Optimal planned missing data design for linear latent growth curve models.

Longitudinal data collection is a time-consuming and cost-intensive part of developmental research. Wu et al. (2016) discussed planned missing (PM) designs that are similar in efficiency to complete designs but require fewer observations per person. The authors reported optimal PM designs for linear latent growth curve models based on extensive Monte Carlo simulations. They called for further formal investigation of the question as to how much the proposed PM mechanisms influence study design efficiency to arrive at a better understanding of PM designs. Here, we propose an approximate solution to the design problem by comparing the asymptotic effective errors of PM designs. Effective error was previously used to find optimal longitudinal study designs for complete data designs; here, we extend the approach to planned missing designs. We show how effective error is a metric for comparing the efficiency of study designs with both planned and unplanned missing data, and how earlier simulation-based results for PM designs can be explained by an asymptotic solution. Our approach is computationally more efficient than Wu et al.'s approach and leads to a better understanding of how various design factors, such as the number of measurement occasions, their temporal arrangement, attrition rates, and PM design patterns interact and how they conjointly determine design efficiency. We provide R scripts to calculate effective errors in various scenarios of PM designs.

Finding the mean in a partition distribution.

BACKGROUND: Bayesian clustering algorithms, in particular those utilizing Dirichlet Processes (DP), return a sample of the posterior distribution of partitions of a set. However, in many applied cases a single clustering solution is desired, requiring a 'best' partition to be created from the posterior sample. It is an open research question which solution should be recommended in which situation. However, one such candidate is the sample mean, defined as the clustering with minimal squared distance to all partitions in the posterior sample, weighted by their probability. In this article, we review an algorithm that approximates this sample mean by using the Hungarian Method to compute the distance between partitions. This algorithm leaves room for further processing acceleration. RESULTS: We highlight a faster variant of the partition distance reduction that leads to a runtime complexity that is up to two orders of magnitude lower than the standard variant. We suggest two further improvements: The first is deterministic and based on an adapted dynamical version of the Hungarian Algorithm, which achieves another runtime decrease of at least one order of magnitude. The second improvement is theoretical and uses Monte Carlo techniques and the dynamic matrix inverse. Thereby we further reduce the runtime complexity by nearly the square root of one order of magnitude. CONCLUSIONS: Overall this results in a new mean partition algorithm with an acceleration factor reaching beyond that of the present algorithm by the size of the partitions. The new algorithm is implemented in Java and available on GitHub (Glassen, Mean Partition, 2018).

Classifiers as a model-free group comparison test.

The conventional statistical methods to detect group differences assume correct model specification, including the origin of difference. Researchers should be able to identify a source of group differences and choose a corresponding method. In this paper, we propose a new approach of group comparison without model specification using classification algorithms in machine learning. In this approach, the classification accuracy is evaluated against a binomial distribution using Independent Validation. As an application example, we examined false-positive errors and statistical power of support vector machines to detect group differences in comparison to conventional statistical tests such as t test, Levene's test, K-S test, Fisher's z-transformation, and MANOVA. The SVMs detected group differences regardless of their origins (mean, variance, distribution shape, and covariance), and showed comparably consistent power across conditions. When a group difference originated from a single source, the statistical power of SVMs was lower than the most appropriate conventional test of the study condition; however, the power of SVMs increased when differences originated from multiple sources. Moreover, SVMs showed substantially improved performance with more variables than with fewer variables. Most importantly, SVMs were applicable to any types of data without sophisticated model specification. This study demonstrates a new application of classification algorithms as an alternative or complement to the conventional group comparison test. With the proposed approach, researchers can test two-sample data even when they are not certain which statistical test to use or when data violates the statistical assumptions of conventional methods.

A Group Comparison Test under Uncertain Group Membership.

An overwhelming majority of articles in psychology compare means, often between multiple groups. However, sometimes we do not know the exact group membership, but only a probability to be in one of the groups. Such information may come from classifiers trained on other datasets, prevalence of group memberships for some parts of the sample, multi-level situations where the group membership is only known as a ratio in an upper level, or expert ratings (e.g., whether a person has a pathological condition or not). We present a simple method that allows to compare group means in the absence of exact knowledge about group membership and investigate the loss of information depending on the probability values theoretically and in a large-scale simulation.

Correction: Using the Dirichlet process to form clusters of people's concerns in the context of future party identification.

[This corrects the article DOI: 10.1371/journal.pone.0212944.].

On the power of multivariate latent growth curve models to detect correlated change.

We evaluated the statistical power of single-indicator latent growth curve models (LGCMs) to detect correlated change between two variables (covariance of slopes) as a function of sample size, number of longitudinal measurement occasions, and reliability (measurement error variance). Power approximations following the method of Satorra and Saris (1985) were used to evaluate the power to detect slope covariances. Even with large samples (N = 500) and several longitudinal occasions (4 or 5), statistical power to detect covariance of slopes was moderate to low unless growth curve reliability at study onset was above .90. Studies using LGCMs may fail to detect slope correlations because of low power rather than a lack of relationship of change between variables. The present findings allow researchers to make more informed design decisions when planning a longitudinal study and aid in interpreting LGCM results regarding correlated interindividual differences in rates of development.