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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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Can you use factor analysis on a table has count data? [on hold]

I am working on a project where my predecesor has been analyzing a table of rows by columns of count data. Brands represent the columns, and statements about those brands represent the rows. The cells ...
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Machine Learning point of view regarding the purpose of EFA [on hold]

From the point of view of Machine Learning, what is the purpose of Factor Analysis (FA)? I used to think that it is a dimensionality reduction, because it is so connected to PCA, but when I read in ...
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Rotational invariance of PPCA

From here (slide 23) and here (page 5, 4th slide) I understand that it is said that PPCA (probabilistic PCA) is rotational invariant. It can be written as follows: $$\text{PPCA}(X) = [\mu, W, \sigma^...
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Signs in SPSS's PCA with rotations with the FACTOR algorithm

I am trying to reproduce the results of the PCA with rotations from SPSS in python. But there is some information I didn't find in their documentation. I am trying to do the PCA like in the FACTOR ...
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11 views

Pearson correlation after principal component analysis and varimax rotation

Is it possible (or does it make sense) to check for correlation after varimax rotation, since varimax assumes that there aren't any correlation between factors (or components)?
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39 views

Factor-loadings vs Variable-loadings

In PCA and Factor Analysis, there is the term loadings, which refers to factor loadings (onto the original variable). Does the term (original) variable loading (onto the latent factor) exist?
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53 views

Fundamental difference between PCA and FA?

According to this, the fundamental difference between PCA and FA can be illustrated via the following image: So, the direction of arrows changes. According to this answer and a few others: ...
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13 views

How can I calculate the standardized root mean square residual (SRMR) from the psych package in R?

The psych package in R provides the root mean square of the residuals (RMSR) when using the principal (principal components analysis) or fa (factor analysis) functions. How could I calculate the ...
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11 views

Appropriate Statistical Analysis for Variable Reduction

I'm planning to conduct a study for clustering a set of observations. For the beginning, I'm planning to include more than 50 variables to my study. Therefore I must apply a relevant statistical ...
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17 views

Converting standardized factor scores back to original scale

According to my EFA, items q1-q5 of my questionnaire load on factor1 (loyalty), and q6-10 load on factor2 (satisfaction). Factor loadings are not similar between items within each factor. I would ...
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10 views

PCA with high amount of repeated measures

I want to create a system that can automatically evaluate a session as success or a failure. Each session generates a lot of data points, and thus I want to start my modeling with dimensionality ...
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26 views

How to interpret low loadings all over PC 1?

My PCA with prcomp in R results in very low "loadings" (i.e. eigenvectors, see figure below). I've tried a rotation with ...
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35 views

Dimension reduction [closed]

Can i apply dimension reduction method such as random forest, lasso, factor anaysis or principle compoenet analysis on data which was extracted from two stage stratfied survey
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Running EFA and CFA on the same population at different time point

The participants filled in the questionnaires at 6-month intervals. Since the questionnaires detect changes, which I think would not affect the factor structure. (And the EFA on the 1st time point do ...
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6 views

Manage covariance, multiple regression, moderated regression

I am having a huge problem with my stats. I am working towards a predictive model. I have 8 continuous IVs, 3 potential categorical IVs (2 of whom I had to compute into dichotomous), and 8 continuous ...
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11 views

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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21 views

Investigating the change of a network / factorial structure over time

I have several variables (questions from a questionnaire) that regroup into several factors (using factor analysis). However, I would be interested in knowing how this factorial structure changes ...
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1answer
18 views

The Meaning Behind the Cross Validation Score in Factor Analysis

In order to choose the best number of underlying factors for my data using factor analysis, I decided to use the tutorial outlined in scikit-learn's documentation. Running ...
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4 views

How to incorporate Fama and French three-factor returns in cross-sectional multiple regression model?

I have a follow -up question about the use of Fama and French three-factor model returns as control variable in a cross-sectional multiple regression: https://quant.stackexchange.com/questions/35016/...
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Factor Score Prediction - Model Developed w/ Database A - Predict Factor Score for Database B

I'm considering apply FA to predict/assess new customer profiles based on Factor Scores. I mean, I will estimate the Loading matrix L based on Yi observations that belong to, say Database A with some ...
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5 views

estimating main effect with two nested factors

Suppose we have two factors sample and temperature and temperature is nested within sample. Is it still possible to estimate the main effect of sample? Thanks very much.
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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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25 views

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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25 views

ICA for noise reduction of covariance matrix

Trying to understand ICA in the context of noise reduction of covariance matrices (of dimensionality M). I understand in PCA, you can reconstruct the covariance matrix by squaring the first N ...
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Factor analysis of a function with binary output

I have a data set and I am interested in determining which factors of this data set contribute most to the output. The data set varies by multiple factors $X_1$, $X_2$, .... $X_n$, and the function ...
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48 views

R: how to interpret the output of factor analysis by “fa {psych}”

Parts of both outputs of the functions "factanal" (base) and "fa" (psych package) are shown below. Interpreting the output of factanal: It says that the (theoretical) factor-model differs ...
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9 views

What tool do you use to Analyze Qualtrics CSV data

I’ve conducted a survey and have the csv export file as the results. What tool do you recommend to analyze the relationships between different factors? I think I can manually do ETL and put the data ...
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26 views

Two-way ANOVA on the effect of gender and age on factor scores obtained through EFA?

A questionnaire consisting of 24 Likert-type questions was developed and distributed to the participants. The questionnaire had not been validated in the past, therefore, exploratory factor analysis (...
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1answer
24 views

How to proceed when collapsing ordinal items with levels that got no answer?

I have a set of 8 Likert-type items with 9 levels each. In no case do we have an item for which responses fill all possibilities and this has shown to be an issue for the SEM I'm trying to run (as ...
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21 views

What is the difference between using the correlation matrix verses the raw data matrix in factor analysis?

I am running an exploratory bifactor analysis on some neuropsychological data using the omega function from the psych R package (...
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1answer
42 views

Further analysis after performing exploratory factor analysis

A questionnaire survey was conducted to explore underlying factors affecting pedestrian road crossing behavior. The respondents were asked to answer Likert type questions along with demographic ...
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40 views

Interpreting Negative Factor Scores

I used self organizing map to cluster factor scores. I used 5 variables for clustering and at the end, I have 4 clusters. In output, some means of factor scores (for every each subscale) are negative. ...
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22 views

Factor Scores and Clustering

I used self organizing map to cluster factor scores. I used 5 variables for clustering and at the end, I have 4 clusters. Some factor score means are negative. How am I supposed to interpret these ...
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10 views

How many levels is to many levels in a multiple factorial ANOVA (MANOVA)?

I performed an experiment where in which I got very good results when I perform the MANOVA analysis using 3 factors with: 3x3x9 levels. Then I tried to get a global perspective of the interactions ...
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49 views

How to interpret reverse-coded items?

I prepared a questionnaire to extract the factors that explain the pedestrian crossing behavior. One section of the questionnaire was constructed so as to measure the "motivation" for walking. It ...
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22 views

Exploratory factor analysis_degree of freedom and significance

I'm trying to do a factor analysis on the data of my project and I encountered some problems. Any feedbacks or suggestions will be appreciated! To be specific, the participants received prompts at ...
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12 views

Correlations driven by one or two groups

Let's say that variable A is known to correlate positively with B and A is also known to correlate positively with C. It is not known whether B correlates with C, but the theory suggests that it ...
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1answer
15 views

can I use factor scores as DV in linear regression?

after EFA , 5 latent variables are extracted....after getting factor scores for these 5 latent variables... can I use one of those variables as dependent variable in multiple linear regression....
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1answer
35 views

Expectation of latent variables in Factor analysis Model

I am going to through the theory behind factor analysis models given here Let's say our model is \begin{align} y_i = \mathcal \Lambda x_i +\epsilon, \end{align} where $y_i$ is the $p$-dimensional ...
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Conducting a Multiple Factor Analysis with large categorical data

I have a combination of continuous and categorical variables, so I have decided to use a MFA. However the categorical variables are landuse type and bioregion, with a large amount of classifications. ...
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Comparing two CFAs in r (each CFA has a different sample)

I conducted separate CFAs on a measure with 4 dimensions. One CFA was conducted in men and the other in women. I have been asked to compare the two models. I can do this in r using the anova function ...
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67 views

Dealing with Heywood Case in EFA using SPSS

I conducted a survey with 10 Likert scale questions. Now, I am running a factor analysis in SPSS using Maximum Likelihood Estimation. Data Description: Sample size = 30 Number of Indicators = 10 ...
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33 views

How to conduct confirmatory factor analysis with small sample size?

I plan to conduct a confirmatory factor analysis, wherein there are 12 observed variables and 3 latent variables. My sample size is 30. However, I read that to conduct a factor analysis, the sample ...
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12 views

Factor model identification

I am trying to understand a proof in a paper by Bai and Wang 2003, Identification and Bayesian Estimation of Dynamic Factor Models: https://www.google.com/url?sa=t&rct=j&q=&esrc=s&...
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19 views

Understanding Dynamic Factor Models

I am currently learning dynamic factor models and factor analysis (and principal components analysis) in general. Currently, I have identified my components using princomp in R. Additionally, I have ...
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1answer
287 views

Exploratory Factor Analysis: How to deal with 0's in Likert scales (1-5)?

I want to conduct an exploratory factor analysis on a small questionnaire that I have. The questionnaire consists of 20 items (N=100) that are scored on a 1-5 Likert scale (strongly agree - strongly ...
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1answer
66 views

What is mean by the non-gaussianity in the independent component analysis(ICA)?

What is mean by non-gaussianity in ICA? Why do we use in ICA? How is Non-Gaussianity is an important and essential principle in ICA estimation? Following is the statement I found in a research paper....
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26 views

Difference between DCC copula and factor copula models

I'd like to see if I understood this correctly (probably not). Assuming I have a data set $[y_1, \dots y_d]$ of returns and I wish to model their dependence through a copula : DCC-copula (Engle 2002)...
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1answer
82 views

Latent variable and Factor analysis ICA

While I was going through the factor analysis for Independent component analysis, I got stuck in one statement. How does it come to co-variance of S* is I? Is A* =ART ? Following is what I was going ...
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23 views

How to maximize regression coefficient instead of factor loadings in SEM?

I wonder if there is a method that allows finding factor loadings so that the factor would predict the distal outcome the best? The ordinary SEM model would estimate factor loadings and regression ...