# 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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### Polychoric Correlations to Fisher's Z Transformation

I'm interested in conducting a meta-analysis of polychoric correlation coefficients using metafor package in R. When performing a meta-analysis with Pearson ...
58 views

### How to interpret polychoric correlation matrix with reverse scored items?

I'm currently working with a dataset with a sample size of 174 from a questionnaire that measures 6 types of personality traits with 5 response options per item (Strongly Agree, Agree, Neutral, ...
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### Factors or components in Stata and R (psych, lavaan): Confusing method labels and diverging results

I have some trouble translating between Stata and R (psych, lavaan) about factors and components with an interest in the loadings/eigenvectors of the items. I seek to validate results (understand the ...
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### How to calculate P value in polychoric correlation

I see that I can get polychoric correlation coefficients using package girth. I have following data: ...
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29 views

### Factor analysis (or similar) for data set with both continuous and dichotomous variables (+control for age?)

As you can tell from the title I'm in a bit of a fix. I have a data set with three continuous variables and one dichotomous one. Data collected from four groups. The data set is a developmental ...
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### What is the relationship between the manifest correlation between ranked variables and the latent, continuous correlation?

Suppose you draw n pairs of observations from a real-valued bivariate distribution. You then convert each observation to its ascending rank order. Given the population correlation for the real-valued ...
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1 vote
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### Mutual Information for unordered variables

Like many others I am seeking for a method to create a "correlation" like matrix for an unpredictable mix of variables which can contain unordered categorical ones as well. While there are ...
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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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189 views

### 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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1 vote
32 views

### 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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352 views

### 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 ...
1 vote
737 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?
388 views

### 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 > ...
81 views

### 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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398 views

### 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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277 views

### 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
823 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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732 views

### 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
225 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
236 views

### 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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