Ideal point estimation and dimensionality reduction have long been utilized to simplify and cluster complex, high-dimensional political data(e. g., roll-call votes and surveys) for use in analysis and visualization. These methods often work by finding the directions or principal components (PCs) on which either the data varies the most or respondents make the fewest decision errors. However, these PCs, which usually reflect the left-right political spectrum, are sometimes uninformative in explaining significant differences in the distribution of the data(e. g., how to categorize a set of highly-moderate voters). To tackle this  issue, we adopt an emerging analysis approach , called contrastive learning. Contrastive learning-e.g., contrastive principal component analysis (cPCA)-works by first splitting the data by predefined groups, and then deriving PCs on which the target group varies the most but the background group varies the least. As a result, cPCA can often find `hidden' patterns, such as subgroups within the target group, which PCA cannot reveal when some variables are the dominant source of variations across the groups. We contribute to the field of contrastive learning by extending it to multiple correspondence analysis (MCA)  to enable an analysis of data often encountered by social scientists---namely binary, ordinal, and nominal variables. We demonstrate the utility of contrastive MCA (cMCA) by analyzing three different surveys : The 2015 Cooperative Congressional Election Study, 2012 UTokyo-Asahi Elite Survey, and 2018 European Social Survey . Our results suggest that, first, for the cases when ordinary MCA depicts differences between groups, cMCA can further identify characteristics that divide the target group ; second, for the caseswhen MCA does not show clear differences , cMCA can successfully identify meaningful directions and subgroups, which traditional methods overlook .
Scaling methods have long been utilized to simplify and cluster high-dimensional data. However, the latent spaces derived from these methods are sometimes uninformative or unable to identify significant differences in the data. To tackle this common issue, we adopt an emerging analysis approach called contrastive learning. We contribute to this emerging field by extending its ideas to multiple correspondence analysis (MCA) in order to enable an analysis of data often encountered by social scientists -- namely binary, ordinal, and nominal variables. We demonstrate the utility of contrastive MCA (cMCA) by analyzing three different surveys of voters in Europe, Japan, and the United States . Our results suggest that, first, cMCA can identify substantively important dimensions and divisions among (sub)groups that are overlooked by traditional methods ; second, for certain cases , cMCA can still derive latent traits that generalize across and apply to multiple groups in the dataset; finally, when data is high-dimensional and unstructured, cMCA provides objective heuristics, above and beyond the standard results, enabling more complex subgroup analysis .
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Ideal point estimation and dimensionality reduction
Scaling methods
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complex,
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political data(e. g., roll-call votes and surveys) for use in analysis and visualization. These methods often work by finding the directions or principal components (PCs) on which either the data varies the most or respondents make the fewest decision errors. However, these PCs, which usually reflect the left-right political spectrum,
data. However, the latent spaces derived from these methods
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in explaining
or unable to identify
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distribution of the data(e. g., how to categorize a set of highly-moderate voters).
data.
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common
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,
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Contrastive learning-e.g., contrastive principal component analysis (cPCA)-works by first splitting the data by predefined groups, and then deriving PCs on which the target group varies the most but the background group varies the least. As a result, cPCA can often find `hidden' patterns, such as subgroups within the target group, which PCA cannot reveal when some variables are the dominant source of variations across the groups.
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the field of contrastive learning by extending it
this emerging field by extending its ideas
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in order
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scientists---namely
scientists -- namely
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: The 2015 Cooperative Congressional Election Study, 2012 UTokyo-Asahi Elite Survey, and 2018 European Social Survey
of voters in Europe, Japan, and the United States
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for the cases when ordinary MCA depicts differences between groups, cMCA can further identify characteristics that divide the target group
cMCA can identify substantively important dimensions and divisions among (sub)groups that are overlooked by traditional methods
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the caseswhen MCA does not show clear differences
certain cases
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successfully identify meaningful directions and subgroups, which traditional methods overlook
still derive latent traits that generalize across and apply to multiple groups in the dataset; finally, when data is high-dimensional and unstructured, cMCA provides objective heuristics, above and beyond the standard results, enabling more complex subgroup analysis