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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Variance estimation in a one-factor linear model

I was given a dataset (a mat file) of $100\: 000$ observations, each with $50$ dimensions (coordinates). Denote matrix $X$ a $50\times 100\:000$ matrix in which each column was generated according to: ...
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63 views

how many factors (new to factor analysis)

I'm using R (factanal) to analyze some data. I know from reading that there are various ways of picking how many factors to use in the analysis. I don't know which to choose, or how to do any of ...
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40 views

Does clustering need scalar data?

I am trying to cluster 43,000 individuals on about 50 variables. The data contained in the variables are minutes of a radio shows which people listened to in the range of 0 - 3,000,000 minutes. My ...
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12 views

Factor analysis cut-off point for small size sample

I am doing factor analysis for pilot study which consists a small sample where n is equal to 40. My question is what is the best cut-off point for small sample size for factor analysis?
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15 views

Generate survey response data from correlation matrix

I would like to create survey response data if possible from a correlation matrix or factor analysis, or any other way if possible. My end goal is to scale up the samples in my data file and run a ...
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19 views

Statistical technique for data when three interventions are administrated and multiple responses measuring different constructs are measured

I have a data where three interventions were administrated on subjects and different response variables (say 15 variables) on Likert Scale were observed. These response variables measure three ...
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26 views

What should can I do with some items loadings on unexpected construct?

I conducted a Principal Component Analysis to reduce the items and dimensions. But some items loaded on unexpected construct and the items have a low face validity with the construct. Is that a ...
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40 views

Fourier vs ARIMA vs Factor analysis vs PCA?

Background I'm currently analysing a timeseries. My data consists of half hourly observations of a certain measurement. This data is human generated, and so we believe there will be daily, or weekly, ...
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35 views

Exploratory factor analysis: the same eigenvalue for the one factor and two factor solution

I did an exploratory factor analysis of four measures. First, I constrained the four measures to load on a single factor(eigenvalue: 2.14, % of variance: 53.4 ). Second, the four measures were allowed ...
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46 views

Factor analysis with varimax rotation gives very different answer from PCA?

I asked expert raters to evaluate several subject on six dimensions of creativity. Now, I am using factor analysis (factanal()) and PCA(princomp()) to see of these dimensions are measuring distinct ...
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17 views

Exploratory Factor Analysis and survey scales

Are there limitations to using EFA on survey data, where some questions have different scales? (ex. some questions are four-point and some are five-point Likert scales; one is on a 10-point scale) ...
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1answer
66 views

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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37 views

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 ...
2
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120 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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317 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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13 views

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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104 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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46 views

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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11 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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24 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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320 views

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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130 views

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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33 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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34 views

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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13 views

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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40 views

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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37 views

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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49 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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23 views

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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32 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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66 views

Does it mean anything when all items load negatively on one factor? [duplicate]

note: A few people have marked this question as duplicate - But my question here is not answered in the other question. Though a fine distinction, what I was asking about here was not whether the ...
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55 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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1answer
149 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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21 views

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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28 views

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 ...
0
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1answer
113 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. ...
4
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1answer
209 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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70 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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57 views

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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22 views

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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2answers
37 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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1answer
98 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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19 views

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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17 views

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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77 views

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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11 views

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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37 views

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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54 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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30 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 ...