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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Why is the following choice of factor loadings optimal in two-state MLE for factor analysis?
Suppose we have $n$, $p$-dimensional, samples
$\overrightarrow{X_i} \sim \mathcal{N}(\mu, \Psi+\mathbf{w^Tw})$. $\Psi$ is a diagonal matrix of specific variances, while $\mathbf{w^Tw}$ composes the ...
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Is there a problem if variables have different levels in factor analysis?
I'm planning to do a factor analysis on data with ordinal variables 1-5, 1-6 and 1-3. I'm new to factor analysis and I wonder if there is any problem that the factors have different levels? Thanks in ...
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How to estimate an unobserved variable?
Suppose I have a time series $\{X_t\}_{t=1}^N$ that is corrupted by Gaussian noise: $Y_t = X_t + \epsilon_t,$ where $ \epsilon_t \sim N(0, \sigma^2)$, and we actually observe $\{Y_t\}$.
We have a ...
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In EFA, what is the advantage of dealing with missing data via an E-M estimate of the correlation matrix rather than individual data points? [on hold]
Edited for clarity of language and to change the context of the question
I am running EFA on 61 variables (221 participants) and have missing data arising from 'don't know' answers (likely MCAR; ...
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Quartimax rotation in Python [closed]
I am trying to use the statsmodels package to do a quartimax rotation on the first two PCs of a dataset. The result is that all but one of the loadings are zero for each of the factors. This seems at ...
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Selecting method for adding a random component to regression estimates during expectation-maximization (goal: EFA)
Edited to update: I now see that I cannot use the 'Regression' option in SPSS to add error variance to data imputed via EM, which was an assumption I made in my original question. However, I am still ...
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Is low variance common with FAMD or other data dimension techniques with categorical variables?
I'm using the FAMD(factor analysis for categorical and numerical variables) function from the FactoMineR package in R. The cumulative variance of my first 4 dimensions is very small. The first 4 ...
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Reverse coding items: missing data + factor analysis
I have a data set which includes a number of variables which need to be reverse coded. I have already completed my missing data analysis, however did not reverse code the items prior to replacing the ...
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Input data for Canonical Correspondence Analysis (CCA)
I'm going to conduct Canonical Correspondence Analysis (CCA). In the tutorial I've found at: CCA
environmental data are discrete ...
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Exploratory data analysis before pefrorming Canonical Correspondence Analysis (CCA)
I want to perform CCA, but I read that,
remember that observations (for example, species abundances) have to present unimodal distributions along gradients (for example, environmental variables). ...
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Guidance on Exploring Categorical Data
I am hoping this is well recevied - based on the meta page, this is the appropriate SE site to ask questions about statistical analysis. I will try to provide a clear explanation of what I am hoping ...
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eigen value decomposition of co-variance a series generated by factor model
Let's assume $N\times T$ series $Y_t$ is generated by the following equation.
$$ Y_t = \begin{bmatrix}A_x & A_m\end{bmatrix}\begin{bmatrix}x_t \\ m_t \end{bmatrix}$$
Where $A_x$ and $A_m$ are $N\...
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Exploratory Factor Analysis and Confirmatory Analysis
I am seeking to apply these methods to psychological questionnaire data. I have read up on the basics but I am curious - and this is not limited to just ECA/CFA, but what is the best method to look up ...
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how to derive eq 21.2.3 in BRML, Factor Analysis (Eigen-approach likelihood optimization)
how to derive eq 21.2.3 in BRML, chapter21 Factor Analysis?
Log Likelihood function (eq. 21.1.13):
$$
\log{p(\mathcal{V} | \mathbf{F}, \mathbf{\Psi})} = -\frac{N}{2}\left( \mathrm{trace}(\mathbf{\...
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Calculating a single Factor value against a table of variables
Ok here's a fun one...
We have to calculate a given referee's strength rating/appropriateness for refereeing a given game. The number we come up with has to be something meaningful, so it should be ...
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How to latently cluster regressors based on regressors' relationship with the outcome?
What is the best way/method to model patterns across coefficients and reduce number of coefficients based on these patterns?
We have hundreds of regressors on the same scale and try to reduce the ...
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A Two-tailed One-sample Test of a Categorical Variable with Multiple Raters
I feel like this should be a Stats 101 question, but I've taught Stats 101, and I can't quite figure it out, so probably not....
I'm using an unsupervised learning technique to create topic models of ...
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Do I estimate factor loadings in a confirmatory factor anlysis (CFA) aimed at verifying an exploratory factor analysis (EFA)?
I decided to use a questionnaire published by another researcher (paper and supplementary here).
In the article they perform an EFA, find two factors, and report the resulting factor loadings (...
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How to perform an oblique rotation on a structure matrix?
I am trying to code an exploratory factor analysis (principal axes factoring) from scratch, on a set of questionnaire items. After determining the appropriate number of factors, I was able to ...
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Theory building with Factor Analysis
I have a dataset with 95 predictors and a binary response. Many of the predictors have high correlations, so I did Factor Analysis and identified 29 latent factors (most of which make logical sense). ...
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Independent Component Regression using sklearn's FastICA
I am trying something along these lines
...
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Parallel analysis for exploratory factor analysis
The suggested number of factors is 2, which is not consistent with my understanding of parallel analysis. In my view, we should keep factors which the eigenvalue of the factor is larger than that of ...
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SEM Configural invariance multigroup: how to calculate statistical significance of coefficients between groups?
I would like to know your opinion about the following issue.
I am estimating a multi-group SEM model on two groups (urban vs. extra-urban). The theory behind states that the factor loadings could ...
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factor analysis of mixed data - difference between quality and contribution
I started to use the R package FactoMineR to perform factor analysis of mixed data (function FAMD).
Could someone please be so kind and explain the difference between quality (cos2) and contribution (...
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What is $X$ in the fundamental equation of factor analysis?
Mulaik (2009) p. 135-136 writes that
Let Y be an $n \times 1$ random vector of random variables whose
variables are the observed random variables $Y_{1}, ... , Y_{n}$.
Assume that $E(Y) = 0$ ...
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Python Factor Analyzer and PCA
I am performing PCA and I need to extract squared loadings.
I found this python library, Factor Analyzer, that can extract eigenvalues and squared loadings, etc., but the results are different from ...
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Maximum likelihood estimator Factor Analysis
I'm looking for a good explanation for how to perform factor analysis using MLE. I'm aware of the factanal function in R, but I'm looking to calculate it manually ...
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MCA in FactoMineR: all variables are the same on Dim 1?
My data is ordinal (1, 2, 3, 4, 5, NA from a likert scale) and doesn't have any obvious pattern looking at the raw data.
My code looks like this:
library(FactoMineR)
df <- data.frame(Var1 ...
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20 views
Significance of factor variable that is an indicator for missing data
I read here and elsewhere that one technique for dealing with NAs in a database is to create a dummy variable that is 1 if an observation (row) has no missing data ...
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explained variance of single item
Assume I've got a factor loading matrix like this:
Now what I am trying to figure out is the percentage of variance in item would be explained by F1 (the first factor).
I'm not sure what that ...
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Can I obtain original data by multiplying varimax-rotated principal components with varimax-rotated unit length loadings?
I have perform conventional Empirical Orthogonal Function (EOF) analysis to my data set and obtain loadings (eigenvector scaled by square root of eigenvalue) and corresponding principal component.
...
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sklearn FactorAnalysis with wide data
I am using sklearn's FactorAnalysis to identify latent factors in my data. I prefer FA to PCA because I cannot assume equal errors or variance across variables. The dataset is wide (275 variables) and ...
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Correlation in Factor Analysis
In the context of factor analysis as in the extract below
Could somebody explain why the correlation between the $j^{th}$ feature and the factor $G$ is $w_j$. Also, why is the correlation between the ...
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Should a factor analysis (for construct validity) be performed in a section of a test that is meant to measure knowledge in a specific subject?
As a part of a study, a survey to measure the impact of an environmental education project is being developed, and to do so, factor analysis and principal component analysis are being performed for ...
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How to assign a prior distribution to a loading matrix that has restrictions?
I came across the paper Fast Variational Bayesian Linear State-Space Model. They work with the following model:
$$\begin{align}
{\bf{x}}_n &= {\bf A} {\bf{x}}_{n-1} + {\text{noise}} \\
{\bf{y}}_n &...
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1answer
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SEM: issue with two correlated latent variables
I am fitting a SEM model that includes socio-economic status (SES) for a household and environmental conditions (env) surrounding this household (road condition, sanitation etc).
My (obvious) ...
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Convergent & Discriminant Validity -Same construct (measured by different meaures) in two different samples
I don't know how to go about looking at the Convergent & Discriminant Validity of the same construct measured with two different scales in two different contexts.
This is a cross-cultural ...
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Why protect “general factor”s in factor analysis?
My Multivariate Analysis textbook states that
As we have noted, a general factor (that is, one on which all the
variables load highly) tends to be "destroyed after rotation." For
this reason, ...
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how to interpret factor analysis results
I’ve just recently started using r and I’m also new in factor analysis and I’m struggling a little understanding the results I’m getting. I used factanal() function and this is the results I got:
With ...
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How to analyze difference in answers between groups across multiple Likert questions? Categorical PCA and Chi Sq?
I'm analyzing this dataset from UCI ML Repo. It's on the perception of Wikipedia amongst university professors/instructors. I'm looking to test the differences between departments in their answers to ...
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Two questions regarding factors/loadings in PCA (Factor analysis)
Sorry if these end up being kind of naive questions, but I'm only starting to get into this type of data analysis technique:
-When I decide to remove a specific variable from my Rotated Component ...
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Cronbach's alpha interpretation - dichotomous data
I have calculated Cronbach's alpha in R using the psych package and I am trying to interpret them now. I want to properly understand this, as it is part of my ...
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How to decide if a rotation is necessary in a factor anaysis?
I have a (self-report) scale with 18 items. The scale as a whole is very reliable ($\alpha = .92$); however, the original authors report two sub-scales.
Here is the interesting thing that I don't ...
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Resampling or simulating orginal data to assess validity of experimental measure
I would like to conduct combination of EFA and CFA to assess if the measure I've designed to evaluate results of an experiment fits into proposed theoretical model or not. My theoretical model ...
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Interesting Way To Implement Factor Analysis From PCA
Is it possible to modify the PCA algorithm so that it actually implements factor analysis? We can assume that the uniquenesses are known.
I'm aware that for a $d$-dimensional data $x$, PCA takes the ...
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Problem with Exploratory Factor Analysis for my 7 items measuring attitude on SPSS
My factor analysis using direct oblimin keeps giving me only partial results, stating 'Attempted to extract 2 factors. In iteration 25, the communality of a variable exceeded 1.0. Extraction was ...
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Hierarchical Factor Analysis - Analyzing the factor structure of an identified factor
Problem Summary
After performing an exploratory factor analysis one of the resulting factors "contains" a lot of variables which make its interpretation very hard.
Since all the other factors have a ...
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1answer
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How can Factor Analysis be used to remove questions from a survey?
Suppose I have a psychological questionnaire asking 30 questions about a person's mental health (on a Likert-scale 1-7). These 30 questions fall into 7 separate, but correlated categories.
The ...
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1answer
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Exploratory factor analysis for clustered data in R
I am new to both R and factor analysis, and I need to run EFA for a dataset that used cluster survey design. Is there any package for FA in R that can handle cluster data?
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1answer
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Is there a point to using EFA for scale validation when you can always fit a second-order CFA?
I have been trying to understand the use of Exploratory Factor Analysis for the purpose of scale validation.
Say you have developed a scale to measure construct X, which is supposed to be one unified ...
