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.

Local Optima in Mixture Modeling.

It is common knowledge that mixture models are prone to arrive at locally optimal solutions. Typically, researchers are directed to utilize several random initializations to ensure that the resulting solution is adequate. However, it is unknown what factors contribute to a large number of local optima and whether these coincide with the factors that reduce the accuracy of a mixture model. A real-data illustration and a series of simulations are presented that examine the effect of a variety of data structures on the propensity of local optima and the classification quality of the resulting solution. We show that there is a moderately strong relationship between a solution that has a high proportion of local optima and one that is poorly classified.

Item Responses in Quantity-Frequency Questionnaires: Implications for Data Generalizability.

Alcohol consumption is an important predictor of a variety of negative outcomes. There is an extensive literature that examines the differences in the estimated level of alcohol consumption between types of assessments (e.g., quantity-frequency [QF] questionnaires, daily diaries). However, it is typically assumed that all QF-based measures are nearly identical in their assessment of the volume of alcohol consumption in a population. Using timeline follow-back data and constructing common QF consumption measures, we examined differences among survey instruments to assess alcohol consumption and heavy drinking. Using three data sets, including clinical to community samples, we demonstrate how scale-specific item characteristics (i.e., number of response options and ranges of consumption assessed by each option) can substantially affect the estimated mean level of consumption and estimated prevalence of binge drinking. Our analyses suggest that problems can be mitigated by employing more resolved measures of quantity and frequency in consumption questionnaires.

A comparison of latent class, K-means, and K-median methods for clustering dichotomous data.

The problem of partitioning a collection of objects based on their measurements on a set of dichotomous variables is a well-established problem in psychological research, with applications including clinical diagnosis, educational testing, cognitive categorization, and choice analysis. Latent class analysis and K-means clustering are popular methods for partitioning objects based on dichotomous measures in the psychological literature. The K-median clustering method has recently been touted as a potentially useful tool for psychological data and might be preferable to its close neighbor, K-means, when the variable measures are dichotomous. We conducted simulation-based comparisons of the latent class, K-means, and K-median approaches for partitioning dichotomous data. Although all 3 methods proved capable of recovering cluster structure, K-median clustering yielded the best average performance, followed closely by latent class analysis. We also report results for the 3 methods within the context of an application to transitive reasoning data, in which it was found that the 3 approaches can exhibit profound differences when applied to real data. (PsycINFO Database Record

Gaussian model-based partitioning using iterated local search.

The emergence of Gaussian model-based partitioning as a viable alternative to K-means clustering fosters a need for discrete optimization methods that can be efficiently implemented using model-based criteria. A variety of alternative partitioning criteria have been proposed for more general data conditions that permit elliptical clusters, different spatial orientations for the clusters, and unequal cluster sizes. Unfortunately, many of these partitioning criteria are computationally demanding, which makes the multiple-restart (multistart) approach commonly used for K-means partitioning less effective as a heuristic solution strategy. As an alternative, we propose an approach based on iterated local search (ILS), which has proved effective in previous combinatorial data analysis contexts. We compared multistart, ILS and hybrid multistart-ILS procedures for minimizing a very general model-based criterion that assumes no restrictions on cluster size or within-group covariance structure. This comparison, which used 23 data sets from the classification literature, revealed that the ILS and hybrid heuristics generally provided better criterion function values than the multistart approach when all three methods were constrained to the same 10-min time limit. In many instances, these differences in criterion function values reflected profound differences in the partitions obtained.

Sex differences in the latent class structure of alcohol use disorder: Does (dis)aggregation of indicators matter?

Many researchers have argued for a differential presentation of alcohol use disorder (AUD) between men and women. Latent class analysis is the most commonly used analytic technique for modeling AUD subcategories, and latent class analyses have supported a variety of class structures of AUD. This article examines whether these differential results are, in part, an artifact of whether researchers have (a) analyzed men and women in the same analysis and (b) aggregated item-level symptoms into AUD diagnostic criteria prior to analysis. These related methodological issues are examined using Wave 2 data from the National Epidemiologic Survey of Alcohol and Related Conditions (N = 22,177). Direct comparison of results when the sexes are modeled separately or together shows that women are classified differently depending on whether men are included in the analysis. A comparison of disaggregated item-level symptoms and aggregated AUD criteria suggests that aggregating data remove a subgroup, individuals who exhibit tolerance but are normative on all other AUD symptoms, which is of theoretical and clinical interest. Consequently, basic methodological issues that are rarely systematically studied appear to be important determinants of studies seeking to determine whether male and female alcoholism are structurally isomorphic.