Bayesian Inference for Growth Mixture Models with Latent Class Dependent Missing Data

Summary We propose a method for estimating parameters in generalized linear models with missing covariates and a non-ignorable missing data mechanism. We use a multinomial model for the missing data indicators and propose a joint distribution for them which can be written as a sequence of one-dimensional conditional distributions, with each one-dimensional conditional distribution consisting of a logistic regression. We allow the covariates to be either categorical or continuous. The joint covariate distribution is also modelled via a sequence of one-dimensional conditional distributions, and the response variable is assumed to be completely observed. We derive the E- and M-steps of the EM algorithm with non-ignorable missing covariate data. For categorical covariates, we derive a closed form expression for the E- and M-steps of the EM algorithm for obtaining the maximum likelihood estimates (MLEs). For continuous covariates, we use a Monte Carlo version of the EM algorithm to obtain the MLEs via the Gibbs sampler. Computational techniques for Gibbs sampling are proposed and implemented. The parametric form of the assumed missing data mechanism itself is not ‘testable' from the data, and thus the non-ignorable modelling considered here can be viewed as a sensitivity analysis concerning a more complicated model. Therefore, although a model may have ‘passed' the tests for a certain missing data mechanism, this does not mean that we have captured, even approximately, the correct missing data mechanism. Hence, model checking for the missing data mechanism and sensitivity analyses play an important role in this problem and are discussed in detail. Several simulations are given to demonstrate the methodology. In addition, a real data set from a melanoma cancer clinical trial is presented to illustrate the methods proposed.

ABSTRACTInequality-restricted hypotheses testing methods containing multivariate one-sided testing methods are useful in practice, especially in multiple comparison problems. In practice, multivariate and longitudinal data often contain missing values since it may be difficult to observe all values for each variable. However, although missing values are common for multivariate data, statistical methods for multivariate one-sided tests with missing values are quite limited. In this article, motivated by a dataset in a recent collaborative project, we develop two likelihood-based methods for multivariate one-sided tests with missing values, where the missing data patterns can be arbitrary and the missing data mechanisms may be non-ignorable. Although non-ignorable missing data are not testable based on observed data, statistical methods addressing this issue can be used for sensitivity analysis and might lead to more reliable results, since ignoring informative missingness may lead to biased analysis. We analyse the real dataset in details under various possible missing data mechanisms and report interesting findings which are previously unavailable. We also derive some asymptotic results and evaluate our new tests using simulations.

Latent class based multiple imputation approach for missing categorical data

BackgroundMissing data due to attrition are rampant in substance abuse clinical trials. However, missing data are often ignored in the presentation of substance abuse clinical trials. This paper demonstrates missing data methods which may be used for hypothesis testing.MethodsMethods involving stratifying and weighting individuals based on missing data pattern are shown to produce tests that are robust to missing data mechanisms in terms of Type I error and power. In this article, we describe several methods of combining data that may be used for testing hypotheses of the treatment effect. Furthermore, illustrations of each test's Type I error and power under different missing data percentages and mechanisms are quantified using a Monte-Carlo simulation study.ResultsType I error rates were similar for each method, while powers depended on missing data assumptions. Specifically, power was greatest for the weighted, compared to un-weighted methods, especially for greater missing data percentages.ConclusionResults of this study as well as extant literature demonstrate the need for standards of design and analysis specific to substance abuse clinical trials. Given the known substantial attrition rates and concern for the missing data mechanism in substance abuse clinical trials, investigators need to incorporate missing data methods a priori. That is, missing data methods should be specified at the outset of the study and not after the data have been collected.

Childhood Socioeconomic Status and Depressive Symptom Trajectories in the Transition to Adulthood in the United States and Canada

A more nuanced understanding of individuals' patterns of alcohol use during adolescence, a key developmental period for the onset of use, is of critical importance for refining preventive interventions in this population. To this end, growth mixture modeling (GMM) is a statistical technique that may be used to identify latent subgroups of individuals who exhibit distinct patterns of alcohol use over time. Decisions regarding the timing and interval of survey assessments are particularly challenging in the context of GMM. Latent subgroups exhibit different trends in alcohol use, and these trends must be adequately captured by the survey assessments. Accordingly, the specific aims of the current research were to investigate how measurement timing (i.e., timing and spacing of assessments) affected the identification of the latent subgroups with: (1) an applied study using alcohol data from the National Longitudinal Survey of Youth (NLSY) 1997 and (2) a Monte Carlo simulation study. Participants from the NLSY1997 were 15 and 16 years old at Wave 1 (n = 2686, 49.44% female). Alterations in measurement timing were examined using five different assessment configurations: all 12 waves, two-year intervals, uneven intervals, the first six waves, and the last seven waves. The outcome, the number of drinks consumed per month, was assessed at each of 12 waves that spanned 11.5 years. The results of the applied study with the NLSY data were used as population parameters in the simulation study. The experimental factors investigated in the simulation study were measurement timing and sample size. First, the applied study revealed that the five-class GMM results were very similar when using all 12 waves versus two-year intervals. Only four participants were misclassified (i.e., assigned to subgroups with different average alcohol trajectories). Second, the five-class GMM results when comparing all 12 waves to either the configuration with uneven intervals or the first six waves showed some degree of discrepancy with approximately 14% of the sample being misclassified. Third, the largest discrepancy in the five-class GMM results was observed when comparing the 12 wave and last seven wave configurations with 62% of the sample being misclassified. The simulation study showed that the 95% coverage estimates of the parameters (i.e., factor means, factor variances, factor covariance) were greater than .90 for four of the five assessment configurations, with the exception being the last seven waves. Three of the five assessment configurations produced average estimates of the parameters that were close to the

Robust growth mixture models with non-ignorable missingness: Models, estimation, selection, and application

Purpose Our objectives were to (a) identify oral and pharyngeal physiologic swallowing impairment severity classes based on latent class analyses (LCAs) of the Modified Barium Swallow Impairment Profile (MBSImP) swallow task scores and (b) quantify the probability of severity class membership given composite MBSImP oral total (OT) and pharyngeal total (PT) scores. Method MBSImP scores were collected from a patient database of 319 consecutive modified barium swallow studies. Because of missing swallow task scores, LCA was performed using 25 multiply imputed data sets. Results LCA revealed a three-class structure for both oral and pharyngeal models. We identified OT and PT score intervals to assign subjects to oral and pharyngeal impairment latent severity classes, respectively, with high probability (probability of class membership ≥ 0.9 given OT or PT scores within specified ranges) and high confidence (95% credible interval [CI] widths ≤ 0.24 for all total scores within specified ranges). OT scores ranging from 0 to 10 and from 14 to 18 yielded assignments in Oral Latent Classes 1 and 2, respectively, while OT = 22 was assigned to Oral Latent Class 3. PT scores ranging from 0 to 13 and from 18 to 24 yielded assignments in Pharyngeal Latent Classes 1 and 2, respectively, while PT = 26 was assigned to Pharyngeal Latent Class 3. Conclusions LCA of MBSImP task-level data revealed significant underlying oral and pharyngeal ordinal class structures representing increasingly severe gradations of physiologic swallow impairment. Clinically meaningful OT and PT score ranges were derived facilitating latent class assignment. Supplemental Material https://doi.org/10.23641/asha.12315677.

Retirement Security: Better Information on Income Replacement Rates Needed to Help Workers Plan for Retirement

Determining the number of factors in exploratory factor analysis is arguably the most crucial decision a researcher faces when conducting the analysis. While several simulation studies exist that compare various so-called factor retention criteria under different data conditions, little is known about the impact of missing data on this process. Hence, in this study, we evaluated the performance of different factor retention criteria—the Factor Forest, parallel analysis based on a principal component analysis as well as parallel analysis based on the common factor model and the comparison data approach—in combination with different missing data methods, namely an expectation-maximization algorithm called Amelia, predictive mean matching, and random forest imputation within the multiple imputations by chained equations (MICE) framework as well as pairwise deletion with regard to their accuracy in determining the number of factors when data are missing. Data were simulated for different sample sizes, numbers of factors, numbers of manifest variables (indicators), between-factor correlations, missing data mechanisms and proportions of missing values. In the majority of conditions and for all factor retention criteria except the comparison data approach, the missing data mechanism had little impact on the accuracy and pairwise deletion performed comparably well as the more sophisticated imputation methods. In some conditions, especially small-sample cases and when comparison data were used to determine the number of factors, random forest imputation was preferable to other missing data methods, though. Accordingly, depending on data characteristics and the selected factor retention criterion, choosing an appropriate missing data method is crucial to obtain a valid estimate of the number of factors to extract.

There is increasing interest in modelling longitudinal dietary data and classifying individuals into subgroups (latent classes) who follow similar trajectories over time. These trajectories could identify population groups and time points amenable to dietary interventions. This paper aimed to provide a comparison and overview of two latent class methods: group-based trajectory modelling (GBTM) and growth mixture modelling (GMM). Data from 2963 mother–child dyads from the longitudinal Southampton Women’s Survey were analysed. Continuous diet quality indices (DQI) were derived using principal component analysis from interviewer-administered FFQ collected in mothers pre-pregnancy, at 11- and 34-week gestation, and in offspring at 6 and 12 months and 3, 6–7 and 8–9 years. A forward modelling approach from 1 to 6 classes was used to identify the optimal number of DQI latent classes. Models were assessed using the Akaike and Bayesian information criteria, probability of class assignment, ratio of the odds of correct classification, group membership and entropy. Both methods suggested that five classes were optimal, with a strong correlation (Spearman’s = 0·98) between class assignment for the two methods. The dietary trajectories were categorised as stable with horizontal lines and were defined as poor (GMM = 4 % and GBTM = 5 %), poor-medium (23 %, 23 %), medium (39 %, 39 %), medium-better (27 %, 28 %) and best (7 %, 6 %). Both GBTM and GMM are suitable for identifying dietary trajectories. GBTM is recommended as it is computationally less intensive, but results could be confirmed using GMM. The stability of the diet quality trajectories from pre-pregnancy underlines the importance of promotion of dietary improvements from preconception onwards.

The Driving Forces Behind Nurses Leaving the Profession

The true missing data mechanism is never known in practice. We present a method for generating multiple imputations for binary variables, which formally incorporates missing data mechanism uncertainty. Imputations are generated from a distribution of imputation models rather than a single model, with the distribution reflecting subjective notions of missing data mechanism uncertainty. Parameter estimates and standard errors are obtained using rules for nested multiple imputation. Using simulation, we investigate the impact of missing data mechanism uncertainty on post-imputation inferences and show that incorporating this uncertainty can increase the coverage of parameter estimates. We apply our method to a longitudinal smoking cessation trial where nonignorably missing data were a concern. Our method provides a simple approach for formalizing subjective notions regarding nonresponse and can be implemented using existing imputation software.

Research in applied areas, such as statistical, psychological, behavioral, and educational areas, often involves the selection of the best available model from among a large set of candidate models. Considering that there is no well-defined model selection criterion in a Bayesian context and that latent growth mixture models are becoming popular in many areas, the goal of this study is to investigate the performance of a series of model selection criteria in the framework of latent growth mixture models with missing data and outliers in a Bayesian context. This study conducted five simulation studies to cover different cases, including latent growth curve models with missing data, latent growth curve models with missing data and outliers, growth mixture models with missing data and outliers, extended growth mixture models with missing data and outliers, and latent growth models with different classes. Simulation results show that almost all the proposed criteria can effectively identify the true models. This study also illustrated the application of these model selection criteria in real data analysis. The results will help inform the selection of growth models by researchers seeking to provide states with accurate estimates of the growth of their students.

Growth mixture models (GMMs) are prevalent for modeling unknown population heterogeneity via distinct latent classes. However, GMMs are riddled with convergence issues, often requiring researchers to atheoretically alter the model with cross-class constraints simply to obtain convergence. We discuss how within-class random effects in GMMs exacerbate convergence issues, even though these random effects rarely help answer typical research questions. That is, latent classes provide a discretization of continuous random effects, so including additional random effects within latent classes can unnecessarily complicate the model. These random effects are commonly included in order to properly specify the marginal covariance; however, random effects are inefficient for patterning a covariance matrix, resulting in estimation issues. Such a goal can be achieved more simply through covariance pattern models, which we extend to the mixture model context in this article (covariance pattern mixture models, or CPMMs). We provide evidence from theory, simulation, and an empirical example showing that employing CPMMs (even if they are misspecified) instead of GMMs can circumvent the computational difficulties that can plague GMMs, without sacrificing the ability to answer the types of questions commonly asked in empirical studies. Our results show the advantages of CPMMs with respect to improved class enumeration and less biased class-specific growth trajectories, in addition to their vastly improved convergence rates. The results also show that constraining the covariance parameters across classes in order to bypass convergence issues with GMMs leads to poor results. An extensive software appendix is included to assist researchers in running CPMMs in Mplus.