Vicente Núñez-Antón

Parametric modelling of growth curve data: An overview

In the past two decades a parametric multivariate regression modelling approach for analyzing growth curve data has achieved prominence. The approach, which has several advantages over classical analysis-of-variance and general multivariate approaches, consists of postulating, fitting, evaluating, and comparing parametric models for the datas mean structure and covariance structure. This article provides an overview of the approach, using unified terminology and notation. Well-established models and some developed more recently are described, with emphasis given to those models that allow for nonstationarity and for measurement times that differ across subjects and are unequally spaced. Graphical diagnostics that can assist with model postulation and evaluation are discussed, as are more formal methods for fitting and comparing models. Three examples serve to illustrate the methodology and to reveal the relative strengths and weaknesses of the various parametric models.

Cellwise Residual Analysis in Two-Way Contingency Tables

MacDonald and Gardner reported the results of a comparative study of two post hoc cellwise tests in 3 X 4 contingency tables under the independence and homogeneity models. Based on their results, they advised against the use of standardized residuals and in favor of adjusted residuals. Here the authors show that the comparison was biased in favor of adjusted residuals because of a failure to consider the nonunit variance of standardized residuals. The authors define a moment-corrected standardized residual that overcomes this bias and present the results of a thorough study including two-way tables of all dimensions between 2 X 2 and 8 X 12 that aimed at comparing moment-corrected standardized residuals with adjusted residuals. Across the entire set of table dimensions included in this study, the results reveal that both residuals yield essentially the same pat-tern of cell-by-cell and experimentwise Type I error rates when the data come from variables with uniform marginal distributions. When the data come from variables with peaked marginal distributions, adjusted residuals behave minimally better than moment-corrected residuals.

ANALYSIS OF LONGITUDINAL DATA WITH UNEQUALLY SPACED OBSERVATIONS AND TIME-DEPENDENT CORRELATED ERRORS

A linear model for repeated measurements is proposed in which the correlation structure includes a transformation of the time scale. This transformation can produce nonstationary covariance structures within subjects with stationarity as a special case. Restricted maximum likelihood methods for parameter estimation are discussed. The method is applied to simulated data as well as speech recognition data from the Iowa Cochlear Implant Project. The growth curve for this audiologic performance measure is shown together with estimates of the standard errors of predictions at given months.

Antedependence Models for longitudinal Data

Introduction Longitudinal data Classical methods of analysis Parametric modeling Antedependence models, in brief A motivating example Overview of the book Four featured data sets Unstructured Antedependence Models Antedependent random variables Antecorrelation and partial antecorrelation Equivalent characterizations Some results on determinants and traces The first-order case Variable-order antedependence Other conditional independence models Structured Antedependence Models Stationary autoregressive models Heterogeneous autoregressive models Integrated autoregressive models Integrated antedependence models Unconstrained linear models Power law models Variable-order SAD models Nonlinear stationary autoregressive models Comparisons with other models Informal Model Identification Identifying mean structure Identifying covariance structure: summary statistics Identifying covariance structure: graphical methods Concluding remarks Likelihood-Based Estimation Normal linear AD(p) model Estimation in the general case Unstructured antedependence: balanced data Unstructured antedependence: unbalanced data Structured antedependence models Concluding remarks Testing Hypotheses on the Covariance Structure Tests on individual parameters Testing for the order of antedependence Testing for structured antedependence Testing for homogeneity across groups Penalized likelihood criteria Concluding remarks Testing Hypotheses on the Mean Structure One-sample case Two-sample case Multivariate regression mean Other situations Penalized likelihood criteria Concluding remarks Case Studies A coherent parametric modeling approach Case study #1: Cattle growth data Case study #2: 100-km race data Case study #3: Speech recognition data Case study #4: Fruit fly mortality data Other studies Discussion Further Topics and Extensions Alternative estimation methods Nonlinear mean structure Discrimination under antedependence Multivariate antedependence models Spatial antedependence models Antedependence models for discrete data Appendix 1: Some Matrix Results Appendix 2: Proofs of Theorems 2.5 and 2.6 References Index

Structured Antedependence Models for Longitudinal Data

Antedependence (AD) models can be a useful class of models for the covariance structure of continuous longitudinal data. Like stationary autoregressive (AR) models, AD models allow for serial correlation within subjects but are more general in the sense that they do not stipulate that the variance is constant nor that correlations between measurements equidistant in time are equal. Thus, AD models are more parsimonious class of models for nonstationary data than the completely unstructured model of the classical multivariate approach.

Longitudinal data with nonstationary errors: a nonparametric three-stage approach

We develop here a three-stage nonparametric method to estimate the common, group and individual effects in a longitudinal data setting. Our three-stage additive model assumes that the dependence between performance in an audiologic test and time is a sum of three components. One of them is the same for all individuals, the second one corresponds to the group effect and the last one to the individual effects. We estimate these functional components by nonparametric kernel smoothing techniques. We give theoretical results concerning rates of convergence of our estimates. This method is then applied to the data set that motivated the methods proposed here, the speech recognition data from the Iowa Cochlear Implant Project.

Length of time spent in Chapter 11 bankruptcy: a censored partial regression model

This paper investigates original issuers of high yield bonds in Chapter 11 bankruptcy to determine which factors affect the length of time spent in Chapter 11. In order to do this analysis a flexible new duration model is proposed, the censored partial regression model. This model allows consideration of the effect of some variables on the duration using a nonparametric functional form. It is found that the choice of prepackaged Chapter 11, the length of time negotiating before filling for Chapter 11, the profitability, the highly leveraged transactions, the participation on different disputes, the role of vulture funds and some institutional changes turn out to be relevant to analyse this duration.

Kernel regression estimates of growth curves using nonstationary correlated errors

We study the nonparametric estimation of the average growth curve under a very general parametric form of the covariance structure that allows for monotone transformation of the time scale. We also investigate the properties of optimal bandwidth selection methods and compare the results with those obtained under stationarity.

Statistical approaches to analyse patient-reported outcomes as response variables: An application to health-related quality of life:

Patient-reported outcomes (PRO) are used as primary endpoints in medical research and their statistical analysis is an important methodological issue. Theoretical assumptions of the selected methodology and interpretation of its results are issues to take into account when selecting an appropriate statistical technique to analyse data. We present eight methods of analysis of a popular PRO tool under different assumptions that lead to different interpretations of the results. All methods were applied to responses obtained from two of the health dimensions of the SF–36 Health Survey. The proposed methods are: multiple linear regression (MLR), with least square and bootstrap estimations, tobit regression, ordinal logistic and probit regressions, beta-binomial regression (BBR), binomial-logit-normal regression (BLNR) and coarsening. Selection of an appropriate model depends not only on its distributional assumptions but also on the continuous or ordinal features of the response and the fact that they are constrained to a bounded interval. The BBR approach renders satisfactory results in a broad number of situations. MLR is not recommended, especially with skewed outcomes. Ordinal methods are only appropriate for outcomes with a few number of categories. Tobit regression is an acceptable option under normality assumptions and in the presence of moderate ceiling or floor effect. The BLNR and coarsening proposals are also acceptable, but only under certain distributional assumptions that are difficult to test a priori. Interpretation of the results is more convenient when using the BBR, BLNR and ordinal logistic regression approaches.

LONGITUDINAL DATA ANALYSIS : NON-STATIONARY ERROR STRUCTURES AND ANTEDEPENDENT MODELS

Non-stationary covariance structures had not been analyzed in detail for longitudinal data mainly because the existing applications did not require their use. Data from the Iowa Cochlear Implant Project showed this type of structure and the problem needed to be addressed. We propose a linear model for longitudinal data in which the correlation structure includes the Box-Cox transformation of the time scale. This transformation can produce nonstationary covariance structures within subjects, with stationarity as a special case. Restricted maximum likelihood methods for parameter estimation (REML) are discussed and the method is applied to speech recognition data from the Iowa Cochlear Implant Project. The growth curve for this audiologic performance measure is shown. Possible extensions for the model are suggested.