# 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 to interpret a polychoric correlation?

I've checked related links to understand what a Polychoric Correlation measures, got some 404's and other unanswered questions. I've seen it used to determine independence between Nominal/Interval ( &...
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### Within ML CFA with categorical data (polychoric correlation), are there not different thresholds for both the within and between level?

I am currently studying multilevel confirmatory factor models of categorical data. In the context of CFAs, categorical data is often analysed through polychoric correlations. Within polychoric ...
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### Non appearance of particular responses on likert scale and the aftermath

I have got a dataset of 18 variables all containing likert data, recoded in 5 points scale. There are no missing values and in 3 of the variables one particular response did not appear (No one ...
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### Testing underlying, latent normality of binary data

I have two multivariate binary datasets of 4 variables (or components) - P, Q, R and S each. Each row of the data is like a test on the components to say if they work (0) or fail (1) when tested. The ...
1 vote
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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 ...
363 views

### polychoric factor analysis and use of factor score in subsequent models

To predict the impact of gender egalitarianism on life satisfaction (7-scale ordinal variable), I wanted to create a factor score from a relevant group of variables (mothers should work: agree to ...
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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 ...
1 vote
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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 ...
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1 vote
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### 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:...
1 vote
183 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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1 vote
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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 ...
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