# Questions tagged [polychoric]

The polychoric correlation coefficient is used for two ordered categorical variables. The tetrachoric correlation coefficient is the special case when both variables are binary.

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### How do I use polychor() to get all pairwise comparisons within a matrix of input? [migrated]

I would like to do a polychoric correlation of all variables in my dataframe (15 columns, 300 rows). I need to use the polychor() function from the "polycor" library in R. Simply plugging in ...
1answer
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### Deriving joint probabilities from marginal probabilities & polychoric correlations

Given three ordered-categorical variables: $u_1, u_2, u_3$ with $K$ categories, I'm trying to derive their expected variance-covariance matrix using their marginal probabilities, thresholds, and ...
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### Huge difference in KMO statistic based on type of correlation (Pearson vs Polychoric)

I am analyzing an engagement survey filled out by teenagers in a school following a randomized trial in which they were assigned to either of two experimental conditions (lessons). The questionnaire ...
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### Poor model fit indices when running exploratory factor analysis with polychoric correlation matrix using psych package in R

I am using the psych package in R to run exploratory factor analysis (oblimin rotation, maximum likelihood estimation method) on a dataset of 203 responses to a 62-item questionnaire, using a 5-point ...
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### Testing the fit of polychoric correlation

I’m using polychoric correlations for my work. According to Kampen and Weeren (2017): In order to prevent this questionable research practice, it is recommended that in applications of the ...
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### CFA Model Saturated, fit perfect

I am running a CFA with three items and one latent factor. My sample size is 900. Each item loads onto the factor between .64 and .89. Why is it saying fit is perfect? I have tried in both STATA and ...
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### Polychoric Corelation — When to use?

I'm analyzing a survey that contains self ranking? Would I use polychoric correlation to compare these scores to nominal variables such as gender?
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### Polychoric or Pearson correlations - pre-EFA analysis in R

I plan to run a series of exploratory factor analysis (EFA) models to investigate the factor structure of a scale in development using the R package psych. My N > ...
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### Correlation between Ordered Variable and Categorical Variable

I am analyzing Opportunities for Sales people. I have a categorical variable which is Status:{Won,Lost} My dependent variable, and other Independent ordered variables like the stages of the ...
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### How to use polychoric correlation using R

I have a data set containing 731 observation and 14 variables. The variables are of mixed type containing both ordinal, nominal and quantitative variable. How can I perform PCA using polychoric ...
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### Computing factor scores for factors when the PAF is based on tetrachoric correlations

I want to create factors from various binary items. Using the polycor package (Fox, 2006) and R-Essentials I created a tetrachoric correlation matrix in SPSS. The items are all exploratory, so I ...
1answer
293 views

### appropriateness of factor analysis using correlation matrix of mixed variable types

I am aware that questions about factor analysis with mixed variable types have already been addressed. My situation is unique: I have datasets from two samples that were administered the exact same ...
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### Do I use eigen values from common factor solution OR from the original matrix? EFA in R, polychoric

I'm currently running an EFA in r, using the cor = "poly" setting with principal axis factoring, and am trying to determine the eigenvalues of the analysis. I am getting two different sets of values:...
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165 views

### Mixed dichotomous correlation matrix

I have a data frame comprising more than two dozen variables, all of which are binary (0/1) with <5% missing data. These variables can be classified into groups that pertain to different aspects of ...
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### Estimating the correlation matrix of a jointly normal distribution when some variables are latent

Suppose that $X_1,..,X_6$ are jointly normally distributed. \$f(\mathbf{x})= \frac{1}{\sqrt { (2\pi)^k|\boldsymbol \Sigma| } } \exp\left(-{1 \over 2} (\mathbf{x}-\boldsymbol\mu)^{\rm T} \boldsymbol\...
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### How to compute component or factor scores when the analysis is based on polychoric/tetrachoric correlations?

[This question is modified based on suggestion from @ttnphns] I am doing linear principal component analysis (PCA) based on polychoric correlations between the variables (rather than on native Pearson ...
1answer
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### Correlation coefficients for ordered data: Kendall's Tau vs Polychoric vs Spearman's rho

It seems like for managing with ordered measurements researchers usually deal with Polychoric Correlation. (For example, for making matrix before doing Factor Analysis.) Why so? Kendall Tau Rank ...