Questions tagged [factor-analysis]

Factor analysis is a dimensionality reduction latent variable technique which replaces inter-correlating variables by 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 tag 'confirmatory-factor'. Also, term "factor" of factor analysis should not be confused with "factor" as categorical predictor of a regression/ANOVA.]

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Can I use optimally scaled variables for a factor analysis to account for rotation? If I can then how?

I have discussed this issue several times in this site, but I am asking it again for a final justification from the experts of our community. I wanted to extract four factors (I should call dimensions ...
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2k views

Cluster analysis vs Factor analysis as a means for “grouping” variables or cases: the differences

I've noticed responses that at face value seem to be in contradiction with each other. For instance, here @peter-flom writes Short answer: Cluster analysis is about grouping subjects (e.g. ...
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Whether to use EFA or CFA to predict latent variables scores?

I have a dataframe of individual observations, that I partitioned to create a training (0.7 prop) and a test set (0.3 prop). I started by running an exploratory factor analysis (EFA) on the training ...
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can I use PCA and PAF on Kendall's and Spearman's correlation matrix?

I have a dataset of 77 items, ranked by 17 people, with many ties (actually: Q-sorted under a forced quasi-normal distribution ...
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The number of free parameters in factor analysis after an orthogonal rotation

Background I'm reading some notes in multivariate data analysis, in particular factor analysis. A data vector $X_{p\times 1}$, with $E(X) = \mu$ A vector $F_{m \times 1} $ of factors, A matrix $L_{...
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What is the rationale behind the “eigenvalue > 1” criterion in factor analysis or PCA?

What is the meaning of "eigenvalue > 1" criterion? I understand what eigenvalues and eigenvectors are. This question is w.r.t. this link and this statement there: By default, VARCLUS stops ...
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586 views

Factor analysis across different levels of data aggregation

I have survey data for thousands of individuals from hundreds of towns. I want to identify factors underlying certain characteristics at the town level and the individual level. The individual level ...
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145 views

How to perform exploratory factor analysis on associative network?

In an article by Teichert and Schontag ("Exploring Consumer Knowledge Structure Using Associative Network Analysis", 2010), the authors perform (page 387) an exploratory factor analysis (EFA) on an ...
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530 views

How to compute the weight matrix for WLS estimation of a multi-group ordinal CFA model

I am attempting to perform a two-group confirmatory factor analysis (CFA) of one continuous factor on six ordinal predictors in OpenMx (...
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122 views

Factor models with small noises

The standard factor model formulation is $y=W x+\epsilon$ where $x \sim \mathcal{N}(0, I)$, $\epsilon \sim\mathcal{N}(0, \Sigma)$. $W$ and $\Sigma$ are typically estimated from MLE. The solution can ...
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What is $X$ in the fundamental equation of factor analysis?

Mulaik (2009) p. 135-136 writes that Let Y be an $n \times 1$ random vector of random variables whose variables are the observed random variables $Y_{1}, ... , Y_{n}$. Assume that $E(Y) = 0$ ...
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1answer
112 views

How can Factor Analysis be used to remove questions from a survey?

Suppose I have a psychological questionnaire asking 30 questions about a person's mental health (on a Likert-scale 1-7). These 30 questions fall into 7 separate, but correlated categories. The ...
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Exploratory Factor Analysis - Method Generating Factor Scores

I want to understand the differences between different methods of generating factor scores in exploratory factor analysis, namely Regression method, Bartlett scores and Anderson-Rubin method. I found ...
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58 views

How to get the MLE estimate of a factor analysis model?

Given a factor analysis model $$ X-\mu = LF + \epsilon$$ Lets denote $cov[\epsilon] = \Psi$ and $cov[X] = \Sigma$. $\Psi$ is assumed to be a diagnal matrix. The iterative MLE estimate exploits the ...
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798 views

Are principal components reflective, formative, both, or neither?

In reading various summaries on the similarities and differences between principal components and common factor models, I have noticed that there seems to be conflicting information about whether PCA ...
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199 views

How does PCA maximise Total Variance without maximising Co-variance?

https://stats.stackexchange.com/a/3374/92071 - In PCA, the components are actual orthogonal linear combinations that maximize the total variance. In FA, the factors are linear combinations that ...
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How to create a scree plot for factor analysis given that eigenvalues depend on the number of extracted factors?

I understand how Kaiser rule works for PCA, as no matter how many components I extract I always get the same eigenvalues. For example, with 3 components I get ...
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Can I try several CFAs on the same data before choosing one for generating factor scores?

I'm interested in matching on latent constructs (see Raykov, 2012), and one way to do so is to match on factor scores generated by CFAs of the items (One could also match on the items themselves, but ...
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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 ...
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Q: Exploratory factor analysis in R

I am trying to do an exploratory factor analysis (EFA) in R with oblique (promax) rotation. From Wikipedia, In oblique rotation, one gets both a pattern matrix and a structure matrix. The ...
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406 views

Factor analysis with severly skewed ordinal data and censored ordinal data

I am aiming to run initial exploratory factor analysis in one sample and then confirmatory in another sample. My indicators are ordinal and so I planned to generate a polychoric correlation matrix and ...
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817 views

What factor loading is recommended to retaining items in a factor analysis?

I received the following question via email and thought it would be suited to this site: I have a debate with a friend about factor loading and squared multiple correlation. ... In my debate ...
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How to use extracted data from factor analysis in subsequent 2x2 factorial design?

I’m conducting a 2x2 between subjects factorial design for my dissertation. IV’s: advertising appeal (two levels: rational appeal vs. emotional appeal) media type (two levels: TV vs. Internet). ...
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How are Taguchi orthogonal arrays derived?

I am implementing statistical analysis in a C# program and am using the Taguchi Method to do it (the Taguchi arrays are about a 1/4th of the way down the page). The article in the above link mentions ...
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1answer
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Highly correlated variables in exploratory factor analysis

Do I have to eliminate variables that are highly correlated before doing an exploratory factor analysis, like it has been discussed for PCA already here? To specify, some items of my data are highly ...
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Exploratory data analysis before pefrorming Canonical Correspondence Analysis (CCA)

I want to perform CCA, but I read that, remember that observations (for example, species abundances) have to present unimodal distributions along gradients (for example, environmental variables). ...
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Longitudinal CFA/SEM with autocorrelated/autoregressed indicators (in R, better with lavaan)

The problem is, I am trying to fit a multilevel factor model to highly autocorrelated (in fact, autoregressive) indicators. More specifically, I have multiple measurements (60-70) per person (5-10 ...
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Using non-parametric transformation (ranking) on variables for factor analysis in R

I have been wrestling with how to simplify a set of mixed variables (some orthogonal, some numeric) some (of both types) of which are significantly skewed. I have run a factor analysis anyway and ...
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Can factor analysis be fit with gradient-based methods?

I know you can fit factor analysis using EM, but can you use gradient-based methods? If so, a reference would be great; otherwise, why not?
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What is meant by correlation between individual scores under a bi-factor and unidimensional model >0.90?

I have been looking at the COSMIN criteria for evaluating the measurement properties of exploratory factor analyses. The criteria for a sufficient bi-factor model are described as “standardized ...
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Intuition: What is the difference between linear factor models and regular linear regression?

So, I have a very vexing theoretical question that I hope some experienced econometricians can help me with. Being in finance, I have recently been exposed to linear factor models, which are models ...
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matrix factorization with non-negative constraint only on one of the factors

I have a 2D spectral data time series with a wavelength dimension and a time dimension, and I'd like to decompose it to the time evolution ($SV^T$ for SVD and $H$ for NNMF) of several spectral ...
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Is it realistic for scree plots generated in factor analysis to show clear, identifiable cutoffs?

I simulated some toy data of students taking a test. Each question in the test fell into one of four categories (which I called "concepts"), and each student had an "ability" for each of those four ...
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Is Multiple Correspondence Analysis applicable to Multi-valued Categorical Variables?

I have a data-set containing only Categorical Variables. I needed to do Principal Component Analysis on the data set. Eventually, I found Multiple Correspondence Analysis and learnt it. But, in MCA, ...
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Factor analysis for time series. Which approach to use?

I'm wondering if it's appropriate to use factor analytic methods in the study of the following case: I have time series data describing the incomes of 12 companies. Each company has three main ...
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123 views

Method to generate random correlation matrices with specified structure.

Within the social sciences there is a popular technique called Factor Analysis and I am interested in generating random correlation matrices that uniformly sample all the space parameterized by one ...
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2D rotation of standardized PCA, how to compute new eigen values, eigen vectors, and loadings ?

I want to apply a 2D rotation of a $\theta$ angle to my two first principal components of a PCA. What I understood from this post is that I have to apply a rotation matrix R : $$ R_\theta = \left( \...
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What to do if not all theoretically related variables are loaded highly on the same factors using EFA?

I'm using EFA to generate regression factor scores for subsequent regression and ANOVA analyses. I want to do use regression factor scores instead of averaging the scores, as I've read in multiple ...
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1k views

Multicollinearity (or not) in exploratory factor analysis

I’m performing an exploratory factor analysis with 28 items, n = 300. I’m confused whether I have a multicollinearity problem or not, and if so whether/how I go about choosing items to remove from the ...
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Is it correct to claim the existence of an 'indirect effect' in A>B>C chain when no significant A>C path is found? Or what else should I call it?

I am working on a SEM where I hypothesize a causal chain where A influences B, which in turn influences C. The data are from a 2x2 between-subjects experiment, N = 297. All the goodness of fit ...
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Factor Analysis - Rotation failed to converge in 25 iterations!

I am conducting a Factor Analysis using PCA. I have used Oblique and Orthagonal Rotations and when I am trying to analyse my results I get the message: "Rotation failed to converge in 25 iterations" ...
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72 views

Cross-loaded indicators in factor analysis (before regression analysis)

I performed exploratory factor analysis, and extracted two underlying factors out of eight indicators. Then, I used confirmatory factor analysis for some theoretical fine-tuning. After minor revisions,...
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How to get values of latent variable in factor anlaysis

I conducted exploratory factor analysis (EFA) to uncover the underlying factor structure(shown as below). My question is how to obtain the value for each latent factor (factor 1,2,3,4)? For example, ...
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Do the problems of stepwise variable selection exist in FA, PCA, SEM?

Note: This is a revision of my original question. I have read the critique of stepwise variable selection and "all possible subsets regression" by Professor Frank Harrell here. Are factor analysis, ...
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62 views

How to obtain statistical information from a Likert scale with a sample size smaller than the number of questions?

Research and sample properties I'm measuring the degree of a certain concept related to marketing and sustainable development throughout an entire industry. The theoretical model is depicted next: ...
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What is meant with “decision level of factor loading”?

I have performed a PCA with some data sets. Prior to performing PCA, I tested the applicability of PCA with KMO and Bartlett's Sphericity tests. I got some critics stating that I have to add "my ...
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236 views

PCA for questionnaire reduction

I'd like to have some opinion regarding if I'm in the right way with my questionnaire reduction. I have a questionnaire with 275 questions and 34 issues (so a couple of questions are related to each ...
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439 views

Does the use of EFA factor scores (vs. sum/average scores) impact statistical power of subsequent analyses?

Imagine a hypothetical scenario: You have data a short survey of 9 questions that participants respond to on a continuous rating scale. You suspect that Questions 1-3 assess one particular factor (...
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223 views

Does weighted factor analysis exist?

I would like to perform factor analysis on a set of responses to a psychological questionnaire. Is there some method that allows me to "weight" each questionnaire item by how important I believe it is ...
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265 views

Two-classes LDA on third class

I am trying to implement a $N$ classes classification with several 2-classes LDAs. I actually am using LDA as a projection method instead of classification, so it might be more a factor analysis. If ...