Factor analysis is a data reduction 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].

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What to do after running an exploratory factor analysis?

Say I asked 1000 people to evaluate 10 items about one product. The data looks like ID item1 item2 …item10 1 2 3….. After running an explorative factor ...
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Minimum cumulative variance to extract in exploratory factor analysis to ensure a good fit

As a part of my exploratory factor analysis, I would like to report the cumulative variance % (eigenvalues). I wonder if there are guidelines on the minimum percentage in order to have a good model ...
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81 views

Where is the indeterminacy of factor values on this plot explaining factor analysis?

It is a well-known fact that in principal component analysis (PCA) we can obtain true values of components but in factor analysis (FA) we cannot obtain true values of common factors. We can compute ...
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144 views

What is component (factor) score coefficient matrix in PCA or factor analysis and how is it calculated?

As per my understanding, in PCA based on correlations we get factor (= principal component in this instance) loadings which are nothing but the correlations between variables and factors. Now when I ...
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Is binary factor analysis appropriate here?

Suppose we have n observations (respondents) and m variables (say, a certain brands of candy), each respondent states whether he/she eats a specific brand of candy (binary data). We want to group the ...
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73 views

Under which conditions do PCA and FA yield similar results?

Under which conditions can principal components analysis (PCA) and factor analysis (FA) be expected to yield similar results?
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How can I verify that variance(factor)=1 from Exploratory factor analysis results?

I am reading upon Exploratory factor analysis. One of the assumptions of the Orthogonal factor model is that $$ \sigma^2(factor)=1 $$. Reference via "Applied Multivariate Statistical Analysis-by ...
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6 views

EFA or CFA for validity

I need to test validity of measurement scales in my survey. 1) Is it true that both can be used to test measurement validity? 2) Or there are some types of validity that can be tested with EFA and ...
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22 views

Why we can simply use the $\mathbb{E}[\mathbf{Z}]$ as the reduced values in Factor Analysis?

In Alpaydin book it is stated that the reduced data set $\mathbf{Z}$ from the original data $\mathbf{X}$ can be obtained by following a multivariate linear regression: ...
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How does “Fundamental Theorem of Factor Analysis” apply to PCA, or how are PCA loadings defined?

I'm currently going through a slide set I have for "factor analysis" (PCA as far as I can tell). In it, the "fundamental theorem of factor analysis" is derived which claims that the correlation ...
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Q: Exploratory factor analysis in R

I am trying to do an exploratory factor analysis (EFA) in R with oblique (promax) rotation. From Wikipedia, In oblique rotation, one gets both a pattern matrix and a structure matrix. The ...
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25 views

How to analyse a factor experiment with feature extraction, clustering and classification algorithms as factors?

Currently I am doing my final project, which consists of designing an experiment to test several combinations of algorithms on a dataset, such as feature extraction, clustering, classifiers and ...
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What to do with a construct item with low factor loading for one group but seems fine for other groups?

I have tested four types of advertisements on four groups. Each group was only given one type of advertisement. The following is two examples of the construct items used on 7 point scale in the ...
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Clustering cases on variables discovered in-sample via factor analysis?

My Data I have 2-hourly readings on approximately 10K sensors taken over the course of a year. The resulting time series look pretty similar day to day (though there are some longer term trends), and ...
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Is there any good reason to use PCA instead of EFA?

In some disciplines, PCA (principal component analysis) is systematically used without any justification, and PCA and EFA (exploratory factor analysis) are considered as synonyms. I therefore ...
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Deciding the Optimal Number of Factors [closed]

In practice, is there generally a difference between having 100 factors and 1000 factors in a model? Is there a well-researched 'upper-bound' to how many factors a given model should have?
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Using Factor Analysis prior to repeated measures ANOVA

Please note, stats is NOT my area (hence why I need help!) and I may not be using the correct terminology. I hope I can explain my question clearly enough. BACKGROUND: I have collected behavioural ...
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40 views

Obtain factor scores in data set with missing values

I would like to obtain factor scores after factor analyzing data that contain missing values. I'm using Stata 13 to run the analysis. Here is the basic code (borrowed from the UCLA site): ...
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question about factor analysis

I have a silly question about EFA. Can EFA be used to identify latent variables in a research design where multiple raters used the same rubric for various essays? Say, using the same rubric, the 1st ...
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28 views

Factor Analysis in scikit learn: Many zero loadings

I am trying to apply Factor Analysis to a dataset with about 200 datapoints and 8 variables. When setting the n_components parameter to 8, I get a loading matrix with loadings for three factors that ...
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41 views

Does it mean anything when all items load negatively on one factor when several factors are output?

So I am fairly familiar with factor analysis, and am aware of answers here and here that tangentially address my question. I believe I am right in my answer to the question I'm asking, but I wanted to ...
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42 views

Correlation of latent variables: Sum-scores vs. SEM correlation

I use a set of about 20 attitudinal items and confirmatory factor analysis (CFA). Loadings and model for are sufficient. In the next step, I want to test for correlations between these latent factors. ...
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88 views

What is the meaning of the R factanal output?

What does all this mean? I'm a factor analysis 'noob' and although I've read a book, it didn't tell me everything apparently. Since the chi square statistic is so high and the p-value so low, it ...
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Why do the residuals from a factor analysis have mean zero?

The model is given below: \begin{align} y_1 - \mu_1 &= \lambda_{11}f_1 + \lambda_{12}f_2 + \dots + \lambda_{1m}f_m + \epsilon_1 \\ y_2 - \mu_2 &= \lambda_{21}f_1 + \lambda_{22}f_2 + \dots + ...
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how many questions per construct to include on survey

I am developing a survey that tests a number of different constructs relevant to a particular educational intervention and subsequent educational outcomes. For most of the constructs, the questions ...
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81 views

Factor analysis on non normal data ( Ordinal data of Likert Scale) [duplicate]

How to check the normality of data collected on 5 point Likert scale? As it is ordinal numbers not continuous. Using SPSS the Shapiro Wilk or Kolmogorov-Smirnov test indicate my data is not normal. ...
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182 views

What is the proper association measure of a variable with a PCA component?

I am using FactoMineR to reduce my data set of measurements to the latent variables. Now, the variable map is clear for me to interpret, but I am confused when ...
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66 views

Performing a factor analysis on categorical data

Let's say that I have the following data on banner advertisements and I want to understand what 'factors' exist within the data. Due to many of the variables being 'similar', I can't use linear ...
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Can factor analysis improve the fit of a predictive regression model?

My company is working with a client who have built a logistic regression model to predict whether kids with psychiatric disorders will successfully complete a State intervention program (Yes or No). ...
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Factor analysis in preparation for Rasch

I'm breaking into Rasch modelling and finding it very useful. However I'm just trying to find a way to begin making use of techniques I was familiar with when using classical test methods, such as ...
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33 views

Confirmatory factor analysis without the raw data

I have the correlation matrix, sample sizes, and descriptive statistics for a set of variables. I know that it is possible to run principal component analysis (PCA) and exploratory factor analysis ...
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82 views

Cointegrated Vector ARMA (CVARMA) Model vs. Dynamic Factor Model (DFM)

Two questions regarding the equivalence (or lack thereof) of vector error correction model (VECM) cointegrated vector ARMA model (CVARMA) and dynamic factor model (DFM): Can every VECM CVARMA be ...
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correlation of ordinal and dichotomous data in confirmatory factor analysis

I want to run a confirmatory factor analysis on a dataset that contains dichotomous (yes/no) and ordinal (Likert scale ranging from 1 to 4) scaled items. I know it is advised -assuming an underlying ...
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Construct validity

I seek to establish the construct validity of a translated questionnaire. I found that the factor analysis is used for this measurement validity. Does the analysis used in the case of unidimensional ...
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How to measure construct validity?

I recently received feedback from a journal (in education) that "The idea that you can assess construct validity through a factor analysis is inconsistent with how we usually think about validity in ...
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first and second order factors

I am not deep into statistics yet, however ,I am reading an article that speaks about measurement scale. It says that some items (A,B,C) are first-order factor, but another item (D) is second-order ...
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Factor analysis: what are the total possible scores for calculated factors based on Likert scale responses?

I have two factors, Peer Social Interaction (PSI) and Sense of Belonging (SB). Four Likert scale questions correspond to each factor. I used the factor loadings for each question to create a ...
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45 views

Factor Analysis vs. Random Forest Feature importance

Could someone explain the intuition behind the difference of feature importance using Factor Analysis vs. Random Forest Feature importance. Does there lie an advantage in RF due to the fact that it ...
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25 views

Reverse scored items lead to different factor loadings

I am doing a factor analysis with principal axis analysis and oblimin rotation. Many of my items are negatively formulated, and seeing that i need to do a reliability analysis, i decided to reversed ...
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Principle of factor analysis

Please is anybody can explain me the principle of factor analysis (exploratory and confirmatory) that I will use in the validation of a questionnaire translated. Do I have to make a survey using the ...
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Factor analysis with repeated measures

Multilevel factor analysis seems to be the technical term for factor analysis with repeated measures, judging from this abstract. To be precise, following Wikipedia's factor analysis notation, the ...
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30 views

Mixture distribution fitting for latent variable analysis

Are there any analytic approaches to using mixture distribution fitting for latent variable analysis? I'm specifically interested in existing approaches to determining whether mixture components ...
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22 views

Variation of binary responses between repeated measures

I am bit confused in terms of analyzing my data. I have done an experiment which involves testing of detection systems with controlled footage.The footage has been grouped based on scene properties ...
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Factor analysis results

I carried out factor analysis on 31 5 likert-scale questions which represent my 6 constructs. The results showed 6 factors, consistent with my hypothesis but the analysis grouped my questions ...
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106 views

How to handle variables with low correlation but high loadings in factor analysis

I am doing factor analysis to check the factorial validity of a 14-items scale with four subscales. Two items have low (less than 0.3) correlations with other items in the subscale to which they ...
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52 views

Determining Relative Weights

I am looking for some recommendations and more specifics about how to do the following: Objective: To determine the weights of a number of stock valuation metrics. I am looking at doing this across ...
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83 views

Use of factor analysis + regression

Independent Variable: I have a survey of 50 states indicating the amount of control the state board of education has in 31 areas answered on a three point scale (1 = total control; 2 = partial ...
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Multiple Factor analysis and squared cosines

I am a bit confused on how to proceed using the MFA analysis from FactoMineR in my data set. I am currently working with activity results of 15 bacteria (b1, b2, b3, b4, b5,.., b15), divided into 3 ...
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571 views

Factor Analysis in SPSS & CFA in AMOS

I'm currently in the middle of analysing data for a masters dissertation and I'm having a lot of trouble with understanding factor analysis. I've collected data using a questionnaire in which I ...