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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extract the idosyncratic error of a factor model

I want to extract the idosyncratic error $e$ of a factor model which has the form $X = F \Lambda' + e$. I estimated the factors $F$ and the loadings $\Lambda'$ by principal components in ...
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Factor analysis - Multiple field test forms with anchors

I'm hoping to conduct a confirmatory factor analysis with some field test data I have. A total of over 1450 students participated in the testing. All of the students took one live assessment and one ...
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47 views

Evaluate output of different dimensionality reduction methods

I used PCA, ICA, and FA to perform dimensionality reduction on my data. How can I measure which method performed best? If I reduce my data to 3 dimensions and plot it, what type of trends would ...
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10 views

Examples of using the fa.poly function in R (psych package) [closed]

I'm looking to do an exploratory factor analysis on some survey data using R. The variables I'm interested in analysing are categorical (factors), so as far I have been able to figure out reading ...
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1answer
34 views

Factor analysis and curved manifolds

I am self-studying Kevin Murphy's book, and one passage on factor analysis states that "the Factor Analysis model assumes that the data lives on a low dimensional linear manifold. In reality - most ...
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14 views

Statistical Test similar to ANOVA for multiple factors with continuous values

I am stumped trying to determine the best method to analyze my data. I have numerical ratings provided by users to describe different objects. Additionally, there are five factors that describe these ...
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34 views

Principal Component of non-centered data and PCA-Transformation

I am reading a chapter about principal component analysis (PCA). It states that for any random varible $X \in \mathbb{R}^p$ with $n$ observations, $E[X] = \mu$ and $Cov[X] = \Sigma$ the i-th PC is ...
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23 views

How to organise an iterative manual rotation of n component pairs?

I am currently building a q.rotate() function for the qmethod R package for Q Methodology. As is desirable for Q, I'd like users to be able to iteratively rotate ...
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1answer
47 views

What is a “principal component factor analysis”?

I am currently researching silence in the social sciences and am reviewing surveys and statistical methods implemented by researchers to get an idea methods in both survey design and the analysis ...
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9 views

What does MR mean in psych factor analysis diagram?

One can create diagrams from factor analysis in psych package as follows: > library(psych) > ff = fa(mtcars, 2) > fa.diagram(ff) What does "MR" mean ...
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1answer
64 views

Significance/confidence intervals for PCA or factor loadings - how can such be defined?

Current discussions here in SSE made me to reconsider the PCA and FA models and procedures. I got curious how one would determine confidence intervals for the components/factor loadings by assuming ...
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32 views

Factor analysis and multiple regression

I have a question about how to do a multiple regression after having the result of the factor analysis. I have the data from a questionnaire and the result of the factor analysis indicate that I have ...
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19 views

Minimum sample size for Factor Analysis? [duplicate]

What is minimum sample size required for using Factor Analysis? I have a data-set with 22 cases and 12 features. Is this sufficient? (I can't increase number of cases in my research, it is restricted ...
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10 views

Information criteria for selecting the number of factors

I´m looking for a package in R to calculate the information criteria by Bai and Ng for selecting the number of factors in the model. I found POET, but it only provides two of three criteria. (see page ...
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39 views

Conceptual question: how is a factor created in exploratory factor analysis?

As a conceptual question: in exploratory factor analysis, how is a factor created? I would like to know your simple answer to this simple question. Imagine, my academic field does not dependent on ...
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23 views

Understanding contradictory results between screeplot (EFA) and CFA

I got some contradictory results. How can one explain that a screeplot and EFA clearly suggest a one-factor solution whereas several model fit parameters of CFA are in favor of a five-factor solution? ...
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54 views

Can I create an Index score using factor scores as weights?

I am creating an Overall Customer Satisfaction Index score based off of 4 factors that comprise satisfaction for callers to a call center: A representatives concern for your needs; ease of navigating ...
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1answer
18 views

If two domains measure the same thing how to approach a cluster analysis?

I would like to perform a cluster analysis on my sample with a set of variables categorized in several domains. This is just fine but my problem is that two domains (one consisting of four and one of ...
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26 views

Factor Analysis of Count Data

I am new to factor analysis. I inherited a project at work from another team. They took 9 variables that are all Poisson-distributed count random variables and ran a "regular" factor analysis in ...
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25 views

What type of analysis will help discover common attributes of collections of items?

Suppose the following situation. You have a list of food items: bottles of milk, ham pieces, eggs, bananas etc. You also have bags of food, where a bag might contain, e.g. 3 bottles of milk, 5 pieces ...
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35 views

Non-negative matrix factorization in recommender systems

As i understand, in NMF we should have our three matrices elements non-negative. But i can't understand how to do it so far. Shouldn't we just initialize our factor matrices at the start with random ...
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63 views

What is the rationale behind the “eigenvalue > 1” criterion in factor analysis or PCA?

What is the meaning of "eigenvalue > 1" criterion? I understand what eigenvalues and eigenvectors are. This question is w.r.t. this link and this statement there: By default, VARCLUS stops ...
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19 views

What will be application in my research - EFA or CFA?

I am trying to construct a model of factors affecting investment behavior where I have identified the factors from different literature (each factor from different research papers which say that the ...
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1answer
18 views

measure development - removing items from an item pool due to ceiling effect

During the early stages of scale development, many items within our item pool were found to have a strong ceiling effect with low score variability. In order to attempt create a meaningful measure ...
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28 views

How to construct a composite measure using several items in SPSS?

For my master thesis, I have to do a regression analysis. But, as an independent variable, I have to construct a composite measure, being perceived importance (of interest groups). I have 9 variables ...
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23 views

Factor scores for EFA with binary data

I am conducting an exploratory study which investigates goal progress predictors. The list of potential predictors is long (42) and I am attempting to reduce the number of predictors using factor ...
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46 views

Estimating static factor model for h-step ahead forecasting (using R)

I am trying to estimate a static factor model of the following form $$y_{t+1} = \beta'F_t+\gamma(L)y_t+\epsilon_{t+1}, \\ X_t=\Lambda F_t+e_t$$ where $F_t=(f'_t,...,f'_{t-q})'$ is $r\times 1$, where ...
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Should I exclude factors loaded by only one variable when computing factor score

I'm writing a thesis on "Factor affecting students academic performance at second cycle institutions." I used factor analysis to extract 20 factors from 63 variables that presumably influence ...
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3answers
85 views

“Two stage” factor Analysis: factoring saved factor scores

I have a model which consists of 19 questions, which are divided in three factors (factor 1 - nine questions, factor 2 - six questions, factor 3 - four questions). For this I did a factor analysis and ...
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333 views

Very different results of principal component analysis in SPSS and Stata after rotation

For my PhD thesis I have to do a Principal Component Analysis (PCA). I didn't find it too difficult in Stata and was happy interpreting the results (I know there is a difference between factor and ...
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41 views

Is continuous inputs an assumption of factor analysis?

Should we use only continuous inputs for factor analysis (FA)? My data is a mix of continuous and categorical inputs: one of the inputs has only 600, 700 and 1000 as values. I found that principal ...
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30 views

Factor Analysis

I have following data regarding Voice traffic(dependent variable) and some 10-12 other variables which are my independent variables. So, to use factor analysis shall I use voice traffic as one of the ...
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1answer
87 views

How is survey respondent segmentation based on market opportunity score done in practice?

As per instructions, I have administered a survey to a sample population that for several different "jobs-to-be-done" asks the survey participants to rate the importance of the "job-tobe-done" and the ...
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1answer
108 views

PCA/factor analysis of mixed (quantitative + qualitative) data: inconsistent results

I have a dataset composed of 4 variables, 2 being numerical and 2 categorical (ordinal in fact). They all represent 4 types of indicators/measures of the same phenomenon . I want to analyse them in a ...
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52 views

Is structural equation modeling (SEM) just another name of confirmatory factor analysis (CFA)?

I am reading some material about structural equation modeling. I found it to be extremely similar to confirmatory factor analysis - modeling a construct as the linear combination of several other ...
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19 views

Unexpected One-Factor in EFA

I have a data set of 4,000 participants. Each has rated 25 sentences on a scale of 1-100 (lowest amount of aggression present to highest amount of aggression present in each scenario portrayed in the ...
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41 views

Factor Analysis - Rotated Component Matrix Error

I haven't got good English but i have a problem: (for my master thesis.) I did factor analysis, deleted 4 questions and the most lower points are: ,392 and ,393. So, i go on and deleted 0,392 ...
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16 views

Single factor solutions - EFA

I am exploring the properties of a 6-item self-report measure. I have about 155 cases and the items are completed on 7-point Likert scales. I have carried out an EFA, and extracted only one underlying ...
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Acceptable to use EFA when using binary data? [duplicate]

I'm working on my dissertation, and my committee has suggested I use Exploratory Factor Analysis to see if my findings conform to the results that previous researchers found after conducting a PCA. ...
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43 views

Is the use of PCA appropriate to validate a designed questionnaire?

I looked at the questions that may already have my answer but unfortunately it is not the case. I would like to ask again my question which has been revised to fit the rules. I am to measure 5 ...
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2answers
65 views

Rotation to get equal loadings in the first principal component or factor

I have the observations of $n$ variables $x_i(t)$ where $t$ is the time, and $i=1,2,\dots,n$ is the number of the variable. They're very correlated, so I wanted to use PCA. The first component ...
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analysis of responses to functional questionnaires in terms of improvement over time, comparing two randomised groups

We studied a population that was randomised into 2 treatment groups, evaluating answers to functional questionnaires at different time intervals (6 weeks, 3 months, 6 months, 1 year). Is it possible ...
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23 views

Can I ignore a single Item Factor and proceed with the remaining factors ? Is it scientifically correct?

I did an EFA and got 7 factors . There were a total of 54 items in the survey instrument. Now, the factors are in such a manner that Factors 1 to 6 have decent number of items loaded ( ranging from ...
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10 views

Co-variance matrix and Factor graph representation

I have problem in fundamental understanding of factor graph representation: I am trying understand the relation between the Co-variance matrix and associated factor graph, of a Normally distributed ...
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25 views

Factor analysis with 2-norm equality constraint

I'm interested in the interpretation of the solution to the factor analysis problem with a 2-norm equality constraint on the columns of the loadings matrix. I plan to decompose $\mathbf{X}_i \in ...
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35 views

Is the Kaiser–Meyer–Olkin measure of sampling adequacy relevant to CFA?

I often see the KMO mentioned in the context of exploratory factor analysis, but have never seen it mentioned in the context of confirmatory factor analysis. Is it appropriate for use in relation to ...
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2answers
129 views

Independent and Dependent variables use different scales

How to deal with questionnaire, where 40 questions that represent 8 independent constructs use 5-point Likert's scales and another 5 questions that represent dependent variable use 6-points Likert's ...
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61 views

Identifiability in factor analysis

Say we model $\mathbf{x}_t \in \mathbb{R}^d$ as a linear combination of factor loadings: $$\mathbf{x}_t = \mathbf{E}\mathbf{F}_t + \boldsymbol{\epsilon}_t, \qquad \boldsymbol{\epsilon}_t \sim ...
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Is sign of loading and score immaterial for interpretation in PCA & Factor Analysis? [duplicate]

Is sign of loading and score immaterial and can be ignored for interpretation? Or is there a important significance for sign when used to interpret the result? I am assuming sign can be ignored ...
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238 views

What is the intuitive reason behind doing rotations in Factor Analysis/PCA & how to select appropriate rotation?

My Questions What is the intuitive reason behind doing rotations of factors in factor analysis (or components in PCA)? My understanding is, if variables are almost equally loaded in the top ...