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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Standardizing sample factor scores: population or standard deviation

I need to standardize a bunch of factor scores for a sample of people. I obviously have all the factor scores to standardize (no sampling there), but the people from which these factors are extracted ...
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25 views

Can I apply factor analysis on multiple choice questions?

I am looking to validate a questionnaire and would like to know if I can use factor analysis on the multiple-choice questions (MCQ). Also, I have another section where I am asking about participants ...
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37 views

must be a representative sample to apply factor analysis?

To apply the exploratory or confirmatory factor analysis, is what we should select a representative sample? And is there any condition to select this sample? I would validate a translated ...
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22 views

What to do with my data [duplicate]

My research work is based on slum health. With other variables, I used 5 point scale (ordinal data) to rate out the provision of facilities in Govt. Hospital and Private hospital. there are 25 ...
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1answer
51 views

Why would one remove items which load on more than one component or factor in PCA or FA?

Why would a researcher remove items which load onto more than one component after rotation in PCA using Varimax? A couple of studies I'm using as the basis for a study I'm conducting have done this ...
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15 views

IV or latent factor to process multiple measures?

I have several measures on different memory tests. I consider these measures may actually measure different aspects of memory functioning and every measure contains a measurement error. I am thinking ...
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24 views

factor analysis in multiple regression

1>suppose I have 1000 variables to predict shop sales...should we use stepwise regression to reduce the number of variables and then use factor analysis o we can just use factor analysis....My goal is ...
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1answer
10 views

SEM and multiple item / dimension scale

I have a 120 item, 18 facet, five factor model I am attempting to validate. I have attacked this by attempting to develop single congeneric models for each of the 18 dimensions, but am at a loss as to ...
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14 views

Calculating summated scales (factor analysis)

I have read that, when calculating summated scales for each scale in the solution of a factor analysis, as an average of sum of the items comprising each scale, the items with high loadings should be ...
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46 views

Can I calculate average factor loadings from cronbachs alpha?

I was wondering if I could post hoc calculate the Fornell-Larcker criterion to assess dicricimant validity given the correlation matrix between several subscales and Cronbachs alpha for each subscale. ...
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9 views

The Effect of Unreliable Observed Variables in Factor Analysis (FA)

My question relates to the impact of unreliable observed variables in common factor analysis. Does common factor analysis treat the unreliable portion of a variable's variance as a unique variance? ...
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2answers
36 views

Can factor scores be used as independent variables in logistic regression?

I have a data set with some categorical variables and factor scores extracted by using factor analysis. Can I use both categorical variables and factor scores in logistic regression?
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8 views

Higher Moments from Factor Models

Suppose that we are fitting a linear factor model to our data $$r=\alpha+Bf+\epsilon$$ where we assume the factors, $f$, are orthogonal. Using this structure we can estimate the mean vector as ...
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1answer
92 views

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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2answers
76 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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2answers
45 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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19 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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22 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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20 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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1answer
27 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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44 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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2answers
37 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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58 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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20 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
75 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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1answer
62 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 ...
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1answer
138 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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1answer
667 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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125 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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54 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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20 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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1answer
360 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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162 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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34 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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43 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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6answers
2k views

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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1answer
41 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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41 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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63 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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36 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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72 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
239 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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1answer
28 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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36 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 ...
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1answer
137 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. ...