Two Pitfalls of Using Standard Regression Diagnostics When Both X and Y Have Measurement Error

Modern exploratory data analysis produces models that are not based on physical theory but that are consistent with pictures of the data. When both X and Y have error this can be risky, because important features are hidden. Two examples are given that show that systematic model departures and heteroscedasticity may not be detectable with standard regression diagnostics.     

Resolving the Mixed Models Controversy

Two standard mixed models with interactions are discussed. When each is viewed in the context of superpopulation models, the mixed models controversy is resolved. The tests suggested by the expected mean squares under the constrained-parameters model are correct for testing the main effects and interactions under both the unconstrained-and constrained-parameters models.     

Chain pooling model selection for two-level fixed effects factorial experiments

As many as three iterated statistical model deletion procedures are considered for an experiment.Population model coeff cients were chosen to simulate a saturated 2⁴experiment having an unfavorable distribution of parameter values.Using random number studies, three model selection strategies were developed, namely, (1) a strategy to be used in anticipation of large coefficients of variation (neighborhood of 65 percent), (2) strategy to be used in anticipation of small coefficients of variation (4 percent or less), and (3) a security regret strategy to be used in the absence of such prior knowledge     

A network algorithm for the exact treatment of the 2×k contingency table

A common statistical problem encountered in biomedical research is to test the hypothesis that the parameters of k binomial populations are all equal. An exact test of significance of this hypothesis is possible in principle, the appropriate null distribution being a normalized product of k binomial coefficients. However, the problem of computing the tail area of this distribution can be formidable since it requires the enumeration of all sets of k binomial coefficients whose product is less than a given constant. Existing algorithms, all of which rely on explicit enumeration to generate feasible binomial coefficients     

On the asymptotic properties of parameter estimates in a regression model with non-normally distributed errors

As pointed out in a recent paper by Amirkhalkhali and Rao (1986) (henceforth referred to as A&R), the usual assumption of normality for the error terms of a regression model isoften untenable. However, when this assumption is dropped, it may be difficult to characterize parameter estimates for the model. For example, A&R (p. 189) state that “if the regression errors are non-normal, we are not even sure of their [e.g., the generalized least squares parameter estimates1] asymptotic properties.” A partial answer, however, is given by Spall and Wall (1984), which presents an asymptotic distribution theory for Kalman filter estimates for cases where the random terms of the state space model are not necessarily Gaussian. Certain of these asymptotic distribution results are also discussed in Spall (1985) in the context of model validation (diagnostic checking)     

A specification strategy for order determination in arma models

In this paper a specification strategy is proposed for the determination of the orders in ARMA models. The strategy is based on two newly defined concepts: the q-conditioned partial auto-regressive function and the p-conditioned partial moving average function. These concepts are similar to the generalized partial autocorrelation function which has been recently suggested for order determination. The main difference is that they are defined and employed in connection with an asymptotically efficient estimation method instead of the rather inefficient generalized Yule-Walker method. The specification is performed by using sequential Wald type tests. In contrast to the traditional testing of hypotheses, these tests use critical values which increase with the sample size at an appropriate rate     

Elliptically contoured model and factorization of wllks1 A

In a series of papers, Kshirsagar (1964, 1971) and McHenry and Kshirsagar (1977), factorize Wilks' A into a number of factors and find the independent null multivariate beta densities of these factors. These factors are the likelihood ratio test criteria for testing the goodness of fit of certain assigned discriminant functions or canonical variables either in the space of independent or dependent variables. Essentially the factors of Wilks' A are the factors of certain multivariate beta distributed matrix or its determinant. The Bartlett decomposition of the underlying multivariate beta distribution into independent factors determines the distribution of these factors. The present paper generalizes Kshirsagar's (1971) normal theory to the elliptically contoured model, and shows that his results are null robust for the elliptically contoured model.     

Influence analysis in multivariate linear general models

In this paper we obtain several influence measures for the multivariate linear general model through the approach proposed by Muñoz-Pichardo et al. (1995), which is based on the concept of conditional bias. An interesting charasteristic of this approach is that it does not require any distributional hypothesis. Appling the obtained results to the multivariate regression model, we obtain some measures proposed by other authors. Nevertheless, on the results obtained in this paper, we emphasize two aspects. First, they provide a theoretical foundation for measures proposed by other authors for the mul¬tivariate regression model. Second, they can be applied to any linear model that can be formulated as a particular case of the multivariate linear general model. In particular, we carry out an application to the multivariate analysis of covariance.     

A class of semiparametric transormation frailty models with application to estimating treatment effects and heterogenity in aids clinical traials

Muitivariate failure time data are common in medical research; com¬monly used statistical models for such correlated failure-time data include frailty and marginal models. Both types of models most often assume pro¬portional hazards (Cox, 1972); but the Cox model may not fit the data well This article presents a class of linear transformation frailty models that in¬cludes, as a special case, the proportional hazards model with frailty. We then propose approximate procedures to derive the best linear unbiased es¬timates and predictors of the regression parameters and frailties. We apply the proposed methods to analyze results of a clinical trial of different dose levels of didansine (ddl) among HIV-infected patients who were intolerant of zidovudine (ZDV). These methods yield estimates of treatment effects and of frailties corresponding to patient groups defined by clinical history prior to entry into the trial.     

A model with long-term survivors: negative binomial Birnbaum-Saunders

Abstract

We propose a cure rate survival model by assuming that the number of competing causes of the event of interest follows the negative binomial distribution and the time to the event of interest has the Birnbaum-Saunders distribution. Further, the new model includes as special cases some well-known cure rate models published recently. We consider a frequentist analysis for parameter estimation of the negative binomial Birnbaum-Saunders model with cure rate. Then, we derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes. We illustrate the usefulness of the proposed model in the analysis of a real data set from the medical area.