Assessment of the effect on statistical power of regression model misspecification by using techniques of mathematical statistics and simulation study

Objectives. This paper seeks to assess the effect on statistical power of regression model misspecification in a variety of situations. ^ Methods and results. The effect of misspecification in regression can be approximated by evaluating the correlation between the correct specification and the misspecification of the outcome variable (Harris 2010).In this paper, three misspecified models (linear, categorical and fractional polynomial) were considered. In the first section, the mathematical method of calculating the correlation between correct and misspecified models with simple mathematical forms was derived and demonstrated. In the second section, data from the National Health and Nutrition Examination Survey (NHANES 2007-2008) were used to examine such correlations. Our study shows that comparing to linear or categorical models, the fractional polynomial models, with the higher correlations, provided a better approximation of the true relationship, which was illustrated by LOESS regression. In the third section, we present the results of simulation studies that demonstrate overall misspecification in regression can produce marked decreases in power with small sample sizes. However, the categorical model had greatest power, ranging from 0.877 to 0.936 depending on sample size and outcome variable used. The power of fractional polynomial model was close to that of linear model, which ranged from 0.69 to 0.83, and appeared to be affected by the increased degrees of freedom of this model.^ Conclusion. Correlations between alternative model specifications can be used to provide a good approximation of the effect on statistical power of misspecification when the sample size is large. When model specifications have known simple mathematical forms, such correlations can be calculated mathematically. Actual public health data from NHANES 2007-2008 were used as examples to demonstrate the situations with unknown or complex correct model specification. Simulation of power for misspecified models confirmed the results based on correlation methods but also illustrated the effect of model degrees of freedom on power.^

Effects of informative censoring on the hazard function: Application to the proportional hazards regression model

The standard analyses of survival data involve the assumption that survival and censoring are independent. When censoring and survival are related, the phenomenon is known as informative censoring. This paper examines the effects of an informative censoring assumption on the hazard function and the estimated hazard ratio provided by the Cox model.^ The limiting factor in all analyses of informative censoring is the problem of non-identifiability. Non-identifiability implies that it is impossible to distinguish a situation in which censoring and death are independent from one in which there is dependence. However, it is possible that informative censoring occurs. Examination of the literature indicates how others have approached the problem and covers the relevant theoretical background.^ Three models are examined in detail. The first model uses conditionally independent marginal hazards to obtain the unconditional survival function and hazards. The second model is based on the Gumbel Type A method for combining independent marginal distributions into bivariate distributions using a dependency parameter. Finally, a formulation based on a compartmental model is presented and its results described. For the latter two approaches, the resulting hazard is used in the Cox model in a simulation study.^ The unconditional survival distribution formed from the first model involves dependency, but the crude hazard resulting from this unconditional distribution is identical to the marginal hazard, and inferences based on the hazard are valid. The hazard ratios formed from two distributions following the Gumbel Type A model are biased by a factor dependent on the amount of censoring in the two populations and the strength of the dependency of death and censoring in the two populations. The Cox model estimates this biased hazard ratio. In general, the hazard resulting from the compartmental model is not constant, even if the individual marginal hazards are constant, unless censoring is non-informative. The hazard ratio tends to a specific limit.^ Methods of evaluating situations in which informative censoring is present are described, and the relative utility of the three models examined is discussed. ^

Phase Transitions in Disordered Systems: The Example of the Random-Field Ising Model in Four Dimensions

By performing a high-statistics simulation of the D = 4 random-field Ising model at zero temperature for different shapes of the random-field distribution, we show that the model is ruled by a single universality class. We compute to a high accuracy the complete set of critical exponents for this class, including the correction-to-scaling exponent. Our results indicate that in four dimensions (i) dimensional reduction as predicted by the perturbative renormalization group does not hold and (ii) three independent critical exponents are needed to describe the transition.

Exports and Capacity Constraints: A smooth transition regression model for six euro-area countries. CEPS Working Document No. 395/May 2014

The significant gains in export market shares made in a number of vulnerable euro-area crisis countries have not been accompanied by an appropriate improvement in price competitiveness. This paper argues that, under certain conditions, firms consider export activity as a substitute for serving domestic demand. The strength of the link between domestic demand and exports is dependent on capacity constraints. Our econometric model for six euro-area countries suggests domestic demand pressure and capacity-constraint restrictions as additional variables of a properly specified export equation. As an innovation to the literature, we assess the empirical significance through the logistic and the exponential variant of the non-linear smooth transition regression model. We find that domestic demand developments are relevant for the short-run dynamics of exports in particular during more extreme stages of the business cycle. A strong substitutive relationship between domestic and foreign sales can most clearly be found for Spain, Portugal and Italy, providing evidence of the importance of sunk costs and hysteresis in international trade.

An analysis of the regression model for nonsaturating logic circuit analysis.

Also issued as thesis (M.S.) University of Illinois.

Persistence in a random bond ising model of socio-econo dynamics

We study the persistence phenomenon in a socio-econo dynamics model using computer simulations at a nite temperature on hypercubic lattices in dimensions up to ve. The model includes a \social" local eld which contains the magnetization at time t. The nearest neighbour quenched interactions are drawn from a binary distribution which is a function of the bond concentration, p. The decay of the persistence probability in the model depends on both the spatial dimension and p. We nd no evidence of \blocking" in this model. We also discuss the implications of our results for possible applications in the social and economic elds. It is suggested that the absence, or otherwise, of blocking could be used as a criterion to decide on the validity of a given model in dierent scenarios.

A laser induced breakdown spectroscopy quantitative analysis method based on the robust least squares support vector machine regression model

Data fluctuation in multiple measurements of Laser Induced Breakdown Spectroscopy (LIBS) greatly affects the accuracy of quantitative analysis. A new LIBS quantitative analysis method based on the Robust Least Squares Support Vector Machine (RLS-SVM) regression model is proposed. The usual way to enhance the analysis accuracy is to improve the quality and consistency of the emission signal, such as by averaging the spectral signals or spectrum standardization over a number of laser shots. The proposed method focuses more on how to enhance the robustness of the quantitative analysis regression model. The proposed RLS-SVM regression model originates from the Weighted Least Squares Support Vector Machine (WLS-SVM) but has an improved segmented weighting function and residual error calculation according to the statistical distribution of measured spectral data. Through the improved segmented weighting function, the information on the spectral data in the normal distribution will be retained in the regression model while the information on the outliers will be restrained or removed. Copper elemental concentration analysis experiments of 16 certified standard brass samples were carried out. The average value of relative standard deviation obtained from the RLS-SVM model was 3.06% and the root mean square error was 1.537%. The experimental results showed that the proposed method achieved better prediction accuracy and better modeling robustness compared with the quantitative analysis methods based on Partial Least Squares (PLS) regression, standard Support Vector Machine (SVM) and WLS-SVM. It was also demonstrated that the improved weighting function had better comprehensive performance in model robustness and convergence speed, compared with the four known weighting functions.

Classification of Texts' Authorship Using a Regression Model on Compressed Data

2010 Mathematics Subject Classification: 68T50,62H30,62J05.

Comparison of Some Improved Estimators for Linear Regression Model under Different Conditions

Multiple linear regression model plays a key role in statistical inference and it has extensive applications in business, environmental, physical and social sciences. Multicollinearity has been a considerable problem in multiple regression analysis. When the regressor variables are multicollinear, it becomes difficult to make precise statistical inferences about the regression coefficients. There are some statistical methods that can be used, which are discussed in this thesis are ridge regression, Liu, two parameter biased and LASSO estimators. Firstly, an analytical comparison on the basis of risk was made among ridge, Liu and LASSO estimators under orthonormal regression model. I found that LASSO dominates least squares, ridge and Liu estimators over a significant portion of the parameter space for large dimension. Secondly, a simulation study was conducted to compare performance of ridge, Liu and two parameter biased estimator by their mean squared error criterion. I found that two parameter biased estimator performs better than its corresponding ridge regression estimator. Overall, Liu estimator performs better than both ridge and two parameter biased estimator.

Efficient numerical methods for the random-field Ising model: Finite-size scaling, reweighting extrapolation, and computation of response functions

It was recently shown [Phys. Rev. Lett. 110, 227201 (2013)] that the critical behavior of the random-field Ising model in three dimensions is ruled by a single universality class. This conclusion was reached only after a proper taming of the large scaling corrections of the model by applying a combined approach of various techniques, coming from the zero-and positive-temperature toolboxes of statistical physics. In the present contribution we provide a detailed description of this combined scheme, explaining in detail the zero-temperature numerical scheme and developing the generalized fluctuation-dissipation formula that allowed us to compute connected and disconnected correlation functions of the model. We discuss the error evolution of our method and we illustrate the infinite limit-size extrapolation of several observables within phenomenological renormalization. We present an extension of the quotients method that allows us to obtain estimates of the critical exponent a of the specific heat of the model via the scaling of the bond energy and we discuss the self-averaging properties of the system and the algorithmic aspects of the maximum-flow algorithm used.

Differentiated effect of advertising: Joint vs. separate consumption

In a context of intense competition, cooperative advertising between firms is critical. Accordingly, the objective of this article is to analyze the potential differentiated effect of advertising on two basic consumption patterns: individual products (i.e. hotel, restaurant) vs. bundle (i.e. hotel + restaurant). This research adds to the extant literature in that, for the first time, this potential differentiated effect is examined through a hierarchical modelling framework that reflects the way people make their decisions: first, they decide whether to visit or not a region; second, whether to purchase an advertised product in that region; and third, whether to buy products together or separately at the region. The empirical analysis, applied to a sample of 11,288 individuals, shows that the influence of advertising is positive for the decisions to visit and to purchase; however, when it comes to the joint or separate consumption, advertising has a differentiated effect: its impact is much greater on the joint alternative (“hotel + restaurant”) than the separate options (“hotel” and “restaurant”). Also, the variable distance moderates the advertising effect.

Evaluating the environmental Kuznets curve

We examine the empirical evidence for an environmental Kuznets curve using a semiparametric smooth coefficient regression model that allows us to incorporate flexibility in the parameter estimates, while maintaining the basic econometric structure that is typically used to estimate the pollution-income relationship. This allows us to assess the sensitivity to parameter heterogeneity of typical parametric models used to estimate the relationship between pollution and income, as well as identify why the results from such models are seldom found to be robust. Our results confirm that the resulting relationship between pollution and income is fragile; we show that the estimated pollution-income relationship depends substantially on the heterogeneity of the slope coefficients and the parameter values at which the relationship is evaluated. Different sets of parameters obtained from the semiparametric model give rise to many different shapes for the pollution-income relationship that are commonly found in the literature.

Random regression analyses using B-splines functions to model growth from birth to adult age in Canchim cattle

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)