Testing for zero-inflation in count series: application to occupational health

Count data series with extra zeros relative to a Poisson distribution are common in many biomedical applications. A score test is presented to assess whether the zero-inflation problem is significant to warrant the analysis by the more complex zero-inflated Poisson autoregression model. The score test is implemented as a computer program in the Splus platform. For illustration, the test procedure is applied to a workplace injury series where many zero counts are observed due to the heterogeneity in injury risk and the dynamic population involved.     

Adjustment of the Profile Likelihood for a Class of Normal Regression Models

We apply the method of McCullagh & Tibshirani (1990) to a generalization of the model for variance components in which the parameter of interest can appear in both the mean and variance. We obtain the exact adjusted profile log-likelihood score function. For the variance components model, we obtain the adjusted profile log-likelihood and show that it equals the restricted log-likelihood of Patterson & Thompson (1971). We discuss an example due to Kempton (1982) of a regression model with autoregressive terms in which the parameter of interest appears in both the mean and variance.     

Skew-normal semiparametric varying coefficient model and score test

In this paper, we consider inference aspects of skew-normal semiparametric varying coefficient models which provide a useful extension of the normal regression models. The maximum likelihood estimation based on B-spline is proposed. Further, we discuss the score test for homogeneity of the variance in skew-normal semiparametric varying coefficient models. Their asymptotical properties are investigated. Some simulated examples are used to examine our proposed methods.     

The score function and a comparison of various adjustments of the profile likelihood

Several adjustments of the profile likelihood have the common effect of reducing the bias of the associated score function. Hence expansions for the adjusted score functions differ by a term, D_ξ, that has small asymptotic order (n ^?½). The effect of D_ξ on other quantities of interest is studied. In particular, we find the bias and variance of the adjusted maximum-likelihood estimate to be relatively unaffected, while differences in the Bartlett correction depend on D_ξ in a simple way.     

Confidence Intervals for the Weighted Sum of Two Independent Binomial Proportions

Confidence intervals for the difference of two binomial proportions are well known, however, confidence intervals for the weighted sum of two binomial proportions are less studied. We develop and compare seven methods for constructing confidence intervals for the weighted sum of two independent binomial proportions. The interval estimates are constructed by inverting the Wald test, the score test and the Likelihood ratio test. The weights can be negative, so our results generalize those for the difference between two independent proportions. We provide a numerical study that shows that these confidence intervals based on large‐sample approximations perform very well, even when a relatively small amount of data is available. The intervals based on the inversion of the score test showed the best performance. Finally, we show that as for the difference of two binomial proportions, adding four pseudo‐outcomes to the Wald interval for the weighted sum of two binomial proportions improves its coverage significantly, and we provide a justification for this correction.     

A score test for monotonic trend in hazard rates for grouped survival data in stratified populations

Models for monotone trends in hazard rates for grouped survival data in stratified populations are introduced, and simple closed form score statistics for testing the significance of these trends are presented. The test statistics for some of the models understudy are shown to be independent of the assumed form of the function which relates the hazard rates to the sets of monotone scores assigned to the time intervals. The procedure is applied to test monotone trends in the recovery rates of erythematous response among skin cancer patients and controls that have been irradiated with a ultraviolent challenge.     

The Value of a Probability Forecast from Portfolio Theory

A probability forecast scored ex post using a probability scoring rule (e.g. Brier) is analogous to a risky financial security. With only superficial adaptation, the same economic logic by which securities are valued ex ante – in particular, portfolio theory and the capital asset pricing model (CAPM) – applies to the valuation of probability forecasts. Each available forecast of a given event is valued relative to each other and to the “market” (all available forecasts). A forecast is seen to be more valuable the higher its expected score and the lower the covariance of its score with the market aggregate score. Forecasts that score highly in trials when others do poorly are appreciated more than those with equal success in “easy” trials where most forecasts score well. The CAPM defines economically rational (equilibrium) forecast prices at which forecasters can trade shares in each other’s ex post score – or associated monetary payoff – thereby balancing forecast risk against return and ultimately forming optimally hedged portfolios. Hedging this way offers risk averse forecasters an “honest” alternative to the ruse of reporting conservative probability assessments.     

Testing for covariate balance using quantile regression and resampling methods

Consistency of propensity score matching estimators hinges on the propensity score's ability to balance the distributions of covariates in the pools of treated and non-treated units. Conventional balance tests merely check for differences in covariates’ means, but cannot account for differences in higher moments. For this reason, this paper proposes balance tests which test for differences in the entire distributions of continuous covariates based on quantile regression (to derive Kolmogorov–Smirnov and Cramer–von-Mises–Smirnov-type test statistics) and resampling methods (for inference). Simulations suggest that these methods are very powerful and capture imbalances related to higher moments when conventional balance tests fail to do so.     

Testing the homogeneity of proportions for clustered binary data without knowing the correlation structure

A robust generalized score test for comparing groups of cluster binary data is proposed. This novel test is asymptotically valid for practically any underlying correlation configurations including the situation when correlation coefficients vary within or between clusters. This structure generally undermines the validity of the typical large sample properties of the method of maximum likelihood. Simulations and real data analysis are used to demonstrate the merit of this parametric robust method. Results show that our test is superior to two recently proposed test statistics advocated by other researchers.     

A Simplified Method of Calculating an Overall Goodness-of-Fit Test for the Cox Proportional Hazards Model

Gronnesby and Borgan (1996) propose an overall goodness-of-fit test for the Cox proportional hazards model. The basis of their test is a grouping of subjects by their estimated risk score. We show that the Gronnesby and Borgan test is algebraically identical to one obtained from adding group indicator variables to the model and testing the hypothesis the coefficients of the group indicator variables are zero via the score test. Thus showing that the test can be calculated using existing software. We demonstrate that the table of observed and estimated expected number of events within each group of the risk score is a useful adjunct to the test to help identify potential problems in fit.