Polychoric and Tetrachoric Correlation
Polychoric correlation estimates the correlation between two latent normal variables underlying observed ordinal ratings; tetrachoric correlation is the special case where both variables are binary.
다분상관은 관찰된 순서형 응답 밑에 있는 두 잠재 정규변수 사이의 상관을 추정하며, 두 변수가 모두 이분형이면 사분상관이 됩니다.
I want to factor-analyse 5-point Likert items; should I use Pearson or polychoric correlations, and what are they?
5점 리커트 문항으로 요인분석을 하려는데, 피어슨 상관 대신 다분상관을 써야 하나요?
Each ordinal item is treated as a coarsened latent normal variable, thresholds are set from the marginal proportions, and the correlation is chosen to maximise the bivariate normal likelihood of the observed cross-table. Because Pearson correlations of coarse categories are attenuated, polychoric matrices are preferred for factor analysis of ordinal items.
When to use Polychoric and Tetrachoric Correlation
- Items are ordinal with few categories, such as Likert or yes/no items
- Preparing a correlation matrix for factor analysis or SEM of ordinal data
- Estimating association between underlying continuous traits
When to use something else
- Variables are truly continuous, where Pearson correlation is appropriate
- The underlying variables are clearly not normal or the categories have no order, where Spearman correlation or Cramér's V is safer
Assumptions and requirements
- Each ordinal variable reflects an underlying normally distributed latent variable
- The latent variables are bivariate normal
- Independent observations
What the analysis reports
- Pairwise polychoric or tetrachoric correlations with SE and CI
- Correlation matrix and smallest eigenvalue
- Bivariate normality G² test per pair
- Pearson correlation for comparison
How to report it
The polychoric correlation between [item 1] and [item 2] was ρ = [value], SE = [value], 95% CI [[value], [value]] (N = [value]).
Related methods
Run Polychoric and Tetrachoric Correlation on Quorant
- Data you need
- a table (CSV or Excel) with item columns (e.g. questionnaire items)
- Price
- 400 credits for one analysis up to 10,000 rows (complexity level 3); larger or wider data costs more. Optional methodologist review: 1800 credits.
- Checking
- Checked by property tests in every deployment
- Before you pay
- A free pre-analysis diagnosis checks your data and gives an exact quote; nothing is deducted until you approve it.