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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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Is it possible to weight items differently in a factor analysis?

Suppose I have 100 targets that have been rated by 1000 individuals. I want to perform a PCA on those 100 targets. Now, I'm curious if I were to take some property of the targets into account, how ...
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How to decide number of retained factors when the scree test and the eigenvalue result in different numbers?

I was trying decide on the number of factors to retain in a factor analysis problem. My scree plot showed an "elbow" after the fourth factor and although the fourth factor had an eigenvalue under ...
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Factor Analysis, Cluster Analysis, or something else?

I'm trying to figure out how to determine how a set of variables tend to group together without discouraging crossloadings. For example, say I had a set of symptoms: sneezing, headache, fever, nausea,...
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After conducting an EFA, how to score a factor for new participants using its constituting variables?

I study psychology, and I'm learning EFA (again autodidactically -_- bloody middle east).. So I hope you help me with this naive question Scenario I have a questionnaire made, and I was able to ...
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Define statistical potential energy [closed]

I am looking for a statistical method that closely relates to the idea of potential energy. Here is a quick google definition for potential energy "...the energy possessed by a body by virtue of ...
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stability of factor analysis

I am using the R "psych" package to run factor analysis. If I check the optim function for convergence, I notice that while I get convergence for say 22 factors, I don't get convergence for 21 factors....
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Too many factors extracted from EFA!

I am constructing a scale. I have 80 items and 300 sample data. I ran EFA - Principal Axis Method of extraction and direct oblimin rotation in SPSS. I have 23 factors (using both Eigen value and ...
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How to use Factors from Exploratory Factor analysis in further analysis?

I have performed an exploratory factor analysis on a large data set as a dimension reduction technique. I have come up with 20 factors that group together my predictor variables. However, I am not ...
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The outcome of a Dynamic Factor Model

A basic question but you might help me a lot. What is the outcome of the Dynamic Factor Model (or Static)? As an example let's assume we have 24 time series in an hourly panel. We apply PCA and we ...
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How to interpret feature importance in a decision tree after applying Factor Analysis

I'm using SKlearn to apply Factor Analysis (FA) to my data before training a Decision Tree. I then want to do an importance analysis. If I had not applied FA to my data, I could just call clf....
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Choosing number of factors in PLSR

Im confused about how many factors I should choose for my prediction model. I am using Unscrambler X to do PLSR. Unscrambler is supposed to suggest the optimal number of factors. It suggests 4 factors ...
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How to control/correct for response bias in survey or questionnaire data for Factor Analysis

I would like to apply Confirmatory Factor Analysis (CFA) to a Likert-type questionnaire data. It is supposed that this data is affected by response bias: some patients either overestimated or ...
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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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Promax PCA interpretation in order to validate singular items - Structure or Pattern Matrix?

I am doing a promax PCA analysis. I have a big dataset (over 1000 subjects) and about 50 items. I am trying to validate the singular items. My final aim is to exclude non-relevant items (those which ...
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Normality of Data for Factor Analysis?

The organization where I'm working at required me to study Factor Analysis to apply it to some of their research. They gave me different textbooks as study material and switching through both of them, ...
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FAVAR estimation Boivin et. al.(2009)

Boivin et. al. (2009) following the paradigm of BBE(2005) manages to decompose the fluctuations of each series into common and series specific components and study shocks into these components ? Do ...
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Why would someone use regression analysis to compute weighted variables?

I stumbled upon a measure that uses multiple regression analysis to compute weighted variables, instead of factorial analysis or other more common methods. I have a feeling this is just bad statistics ...
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Detecting insufficient communalities in R

Given is this sorted factor analysis: ...
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Interpreting PCA with varimax rotation

I have problems understanding the Factor Component Analysis of the paper: "Measuring thirty facets of the Five Factor Model with a 120-item public domain inventory: Development of the IPIP-NEO-120". ...
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is it necessary to have same scale of IDV in PCA [duplicate]

Can PCA be done if my data have both likert data and discrete (ordinal and nominal)as independent variables?
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Is this a valid work-around for collinearity?

A fellow PhD student has monthly data on temperatures (T) and precipitation levels (P) for a certain agricultural region. He would like to use it to predict total farm revenues (Y) for year t: $Y_t=\...
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Modification of Model after EFA and CFA

I have the following problem: for my master thesis I am, or rather was trying to validate a scale on relationship cognitions in a different cultural context (germany/western vs. malaysia/asian) Since ...
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Data analysis mess! Huge data set, 2 factors with 2 levels each, but the levels are the same

To explain the hypothess a little bit: The factors would be emotional words and neutral words; the levels of both factors are left and right visual hemifields. The data is the participants response ...
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Multiple regression data analysis

https://docs.google.com/spreadsheets/d/1czrXmJuxvwalDwNDLHIvt64QqNb8cSTahEEK8DIiQPM/edit?usp=sharing the study: "right and left visual hemifields and duration of the presented stimulus were ...
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EM algorithm for factor analysis,the formula of diagonal matrix stuck

I am trying to learn the factor analysis of CS229,the relative lecture note is here:CS229 Lecture note9 I have stucked at the diagonal matrix formula which is at the page 9: What's the derivation of ...
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Any 'quick' way to test which of 50 variables affects 1 dependent variable?

I've very rusty with my statistics. I know I can test each one by one. But is there a quicker test? Specifically, I have a list of 300 clients with a "contact rate" (dependent variable). If I have ...
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Exploratory Factor Analysis for Smoking cessation RCT?

So I'm planning a RCT where I'm evaluating a smoking cessation application intervention vs usual care among adolescent smokers. For my statistical analysis I'm looking at the point prevalence of ...
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Can I interpret the factor scores in my factor analysis as absolute values? [closed]

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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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 ...