurement error) can correct most of the bias introduced by these interviewer effects in a variety of complex settings, suggesting that more routine adjustment for such effects should be considered in regression analysis using survey data.

This article presents a simple non-polynomial spline that may be used to construct Lorenz curves from grouped data. The spline is naturally convex and works by determining a series of piecewise segments that may be joined to give a smooth and continuous Lorenz curve. The method is illustrated with an empirical example using income decile data from the Philippines from 1991-2003 where the proposed technique is used alongside other parametric and non-parametric methods. We also use the spline to approximate some known Lorenz curves and assess the technique by comparing the estimated Gini coefficient to the known Gini. Our findings suggest that the method is an attractive addition to the body of techniques used for developing Lorenz curves from grouped data.

Non-zero correlation coefficients have non-normal distributions, affecting both means and standard deviations. Previous research suggests that z transformation may effectively correct mean bias for N's less than 30. In this study, simulations with small (20 and 30) and large (50 and 100) N's found that mean bias adjustments for larger N's are seldom needed. However, z transformations improved confidence intervals even for N = 100. The improvement was not in the estimated standard errors so much as in the asymmetrical CI's estimates based upon the z transformation. The resulting observed probabilities were generally accurate to within 1 point in the first non-zero digit. These issues are an order of magnitude less important for accuracy than design issues influencing the accuracy of the results, such as reliability, restriction of range, and N. DOI:10.2458/azu_jmmss_v1i2_gorsuch

This article is an exercise in economic methodology. It replicates two published models of the effect of military expenditure on the United States economy but, in order to study variations in the relevant estimated parameters, applies two different military expenditure data sets to the models (budget vs . National Income and Product Accounts [NIPA] data). In an extension, the article examines coefficient stability when the economically preferred NIPA data are applied across varying time-periods. Two major findings are that economic models should avoid the use of budget data and that even when the preferred NIPA data are used, estimated parameters are highly unstable across time.