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 ...

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CFA: loading exceeding 1

With CFA, is it a problem if a loading exceeds 1? What does it mean to have a loading greater than 1? What steps should be taken to deal with it, if nothing is amiss with the variable itself?
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How can I have more factors than there are variables

I've come to learn about factor analysis as mainly a dimensionality reduction tool. However, can we also use the factor analysis method to have more factors than there are variables? If so, what would ...
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CFA: negative factor loadings

I found that after running a CFA, positive factor loadings and negative factor loadings occurred as appropriate. (An item representing a high score and an item representing a low score on the same ...
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Problem with syntetic data generating for Probabilistic PCA and Factor Analysis (FA) comparison - methodology

I am trying to understand a short example related to dimension reduction from python scikit-learn.org official documentation for long time and unfortunately I am not successful. I don't have problems ...
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What to do when EFA requires more factors but the number of variables is low?

There's a lot of information on the forum about the differences between principal components analysis (PCA) and exploratory factor analysis (EFA) (for example here and here). I am new to both methods, ...
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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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Which tests to perform for quantitative surveying using likert scale? [closed]

Am in an urgent need of help to complete my master thesis report. Any support would be highly appreciated. My study is on impact of emerging technologies on teaching and learning. I have identified 8 ...
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35 views

Variables derived from factor analysis as a response variable in logistic regression

I have a dataset derived from a questionnaire filled out by high school students, with 7 variables (one continuous and six binary). Three variables(binary) are related to "interest in physics". Is ...
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21 views

Using polychoric correlation with non normal ordinal data

I have ordinal data on scale 1-5 for detected pollutants in water (1 = detectable in small proportions; 5= detectable in higher proportions; also 0 was asaigned - not detectable). based on the ...
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Using factor scores in discriminant analysis

I'm looking at indicators of earnings fraud in publicly-held corporations. My classification is dichotomous, Yes, company is likely to engage in EF, or no, it's not. I have 15 financial variables ...
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State space modelling of longitudinal data in r

I have n stations, and for each station there are m time series observations on different days, each of length ...
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Factor analysis without listwise deletion

Can factor analysis be done in a manner which affords missingness on some items? With what methods can a factor analysis be performed in which subjects who are missing on one or two items are ...
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72 views

Do Stata and SPSS give conflicting versions of Anti-Image matrices?

I read on p1 of the Stata Manual glossary that: The image of a variable is defined as that part which is predictable by regressing each variable on all the other variables; hence, the anti-...
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Why are regression coefficients in a factor analysis model called “loadings”?

In this thread @ttnphns writes that Because it is regression coefficients [...] I insist that it is better to say "factor loads variable" than "variable loads factor". I learned from here that ...
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Factor analysis with items on very different scales

What issues might arise with performing EFA or CFA using items on very different scales (likert data on scales of 1-3, 1-4, 1-5, and 1-7 and measurements based on time, in seconds, which can be binned ...
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How to implement SMC in Python as it in R? [closed]

Is there any function in Python similar to Squared Multiple Correlation (SMC) in R? What if I want to implement SMC in Python? Is the only way to do it just rewriting SMC into Python line by line? ...
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When will factors wholly explain the correlations among the observed variables?

Thinking about this question, I came across Bartholemew et al (2011), which lists the following assumptions of the linear factor model, assuming $p$ observed variables: iii) $e_{1}, e_{2}, ..., e_{...
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Using pearson correlation to compare factor loading between two groups

I have two groups (one placebo, one drug) in which I measured a few variables. I performed factorial analysis separately for the two groups and then I want to compare the factor loadings between the ...
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Identification in a gaussian two factor model

I am working with a Gaussian two factor model: $$ X_i = \beta_iZ_1+\gamma_iZ_2+\varepsilon_i, \space i = 1,2,...,n $$ where $Z_j\sim N(0,1), \space Z_1 \perp Z_2 $ and $\varepsilon_i\space iid\space ...
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Do Heywood cases render EFA/CFA solutions invalid?

If communality = 1, then we have a Heywood case, and if a communality > 1, it is known as an ultra-Heywood case. I read in a SAS manual that an ultra-Heywood case renders a factor solution invalid, ...
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Is there Factor analysis or PCA for ordinal or binary data?

I have completed the principal component analysis (PCA), exploratory factor analysis (EFA), and confirmatory factor analysis (CFA), treating data with likert scale (5-level responses: none, a little, ...
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34 views

Can Factor Analysis on Mixed Data be treated like a PCA?

I wanted to do something equivalent to a PCA on a mixed data set containing categorical variables and continuous numerical predictor variables which are normally distributed but measured in very ...
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41 views

errors in the orthogonal factor model

I am using R psych package in order to design a factor model. By default, an oblique rotation (oblimin) is performed by fa. The number of factors (fa.parallel$nfact) has been previously estimated. <...
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to constrain a parameter estimate to obtain unique estimates in R LAVAAN for CFA

I need urgent help, I need the script or command to constrain a parameter estimate to obtain unique estimates in R LAVAAN for CFA. Like If Social Influence got 4 items in a model and I want to put a ...
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Factor Analysis with low sample size

Does anyone know of references to support conducting EFA with a low sample size?
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Why do the loadings returned by psych::principal() in R change with the number of components?

I have been using the principal() function of the psych package in R and setting the number of components after a scree plot analysis (...
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Analytic Hierarchy Process (AHP) - factor weight score

As title mentioned, how to determine the 'scale of relative importance' point for factor weight score? Besides, I have read some example of ahp saying there are 1-9 point, 1-5 point (1,2,3,4,5) and ...
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“*usefulness*” is a bivariate property used in Regression and Anova. Has a generalization (trivariate) analogon been discussed?

Just for selfstudy/exercising of algorithms I looked at the computation of the "usefulness"-measure in multiple regression, which means the part of variance which one independent item contributes to ...
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exploratory factor analysis in models with sub constructs

I have a dataset based on model with 3 second-order latent variables (exogenous + mediator + endogenous), each having 2 first-order latents. when running exploratory factor analysis (PCA) with SPSS, ...
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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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92 views

What is the difference between the anti-image covariance and the anti-image correlation?

What is the difference between the anti-image covariance and the anti-image correlation? How are the matrices of these coefficients computed, and what is the meaning of their elements?
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70 views

How to overcome skewed component in validation of a 3 component likert scale

thanks for the information and input provided in the relevant posts. I intend to develop a psychometric questionnaire using Exploratory Factor Analysis; it gives 3 factors. One of the scales is ...
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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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how to create factor analysis data in R

I recently learnt about factor analysis and now I wanted to test it by generating samples in $X$ like $$X = FL^T + N$$ where $F$ is a matrix with in each row the factors for one sample, $L$ is the ...
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140 views

PCA vs FA vs ICA for dimensionality reduction in questionaire data

I am trying to identify personality traits underlying the multidimensional data from a questionnaire. In more abstract terms this means reducing the dimensionality of my data from N-dimensional (where ...
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identification condition in factor model

Consider the following factor structure: $\Sigma=\Lambda \Lambda' + \Phi$ where $\Sigma$ is $p \times p$, $\Lambda$ is $p \times m$ without any restrictions and $\Phi$ is a $p \times p$ diagonal ...
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Post-hoc for 2x2 mixed design ANOVA using SPSS with two dependent variables

I am analyzing an experiment run with 162 participants using a 2×2 mixed design ANOVA. The experiment has two independent variable with two levels each, and two dependent variables. I need to know ...
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1answer
77 views

Combining two variables

I have a questionnaire about factors that affect trust in online shopping. The questionnaire is split into 5 topics (such as security, privacy, website design etc.) with 2 questions per factor. I've ...
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Getting estimate and CI for dummy variable in linear model

I have a linear model based on some variables (age, gaming and tasks) on response time. It looks like this: ...
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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 ...
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orthogonal latent trend

Assume I have 2 explanatory variables (or factors) X which explain y. I want to extract a trend (and maybe seasonality) from y which is/are orthogonal to X. Is there are a way to do this? Can PLS do ...
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Matrix Factorization in Recommender Systems: Uniqueness of SVD?

I was studying the collaborative filtering approach about recommender system and I read about matrix factorization approach. In SVD version, I have not figured out how the non-uniqueness of the ...
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23 views

The unique variance in Factor analysis

This might be a rather simple question, but this is troubling me a lot? Please help. Suppose in a factor analysis model, there are three variables $x_1$, $x_2$ and $x_3$, and two latent factors $w_1$,...
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Factor Analysis only one Eigen Value above 1

I'm doing a study for HR about a certain company's interviewing style. A number of respondents were given a 7 level likert scale (1 strongly disagree, 7 agree), and I need to find out whether I can ...
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25 views

How to obtain new variables using factor analysis in R?

I am working with 8 variables that are correlated with each other, and want to use factor analysis to construct two factors and then use them in my regression analysis. I typed this in R: ...
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Question: next step after regression analysis? how to tell if multiple variables all co-correlate?

I am new to regression analysis and I have found that my 'independent variable' or predictor correlates with several dependent variables (through multiple linear regression tests) in a way that ...
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1answer
37 views

Factor analysis in Market Research

I am doing a survey to find out customer experience/satisfaction for a specific product. My survey contains a scaling question in which i asked satisfaction level (from 1 to 5) 5 being very ...
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1answer
28 views

Factor Analysis on items measured on two different 5 likert scale items that is one scale is measuring frequency and other the agreement

Can I run factor analysis on items that are measured on two different 5 likert scale, that is one scale is measuring frequency ( i.e never , rarely, occasionally, frequently and always) and other ...
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26 views

Eigenvalues for Factor Model

Suppose that I have a 10 factor factor model. There is a eigenvalue associated to each of the 10 factors. How do I calculate these eigenvalues?
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Correlation Matrix from given R output of Factor Analysis

I carried out a factor analysis of 5 variables using a single factor. How do I estimate the correlation matrix assuming the one factor model holds? The R output is: