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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 I interpret the factor scores in my factor analysis as absolute values? [on hold]

One of my cases has a value of -14.07, putting it at the bottom of the distribution. But it would make more sense if its value were positive. I read that the sign of the factor is meaningless, does it ...
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14 views

Principal component analysis how to find important factors in spss

I did a survey to know the attitude of customers towards various elements of direct banking channels. I have performed Principal Component Analysis on a set of 70 items and generated five factors. I ...
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21 views

PCA's eigenvector with low variance, why people think they are 'noise'?

When we do a textbook PCA decomposition, get a series of eigenvalue $\lambda$ and eigenvector $v$ that fulfill: $ Av= \lambda v $ we can sort these eigenvalues (together with the corresponding eigen ...
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6 views

Sampling from factor analysis

Using the notation of Hinton and Ghahramani, the generative model a random vector $\textbf{x} \in \mathbb{R}^p$ under factor analysis is $$ \textbf{x} = \Lambda \textbf{z} + \textbf{u} \tag{1} $$ ...
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16 views

FAVAR using PCA

I am doing a FAVAR analysis with 2 steps PCA method. I am confused a bit about the second step. When I get the PCs, how should then I estimate VAR? Just including PCs as other variables and simply ...
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12 views

Exploratory factor analysis of a non-normally distributed data set with probable multicollinearity problems

I am trying to develop a scale measuring employee satisfaction regarding organizational support using spss. Most of my variables are positively skewed which should not be a problem in EFA as long as ...
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11 views

Are EFA and/or ESEM models on the same data set with different factor solutions nested models?

Are EFA and/or ESEM models on the same data set with different factor solutions nested models? If yes, how are they nested? Are EFA and/or ESEM models and more restrictive CFA models on the same data ...
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6 views

optimality of LDA dimensionality reduction

typically when you do dimensionality reduction using LDA, you select $n_{class}-1$ vectors with largest eigenvalues as discriminants given the fact that you only need $n-1$ dimensions to classify $n$ ...
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Is it correct to use Exploratory Factor Analysis in a Psychometric analysis study instead of Confirmatory FA?

I´m a Psych student, and I´m currently doing a research on validation and adaptation of a Participation scale made in the U.S. to a Peruvian sample. I think that the main differences between both ...
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10 views

Any way to force positive loadings in factor analysis?

I want something like factor analysis, something that will tend to yield factor loadings that are simple linear combinations of the factors (where most loadings are 0), but I have a very strong prior ...
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11 views

Factor analysis across questionnaires - confirmatory or exploratory?

I am new to factor analysis. The aim of my research is to relate a psychological construct (e.g. depression) to task behaviour I have additionally collected in a large sample of people. I want to ...
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17 views

Does non-Gaussian probabilistic PCA give orthogonal basis?

Probabilistic PCA - Gaussian: In their Probabilistic PCA model, Tipping and Bishop assume the following model $$ \boldsymbol{x} \sim \mathcal{N}(0, \mathbf{I})\\ \mathbf{t} | \boldsymbol{x} \sim \...
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20 views

How does the solve() function produce factor correlation scores in the factanal() function?

Using the factanal() function in R produces factor correlations: ...
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42 views

How does factanal() function in R calculate correlations between factors?

When using the factanal() function from the stats package in R using the promax rotation, you are given factor correlations. ...
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17 views

Analysing a 3-D Array

I have a 3-D Array. Where first dimmension represents the amount of systems I am analysing. The second one represents 15 Minute time ticks of a day and the last one temperatures between -7°C and 26°C. ...
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37 views

Cluster analysis of variables or observations?

I'm very new to cluster analysis. In papers such as Richette et al.1 (which tries to see which concomitant diseases cluster together), authors first cluster the variables and then the observations (i....
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21 views

Aggregating data before factor analysis

I have data on individual sales transactions (customer bought a soap for example) and around 30 different indicators about that sale (price of item, time spend front of item display, shelf number...). ...
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10 views

Good article examples of PAF/PCA

Can anyone give me (and probably to the rest of the world) good article examples which uses especially PAF (and/or PCA) factor analysis with oblique and/or orthogonal rotations?
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21 views

Interpreting factor correlation matrix

I've done principal axis factoring and direct oblimin rotation. Can I interpret "factor correlation matrix" like Pearson's correlation, does these differ when it comes to interpretation?
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27 views

ICA vs EFA: scale ambiguity?

ICA (Independent Component Analysis) Model $$s \sim \text{Non-Gaussian(parameters}_1)$$ $$x=As$$ EFA (Exploratory Factor Analysis) Model $$z \sim \mathcal{N}(0,I)$$ $$\epsilon \sim \mathcal{N}(0,\...
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10 views

LM Stat - Confirmatory Factor Analysis

The output of the Confirmatory Factor Analysis provides the "LM Stat provides a rank order of the 10 largest LM stat for Path Relations." Can we include more than one path into the model or are we ...
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1answer
26 views

Constrained Linear Regression with multiple factors in R [closed]

I am trying to figure out how to run a simple linear model with two factor variables as regressors without the intercept. In particular, I would need to write a code to replicate the Barra Fundamental ...
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15 views

Application of Factor Analysis to a table of count data

I am being asked to apply a statistical technique that I do not think is optimal. I have asked before, but was told my question was vague. I have re-worded it appropriately here. I am being asked to ...
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10 views

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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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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11 views

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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20 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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57 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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79 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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31 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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25 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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14 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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32 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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50 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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11 views

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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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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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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6 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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19 views

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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30 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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39 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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11 views

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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154 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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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 ...