Wing K. Fung

Robust Estimation in Generalized Partial Linear Models for Clustered Data

In this article we consider robust generalized estimating equations for the analysis of semiparametric generalized partial linear models (GPLMs) for longitudinal data or clustered data in general. We approximate the nonparametric function in the GPLM by a regression spline, and use bounded scores and leverage-based weights in the estimating equation to achieve robustness against outliers. We show that the regression spline approach avoids some of the intricacies associated with the profile-kernel method, and that robust estimation and inference can be carried out operationally as if a generalized linear model were used.

Influence diagnostics and outlier tests for semiparametric mixed models

Summary. Semiparametric mixed models are useful in biometric and econometric applications, especially for longitudinal data. Maximum penalized likelihood estimators (MPLEs) have been shown to work well by Zhang and co-workers for both linear coefficients and nonparametric functions. This paper considers the role of influence diagnostics in the MPLE by extending the case deletion and subject deletion analysis of linear models to accommodate the inclusion of a nonparametric component. We focus on influence measures for the fixed effects and provide formulae that are analogous to those for simpler models and readily computable with the MPLE algorithm. We also establish an equivalence between the case or subject deletion model and a mean shift outlier model from which we derive tests for outliers. The influence diagnostics proposed are illustrated through a longitudinal hormone study on progesterone and a simulated example.

Power of exclusion revisited: probability of excluding relatives of the true father from paternity

In parentage testing using DNA markers, the formulae for calculating the probability of exclusion generally overstate the power of a test battery by considering its ability to exclude a random man. It is know that in many cases, in particular immigration applications, the false father is more likely to be a relative, e.g. brother, of the true father than an unrelated man. This work presents formulae that take this consideration into account. A practical example using Hong Kong data is provided to illustrate the effect of the modification. Also discussed is how the expected efficacy of a test battery will be affected when possible mutations and null alleles or genetic inconsistencies are taken into consideration.

Assessing local influence for specific restricted likelihood: Application to factor analysis

In restricted statistical models, since the first derivatives of the likelihood displacement are often nonzero, the commonly adopted formulation for local influence analysis is not appropriate. However, there are two kinds of model restrictions in which the first derivatives of the likelihood displacement are still zero. General formulas for assessing local influence under these restrictions are derived and applied to factor analysis as the usually used restriction in factor analysis satisfies the conditions. Various influence schemes are introduced and a comparison to the influence function approach is discussed. It is also shown that local influence for factor analysis is invariant to the scale of the data and is independent of the rotation of the factor loadings.

Diagnostics in Linear Discriminant Analysis

Abstract Some new diagnostic measures in discriminant analysis are proposed. They can be expressed in terms of the two fundamental influence statistics in discriminant analysis: d i 2 and ψ i . A theorem on the asymptotic distributions of the fundamental statistics is derived. Based on the theorem, the proposed measures can be shown to be asymptotically distributed as functions of independent chi-squared and standard normal random variables. Critical values and expected quantiles of the measures can then be constructed. Hence influential observations are detected using Q-Q plots and significance tests. Two measures have analogous forms in regression. The theorem is also useful for getting the asymptotic distributions of existing measures that are functions of d i 2 and ψ i . A comparison of the diagnostics in linear discriminant analysis, linear regression, and linear logistic regression (discriminant) analysis is made. Although discriminant coefficients can be determined under a regression model, regress...

A Note on Local Influence Based on Normal Curvature

SUMMARY Object functions other than the likelihood displacement, such as a parameter estimate or a test statistic, can also be used in local influence analysis. The normal curvatures of these object functions have been studied in situations where the slopes were non-zero. In these situations, we show that the normal curvature is not scale invariant and thus ambiguous conclusions will be drawn. Comments on the application of the general normal curvature formula are presented.

A new graphical method for detecting single and multiple outliers in univariate and multivariate data

SUMMARY A new graphical approach based on Wilkss (1963) statistic is proposed. The method is found to be useful in the detection of outliers in univariate and multivariate data. Masking and swamping effects in the sample are easily revealed. The method is illustrated with examples and simulations.

Penalized quadratic inference functions for single-index models with longitudinal data

In this paper, we focus on single-index models for longitudinal data. We propose a procedure to estimate the single-index component and the unknown link function based on the combination of the penalized splines and quadratic inference functions. It is shown that the proposed estimation method has good asymptotic properties. We also evaluate the finite sample performance of the proposed method via Monte Carlo simulation studies. Furthermore, the proposed method is illustrated in the analysis of a real data set.

A simulation study comparing tests for the equality of coefficients of variation

The coefficient of variation is commonly used in medical and biological sciences. In this paper, several parametric and non-parametric tests for the equality of coefficients of variation in kappa populations are reviewed. Simulation studies are conducted to compare the sizes and power of these tests. It is found that the parametric tests perform well if the data are normally distributed, but perform poorly if otherwise. The non-parametric test, however, is rather robust against the underlying distribution. An example using data of the Quality Assurance Program from the Hong Kong Medical Technology Association in Haematology and Serology is provided. The insensitivity of the non-parametric test to outliers is demonstrated.

A Logistic Normal Multinomial Regression Model for Microbiome Compositional Data Analysis

Changes in human microbiome are associated with many human diseases. Next generation sequencing technologies make it possible to quantify the microbial composition without the need for laboratory cultivation. One important problem of microbiome data analysis is to identify the environmental/biological covariates that are associated with different bacterial taxa. Taxa count data in microbiome studies are often over-dispersed and include many zeros. To account for such an over-dispersion, we propose to use an additive logistic normal multinomial regression model to associate the covariates to bacterial composition. The model can naturally account for sampling variabilities and zero observations and also allow for a flexible covariance structure among the bacterial taxa. In order to select the relevant covariates and to estimate the corresponding regression coefficients, we propose a group ℓ1 penalized likelihood estimation method for variable selection and estimation. We develop a Monte Carlo expectation-maximization algorithm to implement the penalized likelihood estimation. Our simulation results show that the proposed method outperforms the group ℓ1 penalized multinomial logistic regression and the Dirichlet multinomial regression models in variable selection. We demonstrate the methods using a data set that links human gut microbiome to micro-nutrients in order to identify the nutrients that are associated with the human gut microbiome enterotype.