Local Optima in Mixture Modeling

Psychotic experiences and negative symptoms from adolescence to emerging adulthood: developmental trajectories and associations with polygenic scores and childhood characteristics

BACKGROUND

Psychotic experiences and negative symptoms (PENS) are common in non-clinical populations. PENS are associated with adverse outcomes, particularly when they persist. Little is known about the trajectories of PENS dimensions in young people, nor about the precursory factors associated with these trajectories.

METHODS

We conducted growth mixture modelling of paranoia, hallucinations, and negative symptoms across ages 16, 17, and 22 in a community sample (N = 12 049-12 652). We then described the emergent trajectory classes through their associations with genome-wide polygenic scores (GPS) for psychiatric and educational phenotypes, and earlier childhood characteristics.

RESULTS

Three trajectory classes emerged for paranoia, two for hallucinations, and two for negative symptoms. Across PENS, GPS for clinical help-seeking, major depressive disorder, and attention deficit hyperactivity disorder were associated with increased odds of being in the most elevated trajectory class (OR 1.07-1.23). Lower education GPS was associated with the most elevated trajectory class for hallucinations and negative symptoms (OR 0.77-0.91). Conversely for paranoia, higher education GPS was associated with the most elevated trajectory class (OR 1.25). Trajectory class associations were not significant for schizophrenia, obsessive-compulsive disorder, bipolar disorder, or anorexia GPS. Emotional/behaviour problems and life events in childhood were associated with increased odds of being in the most elevated trajectory class across PENS.

CONCLUSIONS

Our results suggest latent heterogeneity in the development of paranoia, hallucinations, and negative symptoms in young people that is associated with specific polygenic scores and childhood characteristics.

Discovering Exceptional Development of Commitment in Interdisciplinary Study Programs

Abstract. In psychology and the social sciences, it is often of interest how complex structural relations among variables are moderated by profiles or combinations of persons’ attributes. Some state-of-the-art methods, such as latent class analysis, are well-suited for this purpose. However, they can lead to methodological problems (e.g., convergence issues) or interpretative difficulties (e.g., due to nondistinctive profiles). For these cases, two other approaches combining structural equation modeling with machine learning have been proposed, namely structural equation model (SEM) trees and SubgroupSEM. These approaches allow for exploration of how parameters of a SEM differ depending on combinations of a person's attributes. This can be useful for generating hypotheses for future research. In this paper, we provide an empirical illustration of SubgroupSEM using an example from research on the development of commitment in interdisciplinary study programs in German higher education and identify combinations of vocational interests related to exceptional development.

Benchmarking distance-based partitioning methods for mixed-type data

Clustering mixed-type data, that is, observation by variable data that consist of both continuous and categorical variables poses novel challenges. Foremost among these challenges is the choice of the most appropriate clustering method for the data. This paper presents a benchmarking study comparing eight distance-based partitioning methods for mixed-type data in terms of cluster recovery performance. A series of simulations carried out by a full factorial design are presented that examined the effect of a variety of factors on cluster recovery. The amount of cluster overlap, the percentage of categorical variables in the data set, the number of clusters and the number of observations had the largest effects on cluster recovery and in most of the tested scenarios. KAMILA, K-Prototypes and sequential Factor Analysis and K-Means clustering typically performed better than other methods. The study can be a useful reference for practitioners in the choice of the most appropriate method.

A Latent Block Distance-Association Model for Profile by Profile Cross-Classified Categorical Data

Distance association models constitute a useful tool for the analysis and graphical representation of cross-classified data in which distances between points inversely describe the association between two categorical variables. When the number of cells is large and the data counts result in sparse tables, the combination of clustering and representation reduces the number of parameters to be estimated and facilitates interpretation. In this article, a latent block distance-association model is proposed to apply block clustering to the outcomes of two categorical variables while the cluster centers are represented in a low dimensional space in terms of a distance-association model. This model is particularly useful for contingency tables in which both the rows and the columns are characterized as profiles of sets of response variables. The parameters are estimated under a Poisson sampling scheme using a generalized EM algorithm. The performance of the model is tested in a Monte Carlo experiment, and an empirical data set is analyzed to illustrate the model.

Implementing continuous non-normal skewed distributions in latent growth mixture modeling: An assessment of specification errors and class enumeration

Recent advances have allowed for modeling mixture components within latent growth modeling using robust, skewed mixture distributions rather than normal distributions. This feature adds flexibility in handling non-normality in longitudinal data, through manifest or latent variables, by directly modeling skewed or heavy-tailed latent classes rather than assuming a mixture of normal distributions. The aim of this study was to assess through simulation the potential under- or over-extraction of latent classes in a growth mixture model when underlying data follow either normal, skewed-normal, or skewed-t distributions. In order to assess this, we implement skewed-t, skewed-normal, and conventional normal (i.e., not skewed) forms of the growth mixture model. The skewed-t and skewed-normal versions of this model have only recently been implemented, and relatively little is known about their performance. Model comparison, fit, and classification of correctly specified and mis-specified models were assessed through various indices. Findings suggest that the accuracy of model comparison and fit measures are dependent on the type of (mis)specification, as well as the amount of class separation between the latent classes. A secondary simulation exposed computation and accuracy difficulties under some skewed modeling contexts. Implications of findings, recommendations for applied researchers, and future directions are discussed; a motivating example is presented using education data.

A note on the expected value of the Rand index

Two expectations of the adjusted Rand index (ARI) are compared. It is shown that the expectation derived by Morey and Agresti (1984, Educational and Psychological Measurement, 44, 33) under the multinomial distribution to approximate the exact expectation from the hypergeometric distribution (Hubert & Arabie, 1985, Journal of Classification, 2, 193) provides a poor approximation, and, in some cases, the difference between the two expectations can increase with the sample size. Proofs concerning the minimum and maximum difference between the two expectations are provided, and it is shown through simulation that the ARI can differ significantly depending on which expectation is used. Furthermore, when compared in a hypothesis testing framework, multinomial approximation overly favours the null hypothesis.

Fuzzy Profiles

Person-centered approaches to organizational scholarship can provide critical insights into how sets of related constructs uniquely combine to predict outcomes. Within micro topics, scholars have begun to embrace the use of latent profile analysis (LPA), identifying constellations of constructs related to organizational commitment, turnover intentions, emotional labor, recovery, and well-being, to name a few. Conversely, macro scholars have utilized fuzzy set qualitative comparative analysis (fsQCA) to examine numerous phenomena, such as acquisitions and business strategies, as configurations of explanatory conditions associated with firm-level outcomes. What remains unclear, however, is the extent to which these two approaches deliver similar versus unique insights when applied to the same topic. In this paper, we offer an overview of the ways these two methods converge and diverge, and provide an empirical demonstration by applying both LPA and fsQCA to examine a multidimensional personality construct—core self-evaluations (CSE)—in relation to job satisfaction. In so doing, we offer guidance for scholars who are either choosing between these two methods, or are seeking to use the two methods in a complementary, theory-building manner.

Detecting Clusters/Communities in Social Networks

Cohen's κ, a similarity measure for categorical data, has since been applied to problems in the data mining field such as cluster analysis and network link prediction. In this paper, a new application is examined: community detection in networks. A new algorithm is proposed that uses Cohen's κ as a similarity measure for each pair of nodes; subsequently, the κ values are then clustered to detect the communities. This paper defines and tests this method on a variety of simulated and real networks. The results are compared with those from eight other community detection algorithms. Results show this new algorithm is consistently among the top performers in classifying data points both on simulated and real networks. Additionally, this is one of the broadest comparative simulations for comparing community detection algorithms to date.

Examining the effect of initialization strategies on the performance of Gaussian mixture modeling

Mixture modeling is a popular technique for identifying unobserved subpopulations (e.g., components) within a data set, with Gaussian (normal) mixture modeling being the form most widely used. Generally, the parameters of these Gaussian mixtures cannot be estimated in closed form, so estimates are typically obtained via an iterative process. The most common estimation procedure is maximum likelihood via the expectation-maximization (EM) algorithm. Like many approaches for identifying subpopulations, finite mixture modeling can suffer from locally optimal solutions, and the final parameter estimates are dependent on the initial starting values of the EM algorithm. Initial values have been shown to significantly impact the quality of the solution, and researchers have proposed several approaches for selecting the set of starting values. Five techniques for obtaining starting values that are implemented in popular software packages are compared. Their performances are assessed in terms of the following four measures: (1) the ability to find the best observed solution, (2) settling on a solution that classifies observations correctly, (3) the number of local solutions found by each technique, and (4) the speed at which the start values are obtained. On the basis of these results, a set of recommendations is provided to the user.