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The purpose of this study was to examine the effects of different data conditions on item parameter recovery and classification accuracy of three dichotomous mixture item response theory (IRT) models: the Mix1PL, Mix2PL, and Mix3PL. Manipulated factors in the simulation included the sample size (11 different sample sizes from 100 to 5000), test length (10, 30, and 50), number of classes (2 and 3), the degree of latent class separation (normal/no separation, small, medium, and large), and class sizes (equal vs. nonequal). Effects were assessed using root mean square error (RMSE) and classification accuracy percentage computed between true parameters and estimated parameters. The results of this simulation study showed that more precise estimates of item parameters were obtained with larger sample sizes and longer test lengths. Recovery of item parameters decreased as the number of classes increased with the decrease in sample size. Recovery of classification accuracy for the conditions with two-class solutions was also better than that of three-class solutions. Results of both item parameter estimates and classification accuracy differed by model type. More complex models and models with larger class separations produced less accurate results. The effect of the mixture proportions also differentially affected RMSE and classification accuracy results. Groups of equal size produced more precise item parameter estimates, but the reverse was the case for classification accuracy results. Results suggested that dichotomous mixture IRT models required more than 2,000 examinees to be able to obtain stable results as even shorter tests required such large sample sizes for more precise estimates. This number increased as the number of latent classes, the degree of separation, and model complexity increased.
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Theoretical Insights Into Multiclass Classification: A high-dimensional Asymptotic View
Contemporary machine learning applications often involve classification tasks with many classes. Despite their extensive use, a precise understanding of the statistical properties and behavior of classification algorithms is still missing, especially in modern regimes where the number of classes is rather large. In this paper, we take a step in this direction by providing the first asymptotically precise analysis of linear multiclass classification. Our theoretical analysis allows us to precisely character- ize how the test error varies over different training algorithms, data distributions, problem dimensions as well as number of classes, inter/intra class correlations and class priors. Specifically, our analysis reveals that the classification accuracy is highly distribution-dependent with different algorithms achieving optimal per- formance for different data distributions and/or training/features sizes. Unlike linear regression/binary classification, the test error in multiclass classification relies on intricate functions of the trained model (e.g., correlation between some of the trained weights) whose asymptotic behavior is difficult to characterize. This challenge is already present in simple classifiers, such as those minimizing a square loss. Our novel theoretical techniques allow us to overcome some of these chal- lenges. The insights gained may pave the way for a precise understanding of other classification algorithms beyond those studied in this paper.
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- PAR ID:
- 10200055
- Date Published:
- Journal Name:
- Neural Information Processing Systems (NeuRIPS 2020)
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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