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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Is a factor solution with a Heywood case considered legitimate?

I read in an SAS manual consulted here that "Factor analysts disagree about whether or not a factor solution with a Heywood case can be considered legitimate." I was wondering if someone could develop ...
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38 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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62 views

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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6 views

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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12 views

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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32 views

Cluster vs factor analysis for grouping variables and cases

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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43 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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68 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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35 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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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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129 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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46 views

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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27 views

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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70 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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34 views

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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27 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 ...
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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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34 views

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 ...
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32 views

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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20 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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27 views

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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32 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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25 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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25 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:
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In factor analysis what is more stable sample to sample: regression coeffients or structural coefficients?

In Which matrix should be interpreted in factor analysis: pattern matrix or structure matrix? ttnphns remarks "Weak side of pattern matrix is that it is less stable from sample to sample (as usually ...
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21 views

PCA + Parallel Analysis

When I realize the Factor Analysis (I have 16 items), the PCA says I have 5 factors. But in the scree plot there is no elbow at all, just a decreasing line, that makes me think maybe I shouldn't be ...
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25 views

Calculating Eigenvalues in Factor Analysis and Calculating Factor Loads

So, as I wade back into the world of stats, I am finding myself confused about a few things when it comes to Factor Analysis. So I understand the bits about calculating Eigenvalues from a Correlation ...
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23 views

Will CFA produce the same loadings as an obliquely rotated EFA under these conditions?

I have in mind figures like the following, which purport to explain the difference between EFA (left) and a 'standard' CFA (right). I guess in this picture one loading per factor should be fixed, and ...
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49 views

Identification in confirmatory factor analysis

Consider a factor analysis $x_{ik} = a_{i} f_k + u_{ik}$. Usually, this model is estimated with identification restriction, say, with the first component of $f_t$ being one. This is to address the ...
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38 views

PCA on a Likert scale data

I am trying to conduct a small experiment based on Likert style data. I have a total of 20 questions, 10 are referring to a latent construct of happiness, and the other 10 to a latent construct of ...
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29 views

Factor loading of predictor on outcome variable

I know the basic and some more advanced statistics. I want to use multiple lineair regression to see whether the standardized questionnaire PsyCap, leader adaptivity and employability culture can ...
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52 views

What is an intuitive definition/explanation of an intercept in SEM?

Some of my friends/colleagues have recently taken an interest in structural equation modelling, and I have been having to field an increasing number of questions about SEM. Often times, these ...
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Factor analysis Geometric interpretation of common variance [duplicate]

I am trying to understand the fundamental differences between PCA and Factor Analysis. PCA is straight forward in that you take the eigenvectors of the data's variance (and hence considering all the ...
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144 views

What's the relationship between initial eigenvalues and sums of squared loadings in factor analysis?

On the one hand I read in a comment here that: You can't speak of "eigenvalues" after rotation, even orthogonal rotation. Perhaps you mean sum of squared loadings for a principal component, ...
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EFA: interpreting negative factor loadings [duplicate]

I've run an exploratory factor analysis with oblique rotation, and specifying three factors. The first two factors are correlated at almost zero with one another, while there's a negative correlation ...
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29 views

Which Method of Factor Extraction is Preferable With Communality Greater than 1.0?

I am trying to perform Exploratory Factor Analysis using SAS's proc factor with priors=smc, but am not sure which factor ...
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12 views

What kind of multivariate data is this judging from the QQ plot and Scatterplot Matrix?

This dataset is from R "cluster.datasets" package, named life.expectancy.1971. I would like to run Maximin Likelihood EFA(Exploratory Factor Analysis ) and therefore I checked the Multivariate ...
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14 views

How to tell if the survey is good enough/valid?

I just used 15-items questionnaires X which has never been used in my culture C. I've found that in my sample (n=150) α = .77, principal component analysis with 5 factors more than 1 eigenvalue, ...
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31 views

Bootstrapping data for factor analysis

How can I bootstrap my data before doing factor analysis?
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How to determine which factor rotation gives the best model fit? [duplicate]

I have to use factor analysis to determine if it fits my data adequately. I am wondering how rotations play into it. What am I looking for when I change the rotation? The p-value is the same so how I ...
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21 views

Factor rotations in non-negative matrix factorization?

My understanding is that solutions from Non-Negative Matrix Factorization (NMF) are not necessarily unique, and rotations can be imposed during the optimization process or after the solutions have ...
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30 views

We should normalize (or standardize) data before feature selection tests (t-test, related matrix, etc.)?

We should normalize (or standardize) data before these feature selection techniques? Which one for every technique? normalization of standardization? t-test Related matrix Stepwise PCA Factor ...
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60 views

How to use principal components as predictors in regression?

I have a couple of questions involving doing a regression (logistic or linear) after principal component analysis. If I find principal components using Principal component analysis, can I use these ...
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Multiple imputation and factor analyses

I have conducted a survey to collect my thesis data. The data naturally contains some missing values. I want to use multiple imputation but as I want to do a factor analysis this seems a little ...
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Model with factor scores as variables vs original?

I am new to this so please bear with me. I have two models, an original one with many variables, and a new one where I extracted 5 factors. I used both for a cox regression, and the model in which I ...