Exploring Cook's Statistic Graphically

An index plot of Cook's statistic is frequently used to highlight influential observations. In this article we illustrate how enhanced higher dimensional plots of Cook's statistic can provide further useful information about sets of influential observations. We provide examples using normal and generalized linear models.     

Maximum likelihood estimation of multivariate non-linear functional relationships

The results of Dolby (1972) and Dolby and Feeeman (1975) on the estimation of an explicit non-linear functional relationship are examined for the multivariate case with Σknown up to a multiplicative constant. It is shown that in both univariate and multivariate situations the method of scoring for parameters is susceptible to major errors whenever the non-linearity implies asymmetric peaks or valleys and the data is relatively ”noisy”. Amendments to this method are proposed and demonstrated.     

The Stabilisation of Model Parameter Estimates from Repeated Surveys with Rare Observations

In many surveys, the domains of study are small and the samples that carry information on a domain can be very small indeed. If the survey is conducted repeatedly there is often a high degree of overlap in samples over time. We show how to use the richness of information over time to compensate for the paucity of cross‐sectional information. We propose a model‐based estimator of the population total which makes use of stabilised parameter estimates that combine information from different survey periods that are adjacent in time. The motivating example for this research was the ProdCom survey as implemented in the UK.     

A Novel Collinearity-Influential Observation Diagnostic Measure Based on a Group Deletion Approach

High leverage points can induce or disrupt multicollinearity patterns in data. Observations responsible for this problem are generally known as collinearity-influential observations. A significant amount of published work on the identification of collinearity-influential observations exists; however, we show in this article that all commonly used detection techniques display greatly reduced sensitivity in the presence of multiple high leverage collinearity-influential observations. We propose a new measure based on a diagnostic robust group deletion approach. Some practical cutoff points for existing and developed diagnostics measures are also introduced. Numerical examples and simulation results show that the proposed measure provides significant improvement over the existing measures.     

A Comparison of Three-Level Orthogonal Arrays in the Presence of Different Correlation Structures in Observations

When the experimenter suspects that there might be a quadratic relation between the response variable and the explanatory parameters, a design with at least three points must be employed to establish and explore this relation (second-order design). Orthogonal arrays (OAs) with three levels are often used as second-order response surface designs. Generally, we assume that the data are independent observations; however, there are many situations where this assumption may not be sustainable. In this paper, we want to compare three-level OAs with 18, 27, and 36 runs under the presence of three specific forms of correlation in observations. The aim is to derive the best designs that can be efficiently used for response surface modeling.     

Testing hypotheses in truncated samples by means of divergence statistics

In this paper we consider the problem of testing hypotheses in parametric models, when only the first r (of n) ordered observations are known.Using divergence measures, a procedure to test statistical hypotheses is proposed, Replacing the parameters by suitable estimators in the expresion of the divergence measure, the test statistics are obtained.Asymptotic distributions for these statistics are given in several cases when maximum likelihood estimators for truncated samples are considered.Applications of these results in testing statistical hypotheses, on the basis of truncated data, are presented.The small sample behavior of the proposed test statistics is analyzed in particular cases.A comparative study of power values is carried out by computer simulation.     

Tables of critical values for two group interim analyses

Tables of critical values are given, which can be used to execute interim analyses in clinical trials involving two groups when the joint distribution of the test statistics can be approximated by a multivariate normal distribution. Critical values are given for both the one and two interim analyses cases for a variety of partitions of α and correlation structures. Results of power calculations are presented, which reflect the effects of both the correlation structure and partitions of α.Several examples are given, which illustrate how to apply the tables to a variety of experiments     

Serial correlation or random subject effects

In longitudinal data analysis with random subject effects, there is often within subject serial correlation and possibly unequally spaced observations. This serial correlation can be partially confounded with the random between subject effects. In real data, it is often not clear whether there is serial correlation, random subject effects or both. Using inference based on the likelihood function, it is not always possible to identify the correct model, especially in small samples. However, it is important that some effort be made to attempt to find a good model rather than just making assumptions. This often means trying models with random coefficients, with serial correlation, and with both. Model selection criteria such as likelihood ratio tests and Akaike's Information Criterion (AIC) can be used. The problem of modelling serial correlation with unequally spaced observations is addressed. A real data example is presented where there is an apparent heterogeneity of variances, possible serial correlation and between subject random effects. In this example, it turns out that the random subject effects explains both the serial correlation and the variance heterogeneity.     

Latent Variable Models in Heterogeneous Spaces for Observations of Mixed Types

The maximum likelihood approach to the estimation of factor analytic model parameters most commonly deals with outcomes that are assumed to be multivariate Gaussian random variables in a homogeneous input space. In many practical settings, however, many studies needing factor analytic modeling involve data that, not only are not multivariate Gaussian variables, but also come from a partitioned input space. This article introduces an extension of the maximum likelihood factor analysis that handles multivariate outcomes made up of attributes with different probability distributions, and originating from a partitioned input space. An EM Algorithm combined with Fisher Scoring is used to estimate the parameters of the derived model.