# Questions tagged [factor-analysis]

Factor analysis is a dimensionality reduction latent variable technique which replaces inter-correlating variables with a smaller number of continuous latent variables called factors. The factors are believed to be responsible for the inter-correlations. [For confirmatory factor analysis, please use the tag 'confirmatory-factor'. Also, the term "factor" of factor analysis should not be confused with "factor" as categorical predictor of a regression/ANOVA.]

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### Variance after factor analysis in Stata [duplicate]

I run a factor analysis in Stata (-factor- command) and get the eigenvalues for each factor. Then, I do a rotation, and the table presents not the eigenvalues, but the variance. I have two questions: ...
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### Factor Analysis with Multiple Imputation

I have a dataset with 49 Items of a questionnaire (ordinal; 0,1,2,3,4) with 5 diagnostic group of samples (n1: 50, n2: 25; n3:30, n4:23, n5:60). However, the dataset have missings like for 10-12 ...
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### variance decomposition in factor models

Consider a linear model $\textbf{y} = \pmb{\beta}'\textbf{x} + \pmb{\varepsilon}$ with $\textbf{y}$ a $N \times 1$ vector of random variables, $\pmb{\beta}$ a $N \times K$ vector and $\textbf{x}$ a \$K ...
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### KMO calculation for dichotomous variables

The phi coefficient is a measure of association for two dichotomous variables, and a Pearson correlation coefficient estimated for two dichotomous variables will return the phi coefficient. According ...
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### What problems could arise in factor analysis, if I roll out my survey in small parts and do I have to perform validity theme and subtheme level both

I am currently designing an employee engagement survey, which has 6 themes and 20 sub themes and each sub theme got at least 4-5 questions, so I have two questions. Can I roll out survey theme wise ...
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### post processing in PCA and making sense of an example

The example is as follows: A bunch of doctors were asked to score a list of desirable characteristics of sales representatives. The questions were like: "in-depth knowledge about his/her product&...
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### Dealing with covariance

Within my dataset, I employ a variable termed "Instagram reach," quantifying the audience size exposed to a particular post. Simultaneously, "engagement" denotes the count of ...
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### Am I finding redundant columns in my data using Factor Analysis

I have a pandas data frame with 50 columns and 10 rows. The columns represent events and the rows are days. If an event occurs in a day, then the corresponding cell is a "1", else, is a &...
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### Stationarity issue in Factor Analysis

I'm applying Exploratory Factor Analysis (EFA) on 20 variables to identify latent factors. The normalized data (Z-scores) is not stationary (Augmented Dickey-Fuller test). First differencing makes the ...
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### Rank deficiency and interaction term not estimated

I am trying to inspect the data from a 2 x 2 factorial design. The experiment was run by other researchers and the design was settled upon before. Participants were tested 3 times using 3 different ...
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### models MIMIC, predicted probabilities?

I am investigating MIMIC (Multiple Indicators Multiple Causes) models since with them I can do regressions, including factors (made up of several items), and the observed variables (glycemia, ...
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### VAE with linear decoder and nonlinear encoder, does this just learn a linear decomposition of the data?

There are a number of variational autoencoder(VAE) methods that have nonlinear encoders and linear decoders. The concept of using the linear decoder is to improve the interpretability (which features ...
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### Exploratory Factor Analysis vs. PCA

There is a very nice and clear way to illustrate the geometry of PCA. Is there a similar, geometrical way to illustrate Exploratory Factor Analysis? For example, we have 3D data and we’re using 2 ...
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### Are squared loadings and squared distances the same in Principal Component Analysis?

I read online that: Eigenvalue: Represents the variance explained by the principal component. It equals both the sum of squared loadings for that component and the sum of squared projections of data ...
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### Can we use Variable loadings from Multi Factor Analysis to define the variable importance

I wanted to know more in-depth about drawing the relationship between variable loadings that we get from Multi-Factor Analysis to variable importance. In other words, for what purposes can we use ...
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### How to Include a 'No Shift' Scenario in a Temperature Shift DOE

I'm currently working on a Design of Experiments (DOE) for a process that involves temperature shifts at three different times. My challenge is incorporating a 'No Shift' scenario as one of the ...
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### Technical differences between EFA and CFA

I've been looking for the answer everywhere but can't seem to find it. When you do EFA, you'll get how much variance is explained by every single factor (and by the entire factor model as well). When ...
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### How to create social participation index using STATA?

In order to construct the Social Participation Variable (SPV) for older adults, the study employs a comprehensive set of questions designed to capture the diverse spectrum of social activities in ...
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### The Impact of Vector Magnitudes in Recommendation Systems Matrix Factorization Models

I'm currently exploring latent factor models in recommendation systems, specifically focusing on the interaction between vector magnitudes and the angles between these vectors. While it's clear that ...
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### Best way to format this data for exploratory factor analysis, using R?

I originally asked this on StackOverflow, but it's more of a stats question than a coding question. My question is about data formatting. I have this dataset (well, this is just the first two of ...
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### Good reliability analysis with reverse coded items: further checks needed?

After conducting an exploratory factor analysis on a set of data, I have obtained 3 factors, whose items (can) make sense from a theoretical perspective — even though some negatively worded items ...
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### Getting individual level scores from factor analysis with lots of missing data

I have a setting where I'm doing factor analysis in a context where I have lots of rows and where ~90% of data is missing (it's a survey of a couple hundred thousand people, each person was asked a ...
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### Specifics of varimax criterion

The varimax criterion maximises high and low value factor loadings and minimises mid-value factor loadings, in order to achieve the maximum value for its objective function. How does doing this ensure ...
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Are "factor loadings" (orthogonal rotated) in exploratory factor analysis (EFA) correlations or standardized regression weights? For instance in r, the factor loadings are very high, if the ...
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### How does varimax work

I have some questions regarding how varimax works. I read that given an n by k matrix A, the k by k orthogonal matrix B maximises the varimax criterion, which measures the difference of these 2 terms: ...
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### Comparing Factor Structures Between Groups/Difference in Sample Size?

I am comparing the factor structure of an autism screener across two groups (group 1-> toddlers diagnosed with Down syndrome; group 2-> toddlers diagnosed with Cerebral Palsy). The first group ...
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### Generating Composite Index by PCA for a Single Country with Many Variables

I am doing a course project where I am trying to generate an index to measure the overall level of prosperity of a single country - such as the United States. What I hope is that this index could be ...
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How to calculate factor loading manually in CFA? Can anyone explain it by giving the equation and if so, can you give an example too?
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### Comparing two groups using factor analysis

I have a 258*14 dataset, I want to compare the latent factor structure of two sub-groups from this dataset (group1= 146, group2= 112). I started by performing an EFA (using ML and Promax rotation) on ...
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### How to score a psychological scale with three factors [closed]

I have helped to validate a new psychological scale and after conducting exploratory and confirmatory factor analyses, we have found the best fit for the scale is a 3-factor structure. The factor ...
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### Should I go with an unrotated factor analysis model?

I'm running a project on survey data where I have a bunch of very similar operationalizations of my DV (four different indices of my DV). Let's call it support for X behavior. All of them are ...
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### longitudinal measurement invariance - why do loadings for latent factor changed signs?

I have run separate EFAs and then CFAs on the second half of the dataset to confirm the solution and the one-factor solution fits well across time points. One weird thing is happening though when I ...
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### Do you need to correlate factor residuals of factors that are measured at the same time point

I am running a second-order (multiple indicator) latent growth curve. The model has three latent factors (excluding the growth intercept and slope factors) that each have 4-5 indicators. Two of them ...
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### How to Handle Non-Multinormality in the Context of Exploratory Factor Analysis for Logistic Regression

I'm trying to follow the book A Step-by-Step Guide to Exploratory Factor Analysis with R and Rstudio, by Marley W. Watkins, and apply the principles in the book to a real-world data set. Ultimately, ...
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### Should I perform CFA after the EFA and then move to multiple regression analysis with the outcomes?

I have gathered 41 variables that are supposed to explain dependent variable Y in a dataset. Is the following reasonable? First, I will conduct EFA, reduce the dimension, conduct CFA to confirm/reduce....
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Factor analysis can allow the factors to be correlated in 'oblique' rotations. But this seems underdetermined. How would (explanatory) factor analysis distinguish the two cases below (using the data ...
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