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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Rotation in PCA and Factor Analysis

I want to know what elements are (varimax-)rotated when I rotate after PCA and after Factor Analysis. Let’s assume a standardized data vector $X$ of dimension $N \times q$. In PCA, I have the ...
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21 views

Do the values in the second factor from a principal component analysis have to have different signs?

I am computing the principle component matrix of a financial database and to obtain the second factor I extrapolate the second vector. So far, it's easy, but I wonder, do the signs of the second ...
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43 views

Doesn't Factor Analysis always overfit on a theoretical basis

Imagine you have 3 items that measure some "quality", you could take for example a sum score or you can do a factor analysis. When you use a factor analysis, don't you basically completely overfit ...
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30 views

Does the first extracted factor in EFA always have the highest eigenvalue?

I have run many EFAs (exploratory factor analysis) and always find that the first extracted factor has the highest eigenvalue. However, I read in Petscher et al (2013) "Applied Quantitative Analysis ...
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53 views

What is the relation between singular correlation matrix and PCA?

Can anyone kindly give me some information about the statement (last sentence) at the end of below definition. What does it mean by "It can be used when a correlation matrix is singular"? This quote ...
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23 views

can I use PCA and PAF on Kendall's and Spearman's correlation matrix?

I have a dataset of 77 items, ranked by 17 people, with many ties (actually: Q-sorted under a forced quasi-normal distribution ...
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19 views

Q-Methodology: which correlation coefficient to use: Pearson vs Spearman vs Kendall

Please note: This question pertains to Q Methodology, a research method used to study people's subjectivity. Q embodies ontological and epistemological assumptions that sometimes differ markedly ...
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114 views

Goodness of fit chi-square test for a number of PCA components

I have been trying to carry out Principal Component Analysis (PCA) in R using the function psych::principal. However the returned $p$-value has been very low in ...
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19 views

How to determine which variables need to be trimmed in PCA or Factor analysis?

Background: I'm working with log returns for about 400 tech stocks. I want to use PCA to reduce these into principal components (Internet companies, software developers, circuit board manufacturers, ...
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12 views

Model selection (BIC / AIC) ordinal multilevel model containing a factor score and/or part of the factor

I am building a ordinal multilevel model (Stata 13.1; meologit-command). At this stage I am trying to conduct my model selection using the BIC / AIC. I estimated several models and now I need some ...
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61 views

Analyzing Ranked Data: Correlation and Factor Analysis?

I had survey respondents rank a series of items in order of importance, from 1 to 7. So, if a respondent assigned a score of 1 to one variable, then none of the other variables could get a 1 as well. ...
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Measuring positive and negative items in Exploratory Factor Analysis

My research topic is related to motivation regarding product usage and the negative items mainly consist of problems that hinder motivation. My dataset is composed of both positive and negative items ...
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15 views

Is a representative sample necessary to assess construct validity?

To generalize results to a greater population, a representative sample is necessary. In developing a psychometrically valid instrument, via confirmatory factor analysis or item response theory, we are ...
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15 views

How many items were allowed for deletion in EFA?

I removed 7 items out of 20 items in my EFA, that mean 35% of the items were removed. Is there any issues if so many items were removed? Can anyone suggest for references for this matter?
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24 views

Augmenting experiment design matrices

Consider a set of users (rows) where we are already testing several treatments (columns): $$\begin{pmatrix} E & U & E \\ U & E &E \\ \vdots & \vdots &\vdots \\ E & E ...
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16 views

Variable not correlating with other variables - reason for deletion in PCA?

When I run PCA on a set of variables, I notice that there is one variable that has very low correlations with the other variables and also most of the correlations are not statistically significant. ...
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20 views

Problematic variables and number of factors in PCA

I have a problem with two variables in PCA. I obtain a certain number of factors (lets say n factors), but on the last factor I obtain only one variable (I will call it X) that loads high on that ...
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32 views

Standardizing sample factor scores: population or standard deviation

Please note: This question pertains to Q Methodology, a research method used to study people's subjectivity. Q embodies ontological and epistemological assumptions that sometimes differ markedly from ...
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32 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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39 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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71 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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17 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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12 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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17 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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64 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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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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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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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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94 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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87 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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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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20 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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25 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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22 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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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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50 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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38 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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65 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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22 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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97 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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79 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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144 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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1k 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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147 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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56 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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30 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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421 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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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 ...