Detection of outliers in growth curve models

The growth curve model introduced by Potthoff and Roy (1964) is a general statistical model which includes as special cases regression models and both univariate and multivariate analysis of variance models. In this paper, we discuss procedures for detection of outliers in growth curve models for mean-slippage and dispersion-slippage outlier model. The distributions of the test statistics are discussed and the values of significant probabilities are given using Bonferronl's bounds. Some simulation results are also presented.     

Response transformations in repeated measures and growth curve models

This article describes estimation and inference procedures for the parameters of the Box-Cox and foided-power transformations in repeated measures and growth curve models. Procedures for computing maximum likelihood estimates of the transformation and covariance parameters under several covanance structures (omnibus sphericity, local sphericity, and unstructured) are described. Lack of fit statistics and hypothesis tests for comparing these structures also are described. The procedures are illustrated on three data sets. Software for performing the analyses in the SAS System is described and is available from the authors.     

Estimating parameters in extended growth curve models with special covariance structures

In this paper the estimation of the unknown parameters is considered in standard growth curve model with special covariance structures. Based on the unbiased estimating equations, some new methods are proposed. The resulting estimators can be expressed in explicit forms. The statistical properties of the proposed estimators are investigated. Some simulation results are presented to compare the performance of the proposed estimator with that of the existing approaches. Finally, these methods are applied in general extended growth curve model with special covariance structures.     

Estimation and identification of change points in panel models with nonstationary or stationary regressors and error term

This article studies the estimation of change point in panel models. We extend Bai (2010 Bai, J. (2010). Common breaks in means and variances for panel data. Journal of Econometrics 157:78–92.[Crossref], [Web of Science ®] , [Google Scholar]) and Feng et al. (2009 Feng, Q., Kao, C., Lazarová, S. (2009). Estimation and Identification of Change Points in Panel Models, Working paper, Syracuse University. [Google Scholar]) to the case of stationary or nonstationary regressors and error term, and whether the change point is present or not. We prove consistency and derive the asymptotic distributions of the Ordinary Least Squares (OLS) and First Difference (FD) estimators. We find that the FD estimator is robust for all cases considered.     

Application of Dirichlet mixture of normals in growth curve models

In this paper, we present growth curve models with an auxiliary variable which contains an uncertain data distribution based on mixtures of standard components, such as normal distributions. The multimodality of the auxiliary random variable motivates and necessitates the use of mixtures of normal distributions in our model. We have observed that Dirichlet process priors, composed of discrete and continuous components, are appropriate in addressing the two problems of determining the number of components and estimating the parameters simultaneously and are especially useful in the aforementioned multimodal scenario. A model for the application of Dirichlet mixture of normals (DMN) in growth curve models under Bayesian formulation is presented and algorithms for computing the number of components, as well as estimating the parameters are also rendered. The simulation results show that our model gives improved goodness of fit statistics over models without DMN and the estimates for the number of components and for parameters are reasonably accurate.     

Prediction under uncertainty of degree of polynomial in growth curve models

Random coefficient polynomial regression model has been considered for prediction purpose when there is uncertainty about the degree of the polynomialo Expressions for mean square errors of two predictors based on simple estimators have been derived and their perfomaiices have been compared when parameters are estimated from the sample. A modified predictor has also been suggested when parameters in the predicting equations are to be estimated from the sample. Perform-ance ofseveral predictors haife been compared by cross validation technique from a real set of data.     

Longitudinal conditional models with intermittent missingness: SAS code and applications

This work provides a set of macros performed with SAS (Statistical Analysis System) for Windows, which can be used to fit conditional models under intermittent missingness in longitudinal data. A formalized transition model, including random effects for individuals and measurement error, is presented. Model fitting is based on the missing completely at random or missing at random assumptions, and the separability condition. The problem translates to maximization of the marginal observed data density only, which for Gaussian data is again Gaussian, meaning that the likelihood can be expressed in terms of the mean and covariance matrix of the observed data vector. A simulation study is presented and misspecification issues are considered. A practical application is also given, where conditional models are fitted to the data from a clinical trial that assessed the effect of a Cuban medicine on a disease of the respiratory system.     

On tests of linearity for dose response data: asymptotic, exact conditional and exact unconditional tests

The approximate chi-square statistic, X 2 Q , which is calculated as the difference between the usual chi-square statistic for heterogeneity and the Cochran-Armitage trend test statistic, has been widely applied to test the linearity assumption for dose-response data. This statistic can be shown to be asymptotically distributed as chi-square with K - 2 degrees of freedom. However, this asymptotic property could be quite questionable if the sample size is small, or if there is a high degree of sparseness or imbalance in the data. In this article, we consider how exact tests based on this X 2 Q statistic can be performed. Both the exact conditional and unconditional versions will be studied. Interesting findings include: (i) the exact conditional test is extremely sensitive to a small change in dosages, which may eventually produce a degenerate exact conditional distribution; and (ii) the exact unconditional test avoids the problem of degenerate distribution and is shown to be less sensitive to the change in dosages. A real example involving an animal carcinogenesis experiment as well as a fictitious data set will be used for illustration purposes.     

Skew-normal distribution for growth curve models in presence of a heteroscedasticity structure

In general, growth models are adjusted under the assumptions that the error terms are homoscedastic and normally distributed. However, these assumptions are often not verified in practice. In this work we propose four growth models (Morgan–Mercer–Flodin, von Bertalanffy, Gompertz, and Richards) considering different distributions (normal, skew-normal) for the error terms and three different covariance structures. Maximum likelihood estimation procedure is addressed. A simulation study is performed in order to verify the appropriateness of the proposed growth curve models. The methodology is also illustrated on a real dataset.     

An example of a two-part latent growth curve model for semicontinuous outcomes in the health sciences

A new method of modeling coronary artery calcium (CAC) is needed in order to properly understand the probability of onset and growth of CAC. CAC remains a controversial indicator of cardiovascular disease (CVD) risk, but this may be due to ill-equipped methods of specifying CAC during the analysis phase of studies reporting an analysis where CAC is the primary outcome. The modern method of two-part latent growth modeling may represent a strong alternative to the myriad of existing methods for modeling CAC. We provide a brief overview of existing methods of analysis used for CAC before introducing the general latent growth curve model, how it extends into a two-part (semicontinuous) growth model, and how the ubiquitous problem of missing data can be effectively handled. We then present an example of how to model CAC using this framework. We demonstrate that utilizing this type of modeling strategy can result in traditional predictors of CAC (e.g. age, gender, and high-density lipoprotein cholesterol), exerting a different impact on the two different, yet simultaneous, operationalizations of CAC. This method of analyzing CAC could inform future analyses of CAC and inform subsequent discussions about the nature of its potential to inform long-term CVD risk and heart events.     

Optimal designs in growth curve models: Part I Correlated model for linear growth: Optimal designs for slope parameter estimation and growth prediction

In the present paper we discuss the situation for a linear growth with correlated structure of the errors and indicate the nature of optimal designs for estimation and prediction problems. We study the intraclass structure of the error distribution. As regards estimation of the slope parameter, we look for robust optimal designs. Here robustness means that optimality should hold for a large variety of correlation parameters. The robust optimal designs for the prediction problem center around a performance measure of the predictors for all design points simultaneously. We have also studied the autocorrelated error structure and found similar results which are reported very briefly.     

Comparison of different estimation methods in growth curve models for categorical data: A simulation study

This simulation study aims at investigating the performance of maximum likelihood and weighted least-square estimation approaches in growth curve models with categorical data. The goodness-of-fit indices were compared with a number of scenarios (different trajectories, sample sizes, replications, and number of categories). The results show that when the number of categories and replications are small, using weighted least-square estimating methods leads to better goodness-of-fit indices. However, when the number of categories and replications are large, both maximum likelihood and weighted least squares in estimating methods will result in similar fit indices.     

Existence conditions of the uniformly minimum risk unbiased estimators in extended growth curve models

Necessary and sufficient existence conditions are derived for the uniformly minimum risk unbiased estimators of the parameters in extended growth curve models with the general covariance matrix or the uniform covariance structure or the serial covariance structure under convex losses and matrix losses, respectively.     

Estimation of dynamic panel data models with both individual and time-specific effects

This paper proposes a generalized least squares and a generalized method of moment estimators for dynamic panel data models with both individual-specific and time-specific effects. We also demonstrate that the common estimators ignoring the presence of time-specific effects are inconsistent when N→∞$N\to \infty$ but T is finite if the time-specific effects are indeed present. Monte Carlo studies are also conducted to investigate the finite sample properties of various estimators. It is found that the generalized least squares estimator has the smallest bias and root mean square error, and also has nominal size close to the empirical size. It is also found that even when there is no presence of time-specific effects, there is hardly any efficiency loss of the generalized least squares estimator assuming its presence compared to the generalized least squares estimator allowing only the presence of individual-specific effects.     

Selecting the regularization parameters in high-dimensional panel data models: Consistency and efficiency

This article considers panel data models in the presence of a large number of potential predictors and unobservable common factors. The model is estimated by the regularization method together with the principal components procedure. We propose a panel information criterion for selecting the regularization parameter and the number of common factors under a diverging number of predictors. Under the correct model specification, we show that the proposed criterion consistently identifies the true model. If the model is instead misspecified, the proposed criterion achieves asymptotically efficient model selection. Simulation results confirm these theoretical arguments.     

Identification of latent class Markov models with multiple indicators and correlated measurement errors

Statistical Methods & Applications - A necessary condition for identification of latent class models is that the number of unknown independent parameters must not be greater than the number of...     

Approximating cross-validatory predictive evaluation in Bayesian latent variable models with integrated IS and WAIC

Looking at predictive accuracy is a traditional method for comparing models. A natural method for approximating out-of-sample predictive accuracy is leave-one-out cross-validation (LOOCV)—we alternately hold out each case from a full dataset and then train a Bayesian model using Markov chain Monte Carlo without the held-out case; at last we evaluate the posterior predictive distribution of all cases with their actual observations. However, actual LOOCV is time-consuming. This paper introduces two methods, namely iIS and iWAIC, for approximating LOOCV with only Markov chain samples simulated from a posterior based on a full dataset. iIS and iWAIC aim at improving the approximations given by importance sampling (IS) and WAIC in Bayesian models with possibly correlated latent variables. In iIS and iWAIC, we first integrate the predictive density over the distribution of the latent variables associated with the held-out without reference to its observation, then apply IS and WAIC approximations to the integrated predictive density. We compare iIS and iWAIC with other approximation methods in three kinds of models: finite mixture models, models with correlated spatial effects, and a random effect logistic regression model. Our empirical results show that iIS and iWAIC give substantially better approximates than non-integrated IS and WAIC and other methods.     

Model selection information criteria in latent class models with missing data and contingency question

Latent class analysis (LCA) has been found to have important applications in social and behavioural sciences for modelling categorical response variables, and non-response is typical when collecting data. In this study, the non-response mainly included ‘contingency questions’ and real ‘missing data’. The primary objective of this study was to evaluate the effects of some potential factors on model selection indices in LCA with non-response data. We simulated missing data with contingency question and evaluated the accuracy rates of eight information criteria for selecting the correct models. The results showed that the main factors are latent class proportions, conditional probabilities, sample size, the number of items, the missing data rate and the contingency data rate. Interactions of the conditional probabilities with class proportions, sample size and the number of items are also significant. From our simulation results, the impact of missing data and contingency questions can be amended by increasing the sample size or the number of items.     

First difference transformation in panel VAR models: Robustness,estimation, and inference

This article considers estimation of Panel Vector Autoregressive Models of order 1 (PVAR(1)) with focus on fixed T consistent estimation methods in First Differences (FD) with additional strictly exogenous regressors. Additional results for the Panel FD ordinary least squares (OLS) estimator and the FDLS type estimator of Han and Phillips (2010 Han, C., Phillips, P. C. B. (2010). Gmm estimation for dynamic panels with fixed effects and strong instruments at unity. Econometric Theory 26:119–151.[Crossref], [Web of Science ®] , [Google Scholar]) are provided. Furthermore, we simplify the analysis of Binder et al. (2005 Binder, M., Hsiao, C., Pesaran, M. H. (2005). Estimation and inference in short panel vector autoregressions with unit root and cointegration. Econometric Theory 21:795–837.[Crossref], [Web of Science ®] , [Google Scholar]) by providing additional analytical results and extend the original model by taking into account possible cross-sectional heteroscedasticity and presence of strictly exogenous regressors. We show that in the three wave panel the log-likelihood function of the unrestricted Transformed Maximum Likelihood (TML) estimator might violate the global identification assumption. The finite-sample performance of the analyzed methods is investigated in a Monte Carlo study.     

Logistic regression and latent class models for estimating positivities in diagnostic assays with poor resolution

In biomedical research and diagnostic practice it is common to classify objects dichotomously based on continuous observations (x) measuring some form of biological activity, where some proportion of the objects have a level of activity above background. In this paper, we consider the problem of estimating the proportion of positive objects for a typical assay where:(i) the distribution of x for positive objects is unknown. although (ii) the risk of positivity is known to be a monotonic function of x:and (iii) x has been measured for a set of negative control objects. Monte Carlo simulations evaluating four alternative estimators of the positivity, including novel non-parametric mixture decompositions, indicate that where the positives and negatives have distributions of x with a moderate degree of overlap, a non-parametric decomposition using a latent class model provides precise and close to unbiased estimates. The methods are illustrated using data from an autoradiography assay used in cell biology.