Marginalizing pattern-mixture models for categorical data subject to monotone missingness

Many models to analyze incomplete data that allow the missingness to be non-random have been developed. Since such models necessarily rely on unverifiable assumptions, considerable research nowadays is devoted to assess the sensitivity of resulting inferences. A popular sensitivity route, next to local influence (Cook in J Roy Stat Soc Ser B 2:133–169, 1986; Jansen et al. in Biometrics 59:410–419, 2003) and so-called intervals of ignorance (Molenberghs et al. in Appl Stat 50:15–29, 2001), is based on contrasting more conventional selection models with members from the pattern-mixture model family. In the first family, the outcome of interest is modeled directly, while in the second family the natural parameter describes the measurement process, conditional on the missingness pattern. This implies that a direct comparison ought not to be done in terms of parameter estimates, but rather should pass by marginalizing the pattern-mixture model over the patterns. While this is relatively straightforward for linear models, the picture is less clear for the nevertheless important setting of categorical outcomes, since models ordinarily exhibit a certain amount of non-linearity. Following ideas laid out in Jansen and Molenberghs (Pattern-mixture models for categorical outcomes with non-monotone missingness. Submitted for publication, 2007), we offer ways to marginalize pattern-mixture-model-based parameter estimates, and supplement these with asymptotic variance formulas. The modeling context is provided by the multivariate Dale model. The performance of the method and its usefulness for sensitivity analysis is scrutinized using simulations.     

Simulation driven inferences for multiply imputed longitudinal datasets*

In this article, we demonstrate by simulations that rich imputation models for incomplete longitudinal datasets produce more calibrated estimates in terms of reduced bias and higher coverage rates without duly deflating the efficiency. We argue that the use of supplementary variables that are thought to be potential causes or correlates of missingness or outcomes in the imputation process may lead to better inferential results in comparison to simpler imputation models. The liberal use of these variables is recommended as opposed to the conservative strategy.     

三维激光扫描仪应用技术研究

三维激光扫描是近年来迅速发展起来的一种新型空间数据获取手段和工具,利用地面三维激光扫描系统可以快速、准确地进行城市三维重建,因而在城市建模研究与应用方面受到越来越广泛的关注。本文以三维城市建模中的建筑物为研究对象,探讨如何利用三维激光扫描仪获取空间数据并建立相应地物模型的技术方法。     

Measuring the impact of nonignorability in panel data with non‐monotone nonresponse

The analysis of panel data with non‐monotone nonresponse often relies on the critical and untestable assumption of ignorable missingness. It is important to assess the consequences of departures from the ignorability assumption. Non‐monotone nonresponse, however, can often make such sensitivity analysis infeasible because the likelihood functions for alternative models involve high‐dimensional and difficult‐to‐evaluate integrals with respect to missing outcomes. We develop an extension of the local sensitivity method that overcomes computational difficulty and completely avoids fitting alternative models and evaluating these high‐dimensional integrals. The proposed method is applicable to a wide range of panel outcomes. We apply the method to a Smoking Trend dataset where we relax the standard ignorability assumption and evaluate how smoking‐trend estimates in different groups of US young adults are affected by alternative assumptions about the missing‐data mechanism. The main finding is that the standard estimate in the black male group is sensitive to nonignorable missingness but those in other groups are reasonably robust. Copyright © 2010 John Wiley & Sons, Ltd.     

Monotone missing data and pattern-mixture models

It is shown that the classical taxonomy of missing data models, namely missing completely at random, missing at random and informative missingness, which has been developed almost exclusively within a selection modelling framework, can also be applied to pattern-mixture models. In particular, intuitively appealing identifying restrictions are proposed for a pattern-mixture MAR mechanism.     

A Random Effects Transition Model For Longitudinal Binary Data With Informative Missingness

Understanding the transitions between disease states is often the goal in studying chronic disease. These studies, however, are typically subject to a large amount of missingness either due to patient dropout or intermittent missed visits. The missing data is often informative since missingness and dropout are usually related to either an individual's underlying disease process or the actual value of the missed observation. Our motivating example is a study of opiate addiction that examined the effect of a new treatment on thrice-weekly binary urine tests to assess opiate use over follow-up. The interest in this opiate addiction clinical trial was to characterize the transition pattern of opiate use (in each treatment arm) as well as to compare both the marginal probability of a positive urine test over follow-up and the time until the first positive urine test between the treatment arms. We develop a shared random effects model that links together the propensity of transition between states and the probability of either an intermittent missed observation or dropout. This approach allows for heterogeneous transition and missing data patterns between individuals as well as incorporating informative intermittent missing data and dropout. We compare this new approach with other approaches proposed for the analysis of longitudinal binary data with informative missingness.     

The Multilevel Approach to Repeated Measures for Complete and Incomplete Data

Repeated measurements often are analyzed by multivariate analysis of variance (MANOVA). An alternative approach is provided by multilevel analysis, also called the hierarchical linear model (HLM), which makes use of random coefficient models. This paper is a tutorial which indicates that the HLM can be specified in many different ways, corresponding to different sets of assumptions about the covariance matrix of the repeated measurements. The possible assumptions range from the very restrictive compound symmetry model to the unrestricted multivariate model. Thus, the HLM can be used to steer a useful middle road between the two traditional methods for analyzing repeated measurements. Another important advantage of the multilevel approach to analyzing repeated measures is the fact that it can be easily used also if the data are incomplete. Thus it provides a way to achieve a fully multivariate analysis of repeated measures with incomplete data. This revised version was published online in June 2006 with corrections to the Cover Date.     

Inferential Implications of Over‐Parametrization: A Case Study in Incomplete Categorical Data

In the context of either Bayesian or classical sensitivity analyses of over‐parametrized models for incomplete categorical data, it is well known that prior‐dependence on posterior inferences of nonidentifiable parameters or that too parsimonious over‐parametrized models may lead to erroneous conclusions. Nevertheless, some authors either pay no attention to which parameters are nonidentifiable or do not appropriately account for possible prior‐dependence. We review the literature on this topic and consider simple examples to emphasize that in both inferential frameworks, the subjective components can influence results in nontrivial ways, irrespectively of the sample size. Specifically, we show that prior distributions commonly regarded as slightly informative or noninformative may actually be too informative for nonidentifiable parameters, and that the choice of over‐parametrized models may drastically impact the results, suggesting that a careful examination of their effects should be considered before drawing conclusions.     

Improving forecasting for telemarketing centers by ARIMA modeling with intervention

In this study we analyze existing and improved methods for forecasting incoming calls to telemarketing centers for the purposes of planning and budgeting. We analyze the use of additive and multiplicative versions of Holt–Winters (HW) exponentially weighted moving average models and compare it to Box–Jenkins (ARIMA) modeling with intervention analysis. We determine the forecasting accuracy of HW and ARIMA models for samples of telemarketing data. Although there is much evidence in recent literature that “simple models” such as Holt–Winters perform as well as or better than more complex models, we find that ARIMA models with intervention analysis perform better for the time series studied.     

How to handle missing data in regression models using information criteria*

An important application of multiple regression is predictor selection. When there are no missing values in the data, information criteria can be used to select predictors. For example, one could apply the small‐sample‐size corrected version of the Akaike information criterion (AIC), the (AICC). In this article, we discuss how information criteria should be calculated when the dependent variable and/or the predictors contain missing values. Therewith, we extensively discuss and evaluate three models that can be employed to deal with the missing data, that is, to predict the missing values. The most complex model, that is, the model with all available predictors, outperforms the other models. These results also apply to more general hypotheses than predictor selection and also to structural equation modeling (SEM) models.     

The influence of seller learning and time constraints on sequential bargaining in an artificial perishable goods market

This paper investigates the formation of prices in a perishable goods market where agents bargain repeatedly through pair-wise interactions. After extensive field observations, we chose to focus on two aspects that seem important to actors of this market: the passage of time and update in judgement when gathering information. The main feature of the market is that a seller bargaining with a buyer has incomplete information about buyer's willingness to pay and is not sure how her trading partner will evaluate an offer or compare it with other options. On the other hand, buyers have limited time to look for goods and cannot meet all possible sellers before making a decision. Hence agents cannot calculate the best price to offer but receive information through limited interactions, and use this information to choose their actions.An agent-based model was built to represent a framework that mimics the observed market institution and where agent's possible behaviors and learning was made as consistent as possible with gathered data. Simulations were run, first for sensitivity analysis concerning main parameters, then to test the dependance of agents’ learning to (a) the time buyers can spend on the market and (b) the frequency of update in learning by sellers. To validate the model, features produced by the simulated market are compared to the stylized facts gathered for negotiation about four goods. We reproduce the main features of the data on the dynamics of offers, transaction prices and agents’ behavior during the bargaining phases.     

Comparing Time Series Cross-Section Model Specifications: The Case of Welfare State Development

In recent years, an impressive number of pooled time series (TSCS) cross-section models have been estimated in order to test hypotheses on welfare state development. Although most of these models share several of the variables, they can often be distinguished by the model specification adopted. This begs the question: what is the appropriate specification for modeling welfare state development? In order to answer this question some leading specifications are evaluated with respect to their ability to meet the theoretical assumptions about the theory of welfare state evolution in addition to the econometric canons on panel analysis. The main conclusions of this paper are the following. First, all specifications in levels are econometrically unfounded because most of the variables typically used for analyzing this topic cannot be considered to be stationary. Second, although a first difference model performs better from an econometric point of view, it is unable to test the hypothesized long-term relationships underlying welfare state dynamics. Third, and more importantly, the single equation error correction model represents the best pooled TSCS specification for modeling welfare state development since it is able tocapture long-run effects even in the presence of nonstationary processes.     

Continuous time modeling of panel data: SEM versus filter techniques

Although convincing arguments have been put forward for continuous-time modeling, its use in panel research is rare. In one approach, classical N  = 1 state-space modeling procedures are adapted for panel analysis to estimate the exact discrete model (EDM) by means of filter techniques. Based on earlier less satisfactory indirect methods, a more recent approach uses structural equation modeling (SEM) to get the maximum likelihood estimate of the EDM by the direct method. After an introduction into continuous-time state-space modeling for panel data and the EDM, a thorough comparison is made between the two distinct approaches with quite different histories by means of Monte Carlo simulation studies. The model used in the simulation studies is the damped linear oscillator with and without random subject effects.     

Handling Missing Data by Re-approaching Non-respondents

When handling missing data, a researcher should be aware of the mechanism underlying the missingness. In the presence of non-randomly missing data, a model of the missing data mechanism should be included in the analyses to prevent the analyses based on the data from becoming biased. Modeling the missing data mechanism, however, is a difficult task. One way in which knowledge about the missing data mechanism may be obtained is by collecting additional data from non-respondents. In this paper the method of re-approaching respondents who did not answer all questions of a questionnaire is described. New answers were obtained from a sample of these non-respondents and the reason(s) for skipping questions was (were) probed for. The additional data resulted in a larger sample and was used to investigate the differences between respondents and non-respondents, whereas probing for the causes of missingness resulted in more knowledge about the nature of the missing data patterns.     

Estimating latent class model parameters for filter questions with skip patterns

Filter questions with skip patterns have been widely used in survey research, and latent class models (LCM) are often used to analyze this type of categorical data. The LCM parameters are usually estimated by means of an EM (expectation maximization) algorithm. When the pattern is present, the non-response of the skip pattern cannot be treated as random missingness. We thus propose a modified algorithm to estimate the latent class parameters when non-response is present, and the approach is attractive for two reasons. First, the latent class model with the algorithm is very flexible in the sense that it can model the association of variables with the skip patterns under study. Secondly, the algorithm can be easily implemented using any computer language. An empirical example is used to demonstrate the usefulness of the algorithm. The algorithm may also be flexibly generalized to more complex surveys, for example, polytomous responses.     

A composite indicator of social inclusion for EU based on the inverted BoD model

In this paper, after reviewing the existing modeling approaches for reverse indicators, we opt for the use of the inverted Benefit-of-the-doubt (IBoD) model when all the considered indicators are reverse, as is the case with composite indicators related to social inclusion. Using EU data for 2014 we provide comparative empirical results using the IBoD model and three data transformations employed by previous studies. We also provide a thorough analysis of the performance of EU countries during the period 2011–2020 in terms of the composite indicator obtained from the IBoD model. Our empirical results indicate that relative performance across the EU has neither improved nor deteriorated and there is evidence supporting local instead of global convergence in social inclusion with certain groups of countries.     

The Lognormal Distribution as a Model for Survival Time in Cancer, With an Emphasis on Prognostic Factors

Despite their long history, parametric survival-time models have largely been neglected in the modern biostatistical and medical literature in favour of the Cox proportional hazards model. Here, I present a case for the use of the lognormal distribution in the analysis of survival times of breast and ovarian cancer patients, specifically in modelling the effects of prognostic factors. The lognormal provides a completely specified probability distribution for the observations and a sensible estimate of the variation explained by the model, a quantity that is controversial for the Cox model. I show how imputation of censored observations under the model may be used to inspect the data using familiar graphical and other technques. Results from the Cox and lognormal models are compared and shown apparently to differ to some extent. However, it is hard to judge which model gives the more accurate estimates. It is concluded that provided the lognormal model fits the data adequately, it may be a useful approach to the analysis of censored survival data.     

Technical efficiency in competing panel data models: a study of Norwegian grain farming

Estimation of technical efficiency is widely used in empirical research using both cross-sectional and panel data. Although several stochastic frontier models for panel data are available, only a few of them are normally applied in empirical research. In this article we chose a broad selection of such models based on different assumptions and specifications of heterogeneity, heteroskedasticity and technical inefficiency. We applied these models to a single dataset from Norwegian grain farmers for the period 2004–2008. We also introduced a new model that disentangles firm effects from persistent (time-invariant) and residual (time-varying) technical inefficiency. We found that efficiency results are quite sensitive to how inefficiency is modeled and interpreted. Consequently, we recommend that future empirical research should pay more attention to modeling and interpreting inefficiency as well as to the assumptions underlying each model when using panel data.     

Analysis of treatment response data without the joint distribution of potential outcomes

In this paper we show how it is possible to develop a Bayesian framework for analyzing structural models for treatment response data without the joint distribution of the potential outcomes. That this is possible has not been noticed in the literature. We also discuss the computation of the model marginal likelihood and present recipes for finding relevant treatment effects, averaged over both parameters and covariates. As compared to an approach in which the counterfactuals are part of the prior-posterior analysis (as in the work to date), the approach we suggest is simpler in terms of the required prior inputs, computational burden and extensibility to more complex settings.