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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Dependent Variable in Factor Analysis. How to measure attitude toward application usage?

I am performing an analysis to evaluate the attitude of our marketers toward Apps. I have done the explanatory factor analysis (principal component)and I have received 4 factors (one of my factors is ...
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why are these two ways of computing EFA in R not identical?

I am confused trying to understand the difference between two ways of executing an EFA in R that I previously assumed to be completely equivalent. First, I make some data up: ...
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Comparison indices

I am comparing different models in Confirmatory Factor Analysis (CFA) to decide what my optimal number of factors and factor structure should be. The main indices I have been using are chi square , ...
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Is "cluster" rotation of psych R package Harris-Kaiser independent cluster rotation?

In the documentation (https://cran.r-project.org/web/packages/psych/psych.pdf) it says: "none", "varimax", "quartimax", "bentlerT", "equamax", "...
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Within item response theory, what is the $\theta$-grid?

Within item response theory, the latent trait (e.g., ability) is often depicted as $\theta$. Within item response theory, I have also come across the term $\theta$-grid. For example, the description ...
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Why is the correlation between two coordinate axes measured by cosine?

In factor analysis, I believe, the correlation between two factors is measured by the cosine of degree between the factors. For instance, the correlation between two factors below is cosine θ, the ...
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Why the correlation between factors are penalized when weight is large negative in Oblimin rotation?

I'm facing difficulties in interpreting the criterion for the Oblimin rotation. In my knowledge, the following criterion shall be minimized in oblimin rotation. $$\sum_{ij} (\sum_{v}{l_i}^2{l_j}^2 - \...
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Explaining Variance in Regression Model of highly correlated data

I am currently tracking an Index fund of stock and it's underlying Alpha Factors(Liquidation, Volume, Investor Sentiment etc). I have the historical data of these Alpha Factors, as well as the Index's ...
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Does Quartimax rotation really maximize the variance of rows in the loading matrix?

The textbook I'm currently reading says that the quartimax rotation in the factor analysis maximizes the rows' variance in the loading matrix. In order to do that, it says, the quartimax rotation ...
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Loadings to reproduce Correlation Coefficients between original variables?

The textbook I have says that, in factor analysis, loadings can be used to reproduce the correlation coefficients between original variables, as it is depicted in the image. For instance, the book ...
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High explained variance but low p-value in output of factor analysis

I'm trying to perform a factor analysis on some survey data (bit new to the subject) using R's built-in factanal function, but I'm failing to interpret its output. ...
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How many observations should there be for the less frequent level of a binary variable, in order to include it in MCA?

I am conducting a multiple correspondence analysis (MCA) on several binary variables. This link says: The graphs above can be used to identify variable categories with a very low frequency. These ...
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In lavaan, how do you allow all manifest indicators to covary?

When building and developing a model with lavaan, e.g., ...
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Multicollinearity and factor analysis

I’m carrying out and principal axis factor analysis to validate an existing questionnaire in a different population. The determinant of the R-matrix is incredibly low and way below the threshold 0....
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What is a "method factor" in confirmatory factor analysis and structural equation modeling?

Researchers employing structural equation models and confirmatory factor analyses often choose to include a "method factor" in their models. My understanding is that this is intended to ...
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EFA cross-loadings [duplicate]

apologies for the silly question, trying to figure out stats by myself. I've performed EFA using the principal axis method on a 48 item questionnaire (with likert responses from 0 to 3). I've gotten ...
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How to test the significance of contribution of a variable in Factor analysis and what is the resonable rule for removing a variable from FA?

My question is about the credibility from the statistical point of view of what I have seen in some papers where the researchers (non-statistician) define some kind of staged factor analysis (FA) and ...
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How to mathematically interpret orthogonal rotation in principal components analysis for more than 2 factors

When performing orthogonal rotations for a loading matrix in principal components analysis, the mathematical interpretation is relatively simple - rotate the two axes while keeping them perpendicular. ...
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Required sample size of CFA using power analysis from semPower

I want to conduct a confirmatory factor analysis (CFA) for a model with 4 latent variables and 60 indicator variables (15 per factor, uncorrelated factors, hence 1,710 degrees of freedom, that is, ...
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Clustering algorithms that support FA rather than PCA

In our social sci research we've used Factor Analysis rather than PCA. It would be helpful for us to use a clustering algorithm to group respondents into the most logical factor groups. Kmeans seems ...
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Structural equation software can seemingly do factor analysis with more variables than observations

I have discovered that the function umxEFA in the R package umx can do a factor analysis with more variables than observations. A normal factor analysis cannot do this because the covariance matrix ...
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Is it necessary to do a second order CFA to create a total score summing across factors?

I am in the process of developing a scale. I have already performed EFA on the first dataset I collected, which showed strong support for a 4 factor structure. I am now planning to collect another ...
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Factor analysis with multiple correct responses to questions

I have a data relating to a questionnaire that takes form of a knowledge test, in which each question has multiple correct responses and the respondents can check all responses they consider to be ...
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Scale development

I am in the process of developing a scale that is supposed to measure construct X with 4 factors. I have already found support for a 4-factor model to the data using exploratory factor analysis. Now, ...
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How is factor analysis used on time series data?

Factor analysis is used for cross-sectional data where the observations are independent. How is this concept applied on time series data where the observations are not independent?
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Why standardized factor loading > 1 ? (CFA in lavaan)

I am runing CFA in R with the lavaan package. My model is one factor with 5 variales. I set std.lv = TRUE, but the estimated factor loading is still > 1. Can I report the std.all column as my ...
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How to theoretically motivate factor scores?

For this question, I begin by explaining my factor model, and then ask how to theoretically motivate factor scores given my setup. I would also be very grateful for clarification about any mistakes I ...
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Factor Analysis or PCA on part of or grouped variables

I am working on industrial time series data. (Such as sensor and controller signals, etc.) I have 150 features. Some of my features/indepentdent variables are highly correlated with each other. (75-80-...
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Why do our devices fail?

I would like to figure out why some devices of my company fail. Therefore, I'm able to use a list in which around 300 devices are listed together with about 70 parameters while only half of it is ...
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Bifactor model. Specific factor collapsed and shifted

I ran a bifactor model and there was a strongly defined general factor and appreciable leftover variance for specific factor A but not specific factor B. When I removed one item that loaded poorly to ...
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Are multitable analyses like Multifactor Analysis (MFA), STATIS, and Partial Triadic Analysis (PTA) JUST exploratory methods? Can I use PC Scores?

If I perform PCA on a simple table, I can take the resulting principal component scores as variables and then perform regression to predict an outcome from my original data. I would do this for ...
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Factor Analysis does not give a better covariance estimate than the Empirical Covariance matrix?

I do not see that Factor Analysis gives a better covariance estimate than the empirical covariance estimate, from the toy data simulation with explanation and code below. Am I doing something wrong? ...
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Multiview CCA with one source set and multiple independent target sets

I have 5 datasets from the same subjects that can be interpreted as different data modalities for these subjects. 4 of these datasets describe brain-related data and the last one contains behavioral ...
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Interpretation of PCA/FAMD results

I wrote a code about a mix PCA (FAMD - factor analysis of mixed data), where I have a dataset with some categorical variable and some numerical variable. This is my example code in R: ...
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what is the difference between factor analysis and SVD? factanal() vs svd()

I am doing factor analysis. Some sources tell me that I should use factanal() to do (exploratory) factor analysis; my goal is to find common sources of latent ...
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Fast likelihood evaluation for Gaussian distribution with diagonal plus low rank covariance

Let's assume the likelihood $$ y \sim\mathcal N_p(0, \Sigma + \Lambda\Lambda^\top) $$ where $\Sigma$ is diagonal and $\Lambda$ is a $p \times d$ matrix with $d \ll p$. What is the fastest way to ...
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Chi-Square Tests with MLE in Confirmatory Factor Analysis

I have a basic question about confirmatory factor analysis. When performing CFA, Chi-square test is often used. I read from the book that after using MLE for factor extraction (computing covariance ...
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what are the right or common steps to successfully build a structural equation model?

I have learned theories about structural equation modeling but don't have enough experience building a structural equation model. I have spent too much time struggling with building a good SEM. I have ...
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test significance and stability of PCA/MFA eigenvalues and statistics based on bootstrap

I have a dataset of a cross design experiment with (subjects * stimuli = all subjects go through all stimuli) and I measured 2 groups of variables (3 biological response measures and 2 ratings. My ...
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Can you use an Exploratory Factor Analysis (EFA) model to compute factor scores on a different population?

I am interested in reading whether factor models can be extrapolated to populations outside of those used to construct the model. For example, if we seek to identify factors that influence depression ...
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Justify the deletion of a factor in EFA

I have done an EFA on 180 observations. In order to explain my latent variables I have considered 24 variables and I get 7 factors. Unfortunately 2 factors among the 7 have a cronbach's alpha around 0....
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Within ML CFA with categorical data (polychoric correlation), are there not different thresholds for both the within and between level?

I am currently studying multilevel confirmatory factor models of categorical data. In the context of CFAs, categorical data is often analysed through polychoric correlations. Within polychoric ...
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Why can't I correlate my first-order factors in this SEM?

I am trying to estimate a "typical" intelligence model with three latent factors (the intelligence domains PS, WM and Gf) two of which have two indicators and one of which has four ...
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Confirmatory Factor Analysis (CFA) for nested data

I would like to conduct CFA to examine support for a 3-factor model with team_cohesion, team_trust, and team_performance variables. I have the data in the following format with individuals rating the ...
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Warning about factor score estimation method when using omega() from psych

I am a beginner in statistics with R. I am currently analyzing the results of a questionnaire in my PhD research. I am trying to measure reliability using McDonald's omega rather than Cronbach's alpha....
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Factor analysis L is only determined up to rotation

I have a question regarding a statement in factor analysis, while I understand the factor analysis model $$ X = \mu + LF + \epsilon $$ In my lecture book the following is stated: "L is only ...
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All eigenvalues less than 1 in factor analysis

Is it possible to have all eigenvalues less than 1 during factor analysis? then what can be concluded here? since a factor is considered a factor when the eigenvalue of the factor is greater than 1. ...
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How to interpret and deal with bad survey items found in EFA

I am new to data analysis so pardon my low knowledge. I conducted an experiment/questionnaire with 40 questions containing 10 constructs/dimensions. I then did exploratory factor analysis with help ...
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How to get the coefficients of determination (R Squared) from factor loadings in FAVAR?

I estimated a FAVAR (Factor Augmented VAR) model for forecasting purposes. The FAVAR gave a very low RMSE value compared to VAR. However, I am unable to interpret the factors through factor loadings. ...
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The scale I am developing for a main study has partial metric and partial scale invariance. Can I still use this in my study?

I'm developing a scale that will be later used in a main study. This study will take place in the UK and France. The scale itself consists of 9 items. I initially tested the scale in UK participants ...
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