A unified approach to multilevel sample selection models

Abstract

We propose a unified approach for multilevel sample selection models using a generalized result on skew distributions arising from selection. If the underlying distributional assumption is normal, then the resulting density for the outcome is the continuous component of the sample selection density and has links with the closed skew-normal distribution (CSN). The CSN distribution provides a framework which simplifies the derivation of the conditional expectation of the observed data. This generalizes the Heckman’s two-step method to a multilevel sample selection model. Finite-sample performance of the maximum likelihood estimator of this model is studied through a Monte Carlo simulation.     

An improved comorbidity summary score for measuring disease burden and predicting mortality with applications to two national cohorts

Abstract

Research involving administrative healthcare data to study patient outcomes requires the investigator to account for the patient’s disease burden in order to reduce the potential for biased results. Here we develop a comorbidity summary score based on variable importance measures derived from several statistical and machine learning methods and show it has superior predictive performance to the Elixhauser and Charlson indices when used to predict 1-year, 5-year, and 10-year mortality. We used two large Veterans Administration cohorts to develop and validate the summary score and compared predictive performance using the area under ROC curve (AUC) and the Brier score.     

Confidence sets based on sequential Tests

For given (small) a and β a sequential confidence set that covers the true parameter point with probability at least 1 - a and one or more specified false parameter points with probability at most β can be generated by a family of sequen-tial tests. Several situations are described where this approach would be a natural one. The following example is studied in some detail: obtain an upper (1 - α)-confidence interval for a normal mean μ (variance known) with β-protection at μ - δ(μ), where δ(.) is not bounded away from 0 so that a truly sequential procedure is mandatory. Some numerical results are presented for intervals generated by (1) sequential probability ratio tests (SPRT's), and (2) generalized sequential probability ratio tests (GSPRT's). These results indicate the superiority of the GSPRT-generated intervals over the SPRT-generated ones if expected sample size is taken as performance criterion     

Unbiased F Tests for Factorial Experiments for Correlated Data

This paper finds a general form of the correlation matrix that may be used to provide unbiased F tests in a.k-way factorial experiment.     

Maximum likelihood ridge displays

I illustrate likelihood methods for estimating the consequences of shrinkage along any ridge path as well as methods for picking a two-hyperparameter path of optimal curvature and the optimal point on that path. In addition to my published "classical" methods, I also illustrate both the empirical Bayes and the random coefficient maximum likelihood approaches. Traces of risks for known parameters and losses for simulated responses are followed by traces of estimates that can reveal the same general information.     

Tests for the two-sample problem based on empirical probability measures

Tests are proposed for the equality of two unknown distributions. For empirical probability measures that are defined for samples from the two distributions, the proposed tests are based on the supremum of the absolute differences between the corresponding empirical probabilities, the supremum being taken over all possible events (Borel sets). In contrast, competing EDF tests compare only empirical probabilities of a subclass of Borel sets. The proposed tests are compared for simulated samples to the Kolmogorov-Smirnov, Cramér-von Mises, Kuiper, and Mann-Whitney-Wilcoxon tests     

Re-examining two tests for bivariate normality

Many goodness of fit tests for bivariate normality are not rigorous procedures because the distributions of the proposed statistics are unknown or too difficult to manipulate. Two familiar examples are the ring test and the line test. In both tests the statistic utilized generally is approximated by a chi-square distribution rather than compared to its known beta distribution. These two procedures are re-examined and re-evaluated in this paper. It is shown that the chi-square approximation can be too conservative and can lead to unnecessary

rejection of normality.     

Influential observations in the analysis of variance

The effect of influentia lob servations on t h e parameter estimates of ordinary l e a s t squares regression models has received considerable attentio n fn the last decade. However, very little attention has been given t o the problem of in fluent ia lobserva- tions in the analysis of variance . The purpose of t h i s paper is t o show by way of examples that influential observations can alter the conclusions of tests of hypotheses in the analysis of variance . Regression diagnostics for identif y in g both extreme points and outliers can be used to reveal potential data and design problems.     

A test for variance-covarianch parameters in normal linear models

This paper derives a test statistic for the variance-covariance parameters which is a quadratic function of their MINQUE (Minimum Norm Quadratic Unbiased Estimation) estimates. The test is a Wald-type test, and its development closely parallels the theory used to derive a similar test for the coefficients in linear models. In fact, the derivation proceeds by first setting up the estimation problem in a derived linear model in which the dispersion parameters are the coefficients. The test statistic is shown to be the sum of the squares of independent standardized x² variables.     

Isotontic regression for interval censored survival data using an e-m algorithm

This paper develops a nonparametric model of the relationship between survival S and a dichotomous random variable X under the order constraint that P(X=1|S=s) is increasing (or decreasing) with s. The estimation procedure, called isotonic regression, has been studied in some depth for the case of uncensored data, but we give a methodology which is appropriate in the more general context of right, left, and interval censored data. An E-M Algorithm (Dempster et. al., 1977) is used for maximum likelihood estimation.