A Comparison of Label Switching Algorithms in the Context of Growth Mixture Models

Abstract

Simulation studies involving mixture models inevitably aggregate parameter estimates and other output across numerous replications. A primary issue that arises in these methodological investigations is label switching. The current study compares several label switching corrections that are commonly used when dealing with mixture models. A growth mixture model is used in this simulation study, and the design crosses three manipulated variables-number of latent classes, latent class probabilities, and class separation, yielding a total of 18 conditions. Within each of these conditions, the accuracy of a priori identifiability constraints, a priori training of the algorithm, and four post hoc algorithms developed by Tueller et al.; Cho; Stephens; and Rodriguez and Walker are tested to determine their classification accuracy. Findings reveal that, of all a priori methods, training of the algorithm leads to the most accurate classification under all conditions. In a case where an a priori algorithm is not selected, Rodriguez and Walker's algorithm is an excellent choice if interested specifically in aggregating class output without consideration as to whether the classes are accurately ordered. Using any of the post hoc algorithms tested yields improvement over baseline accuracy and is most effective under two-class models when class separation is high. This study found that if the class constraint algorithm was used a priori, it should be combined with a post hoc algorithm for accurate classification.

Keywords: growth mixture model; label switching; mixture modeling; simulation; training data set.

Figure 1.

(a) Two-class model classification accuracy for single algorithms. (b) Two-class model classification accuracy for combinations of algorithms. (c) Three-class model classification accuracy for single algorithms. (d) Three-class model classification accuracy for combinations of algorithms. (e) Four-class model classification accuracy for single algorithms. (f) Four-class model classification accuracy for combinations of algorithms.

Figure 2.

(a) Two-class model average classification accuracy for individuals by condition and algorithm. (b) Three-class model average classification accuracy for individuals by condition and algorithm. (c) Four-class model average classification accuracy for individuals by condition and algorithm.