# 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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### Full factorial design involving two discrete variables with replicates as blocking factor; needed ANOVA details

I found this question (link) and I am intersted to know the answer from the experts. I have run a full factorial design involving two discrete variables, A at 4 levels, and B at 5 levels. I have ...
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In my novice understanding of ICA, we generate two matrices: a source matrix, which describes the contribution of variables to the independent components (analogous to loadings in PCA..?) and the ...
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### What does it mean if EFA shows worse fit than conceptual CFA?

I'm in the middle of developing a psychometric scale and running a few factor analyses here and there. I already have a theory in mind and the scale was developed with 4 factors. I ran a confirmatory ...
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### Factor Analysis Cumulative Explained Variance Exceeding 100% when k-factors < p-variables [closed]

I'm new to Factor Analysis and having a rather frustrating result. I'm using the Factor Analysis implementation from statsmodels in Python with 119 variables and would like to reduce down to k-factors....
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### Ideas for categorical data when analyzing OECD's Better Life Index [closed]

This is a really rookie question, but bear with me. I am statistic student and I am trying to do a project for school using the Better life Index data. I have got to the part where I need to do ...
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### Is there a standard measure of fit to validate Exploratory factor analysis?

I am modeling Exploratory Factor Analysis in R, Python, Mplus, and SPSS with maximum likelihood method and Varimax orthogonal rotation. However, each software gives different measures of fit and I am ...
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### Exploratory Factor Analysis (EFA) within a CFA framework in R: How to select anchor items?

In cases, data is ordered categorical, exploratory factor analysis (EFA) is best implemented using polychoric correlations and diagonally weighted least squares (for example, see here). To my ...
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### Are properly-defined Heywood cases a problem for factor analyses that use oblique rotation?

I am running an Exploratory Factor Analysis (EFA) in R, using the package mifa and the package mice to impute data, then feeding the correlation matrix to the psych package. I am using principal axis ...
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### Are my data a good candidate for EM imputation followed by exploratory factor analysis?

I am doing Exploratory Factor Analysis (EFA) in R, using principal axis factoring in the psych package. I have missing data that prevent me getting factor scores, so I am imputing data. I am using ...
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### Negative factor-level correlations between factors, which don't show at the manifest level

I am developing a scale which consists of six scale dimensions, six items per dimension, with hypothesized positive relationships between all factors. All scale dimensions have positive correlations ...
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### How can I simulate observations from a dynamic factor model?

Consider the following dynamic factor model where for $t = 1, 2, \ldots, T$ \begin{align} x_t &= \Lambda f_t + e_t \quad \text{ where } e_t = \Phi_1 e_{t-1} + \epsilon_t \text{ and } \epsilon_t \...
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### Which Chi-square value is more significant than the other?

I'm running factor analysis on two data(both N = 200) and trying to discuss which result is more significant than the other. ...
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### Help please! One factor but one item poorly correlated with others

Can anyone give me a simple answer to why Parallel Analysis is telling me it is a one factor solution when one of the ten items is very weakly correlated with the others?
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I ran factor analysis to drop the variables but confused how to read the result and how to select variables from factor loadings
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### Comparing the first principal component with an observed variable (mean)?

I want to see how using the mean of my variables instead of the first principal component helps represent (the first dimension) of my data. The idea is that if those are similar enough, I might as ...
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### Factor expressed as standardised variable in factor analysis

I know that in principal component analysis, we can express PCs as a linear combination of the variables, but is it possible to do that for factors in factor analysis? For my task I am given a ...
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### Difference between IRT and EFA to find factors

I am learning about Item Response Theory in which items are used to assess ability. In principle, multiple latent abilities may exist and some items test the one, while other items test another. This ...
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### Assigning Weighting Factors

I have a hypothetical example that closes to my research problem: Assume you are a boss and you have different types of tasks that you need to assign to your employee. Sensitive task (very classified)...
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### Correlation Matrix Low Correlations, and Factorability of Data

I’m undertaking doctoral research about behaviours in relationships, for the purpose of developing a new scale. My intention is to undertake Exploratory Factor Analysis to consolidate a large initial ...
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### Using dimension reduction techniques for poverty/wealth indicator

I would like to create an indicator/index of a person's wealth (or socio-economic status, SES). I have about 20 variables that are a combination of education, household assets, access to money, and ...
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### Multiple factor analysis: Getting more number of factors than the number of dimensions/ features

I am trying to apply multiple factor analysis on a survey data, which has all sorts of features - numerical, categorical and ordinal. In total, there are 109 features. Now, when I did multiple factor ...
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I wanted to confirm my intution about the meaning of "loadings" I have made out of eigenvalue/eigenvector decomposition, but I still fail to do that. Note that I made 3 pairs of highly correlated ...
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### Why the first principal component is mostly negative while the second component is mostly positive?

I am running PCA for a fleet management data frame $X$, where each column is a city, each row is a date, there are 50 cities and 500 dates. I run PCA on $A=X^{T}X$. Then the first component $v_{1}$ ...
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### Minimum number of variables for factor analysis?

Is there a minimum number of input variables that an exploratory factor analysis requires?
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### How to do Bayesian estimation when factors enter equation as a product?

I am trying to write down an algorithm for Bayesian estimation with Gibbs sampling. A certain part of the model involves the following pattern: \begin{align} &Y_{11}=\beta X_{11}+\alpha_{11}\theta^...
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### Which has more mutual information with a multivariate Gaussian: its first principal component, or its first factor?

I have a $k$-dimensional Gaussian random variable $X\sim\mathcal{N}(0, \Sigma_X)$. What I want is a 1-dimensional scalar r.v. $Y\sim\mathcal{N}(0,1)$ that is jointly Gaussian with $X$ while maximizing ...
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### Generalizability study of subscaled rating instrument

I have a school rating ($1$ thru $4$) instrument that consists of $9$ subscales (e.g., classroom instruction, school management etc.). Under each subscale, I have $6$ items on which rating occurs. I ...
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### Minimum value for Squared multiple correlations between items and factors

When building a CFA model, each of item that form a latent variable has its own squared multiple correlation coefficient or reability. Is there a minimum value for squared multiple correlations (R^2)? ...
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### Is it possible to compute Kaiser-Meyer Olkin (KMO) for all scale items and how?

In another post, what are the assumptions of factor analysis, someone mentioned that it is possible to compute Kaiser-Meyer Olkin (KMO) not just for the whole correlation matrix but for each scale ...
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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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### 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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### 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 ...