Factor analysis is a dimensionality reduction latent variable 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 ...

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Step by step guide for GRS test in R? [on hold]

I'm new to R. I have basic knowledge in R. I'm testing a factor model. I have to use GRS test. But not sure how to do it. Please help me. I have found this recipe for GRS online. http://faculty....
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How to obtain statistical information from a Likert scale with a sample size smaller than the number of questions?

Research and sample properties I'm measuring the degree of a certain concept related to marketing and sustainable development throughout an entire industry. The theoretical model is depicted next: ...
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18 views

Statistical methods to group similar variables

I work with a data set of 50 variables which measure the performance of hockey players (e.g. number of duels lost, goals scored etc.). I deal only with count data - positive integers which are not ...
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17 views

shall I remove an item based on cronbach's alpha if item deleted

In my EFA analysis with 127 items, I got 8 factors including 56 items. There is one factor which has 4 items with loadings like 0.914, 0.966, 0.844, 0.567. The 4th item seems weak in this factor. ...
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cluster analysis after factor analysis: do I need to use all factors for cluster analysis?

I have a 127-question survey with 6-level likert type answers. With EFA I have kept 56 items and got 8 factors. With CFA (on sample not used in EFA) I confirmed these factors. so far all good. When I ...
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10 views

converting annual series into quarterly series using MARSS?

I am trying to generate quarterly values for a series which is available in annual frequency using two other series using MARSS package in R. ...
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What is meant with “decision level of factor loading”?

I have performed a PCA with some data sets. Prior to performing PCA, I tested the applicability of PCA with KMO and Bartlett's Sphericity tests. I got some critics stating that I have to add "my ...
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24 views
+50

why Matrix Factorization map the two spaces into same space?

It's a common sense that Matrix Factorization map the two space(e.g. user and item) into same factor space. But is there any more formal way to explain the fact they are the same ? Say, I have $$\...
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9 views

wrong number of factors

I am supposed, based on literarture, to get 3 factors from a scale I applied. However, the exploratory factor analysis leads me to a 5 factor solution. Is there anything wrong? What should I check?
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Factor analysis - Low and High conditions

So I'm conducting a factor analysis and also want to test the reliability of the scale. I have 2 conditions (between subjects) : low involvement and high involvement, both composed by the same items. ...
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Exploratory factor analysis using oblique and bifactor rotation : different pattern loadings

When I try to compare oblique rotated factor analysis (promax, ML) with bifactor rotated analysis (ML), I get different pattern loadings. I don't know which solution should be retained; I am planning ...
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13 views

Test signifance of each slope (corresponding to each level of a factor) in ANCOVA in R

Using Ancova, we can test the homogeneity of slope (or intercept) across different level of the a factor. Is there a way to test whether the individual slope is significantly different from zero using ...
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10 views

Using the Kalman Filter with mixed measurements over time

I am aiming to use the Kalman Filter to estimate a linear dynamic factor model. One issue i have is that the measurement equations vary dramatically over time. The question is then, is it possible ...
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59 views

PCA for questionnaire reduction

I'd like to have some opinion regarding if I'm in the right way with my questionnaire reduction. I have a questionnaire with 275 questions and 34 issues (so a couple of questions are related to each ...
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13 views

factor analysis : creteira and steps to remove weak items

When doing factor analysis, some low loading items will be removed. Are the following practice right? remove weak items one by one, from the one with the lowest communality, do factor analysis again, ...
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27 views

Interpreting the regression coefficient when the regressor is polychoric-based principal component

I have a regression where I am trying to interpret the regression coefficient of the first principal component on some outcome variable. The component scores variable was obtained in a polychoric ...
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13 views

factor analysis using Maximum likelihood or Principle axis factor to extract factors for 6 point likert type questions?

We have a questionnaire, which have many questions on 6-point likert scale. So these variables are ordinal, not normally distributed. In performing factor analysis, there are two major methods in ...
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for a survey conducted in 3 countries, how to examine the equivalence of factor structure by country?

We conducted a survey in 3 countries, and we want to run factor analysis (EFA) to identify latent factors. With the combined data sets, we can run EFA to develop factors. But to examine the ...
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Can I try several CFAs on the same data before choosing one for generating factor scores?

I'm interested in matching on latent constructs (see Raykov, 2012), and one way to do so is to match on factor scores generated by CFAs of the items (One could also match on the items themselves, but ...
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28 views

CFA: loading exceeding 1

With CFA, is it a problem if a loading exceeds 1? What does it mean to have a loading greater than 1? What steps should be taken to deal with it, if nothing is amiss with the variable itself?
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16 views

How can I have more factors than there are variables

I've come to learn about factor analysis as mainly a dimensionality reduction tool. However, can we also use the factor analysis method to have more factors than there are variables? If so, what would ...
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1answer
44 views

CFA: negative factor loadings

I found that after running a CFA, positive factor loadings and negative factor loadings occurred as appropriate. (An item representing a high score and an item representing a low score on the same ...
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16 views

Problem with syntetic data generating for Probabilistic PCA and Factor Analysis (FA) comparison - methodology

I am trying to understand a short example related to dimension reduction from python scikit-learn.org official documentation for long time and unfortunately I am not successful. I don't have problems ...
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What to do when EFA requires more factors but the number of variables is low?

There's a lot of information on the forum about the differences between principal components analysis (PCA) and exploratory factor analysis (EFA) (for example here and here). I am new to both methods, ...
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81 views

Does the use of EFA factor scores (vs. sum/average scores) impact statistical power of subsequent analyses?

Imagine a hypothetical scenario: You have data a short survey of 9 questions that participants respond to on a continuous rating scale. You suspect that Questions 1-3 assess one particular factor (...
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1answer
36 views

Variables derived from factor analysis as a response variable in logistic regression

I have a dataset derived from a questionnaire filled out by high school students, with 7 variables (one continuous and six binary). Three variables(binary) are related to "interest in physics". Is ...
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28 views

Using polychoric correlation with non normal ordinal data

I have ordinal data on scale 1-5 for detected pollutants in water (1 = detectable in small proportions; 5= detectable in higher proportions; also 0 was asaigned - not detectable). based on the ...
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36 views

Using factor scores in discriminant analysis

I'm looking at indicators of earnings fraud in publicly-held corporations. My classification is dichotomous, Yes, company is likely to engage in EF, or no, it's not. I have 15 financial variables ...
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23 views

State space modelling of longitudinal data in r

I have n stations, and for each station there are m time series observations on different days, each of length ...
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13 views

Factor analysis without listwise deletion

Can factor analysis be done in a manner which affords missingness on some items? With what methods can a factor analysis be performed in which subjects who are missing on one or two items are ...
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1answer
76 views

Do Stata and SPSS give conflicting versions of Anti-Image matrices?

I read on p1 of the Stata Manual glossary that: The image of a variable is defined as that part which is predictable by regressing each variable on all the other variables; hence, the anti-...
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1answer
103 views

Why are regression coefficients in a factor analysis model called “loadings”?

In this thread @ttnphns writes that Because it is regression coefficients [...] I insist that it is better to say "factor loads variable" than "variable loads factor". I learned from here that ...
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35 views

Factor analysis with items on very different scales

What issues might arise with performing EFA or CFA using items on very different scales (likert data on scales of 1-3, 1-4, 1-5, and 1-7 and measurements based on time, in seconds, which can be binned ...
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23 views

How to implement SMC in Python as it in R? [closed]

Is there any function in Python similar to Squared Multiple Correlation (SMC) in R? What if I want to implement SMC in Python? Is the only way to do it just rewriting SMC into Python line by line? ...
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17 views

When will factors wholly explain the correlations among the observed variables?

Thinking about this question, I came across Bartholemew et al (2011), which lists the following assumptions of the linear factor model, assuming $p$ observed variables: iii) $e_{1}, e_{2}, ..., e_{...
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Using pearson correlation to compare factor loading between two groups

I have two groups (one placebo, one drug) in which I measured a few variables. I performed factorial analysis separately for the two groups and then I want to compare the factor loadings between the ...
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9 views

Identification in a gaussian two factor model

I am working with a Gaussian two factor model: $$ X_i = \beta_iZ_1+\gamma_iZ_2+\varepsilon_i, \space i = 1,2,...,n $$ where $Z_j\sim N(0,1), \space Z_1 \perp Z_2 $ and $\varepsilon_i\space iid\space ...
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Do Heywood cases render EFA/CFA solutions invalid?

If communality = 1, then we have a Heywood case, and if a communality > 1, it is known as an ultra-Heywood case. I read in a SAS manual that an ultra-Heywood case renders a factor solution invalid, ...
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379 views

Is there Factor analysis or PCA for ordinal or binary data?

I have completed the principal component analysis (PCA), exploratory factor analysis (EFA), and confirmatory factor analysis (CFA), treating data with likert scale (5-level responses: none, a little, ...
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40 views

Can Factor Analysis on Mixed Data be treated like a PCA?

I wanted to do something equivalent to a PCA on a mixed data set containing categorical variables and continuous numerical predictor variables which are normally distributed but measured in very ...
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41 views

errors in the orthogonal factor model

I am using R psych package in order to design a factor model. By default, an oblique rotation (oblimin) is performed by fa. The number of factors (fa.parallel$nfact) has been previously estimated. <...
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7 views

to constrain a parameter estimate to obtain unique estimates in R LAVAAN for CFA

I need urgent help, I need the script or command to constrain a parameter estimate to obtain unique estimates in R LAVAAN for CFA. Like If Social Influence got 4 items in a model and I want to put a ...
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13 views

Factor Analysis with low sample size

Does anyone know of references to support conducting EFA with a low sample size?
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1answer
109 views

Why do the loadings returned by psych::principal() in R change with the number of components?

I have been using the principal() function of the psych package in R and setting the number of components after a scree plot analysis (...
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11 views

Analytic Hierarchy Process (AHP) - factor weight score

As title mentioned, how to determine the 'scale of relative importance' point for factor weight score? Besides, I have read some example of ahp saying there are 1-9 point, 1-5 point (1,2,3,4,5) and ...
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11 views

“*usefulness*” is a bivariate property used in Regression and Anova. Has a generalization (trivariate) analogon been discussed?

Just for selfstudy/exercising of algorithms I looked at the computation of the "usefulness"-measure in multiple regression, which means the part of variance which one independent item contributes to ...
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15 views

exploratory factor analysis in models with sub constructs

I have a dataset based on model with 3 second-order latent variables (exogenous + mediator + endogenous), each having 2 first-order latents. when running exploratory factor analysis (PCA) with SPSS, ...
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Cluster analysis vs Factor analysis as a means for “grouping” variables or cases: the differences

I've noticed responses that at face value seem to be in contradiction with each other. For instance, here @peter-flom writes Short answer: Cluster analysis is about grouping subjects (e.g. ...
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1answer
129 views

What is the difference between the anti-image covariance and the anti-image correlation?

What is the difference between the anti-image covariance and the anti-image correlation? How are the matrices of these coefficients computed, and what is the meaning of their elements?
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How to overcome skewed component in validation of a 3 component likert scale

thanks for the information and input provided in the relevant posts. I intend to develop a psychometric questionnaire using Exploratory Factor Analysis; it gives 3 factors. One of the scales is ...