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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correlations between factors in r- scores or loadings?

I've conducted a factor analysis in r with three factors (function=fa {psych};rotation=promax ; method=GLS). ...
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Structural Equation Modeling in R throws an error: system is computationally singular [on hold]

I am using Structural Equation Modeling in R. Below is the model that I have specified. The error that I am getting while training the model is: system is computationally singular: reciprocal ...
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8 views

Which CFA model is the best fit in my translation & validation study?

I have translated and adapted a questionnaire (based on a 5 factor model; 23 items) into my native language by following ITC and MAPI guidelines. Forward / backward translation, expert panel review, ...
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21 views

Comparing factor structure to network analysis using a community detection algorithm

I am interested in the use of weighted correlational network analysis to explore high dimensional data, instead of latent variable models like exploratory factor analysis (EFA). My approach is to: ...
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35 views

Correlation, probabilities and alternative grading system in high school problem [closed]

For strictly educational purposes, our fictitious high school utilizes a GPA grading system represented by ordinal variable ranging from 0 to 4 (5 potential inputs) and the board test submitted for ...
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14 views

How to allocate questions to factors using R output?

I have the R output below, but don't know how to allocate questions to the factors. Any advice? ...
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1answer
40 views

Is Predicted R-squared a Valid Method for Rejecting Additional Explanatory Variables in a Model?

I'm building a model to understand the important drivers from a set of possible drivers for a time series of data. In my case the possible drivers are other time series. Like most statistical models ...
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16 views

First factor in Exploratory Factor Analysis and Principal Component Analysis

I am conducting an Exploratory Factor Analysis (EFA) and I was wondering if it is common or appropriate to say that the first factor is the strongest or most important of the model as it is explaining ...
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14 views

Finding MLE by factor analyzing the correlation matrix

In the book "Applied Multivariate Statistical Analysis" written by Johnson and Wichern, they have mentioned that the MLEs ($\hat{L_z}$) are obtained from the the correlation matrix $R$ by inserting ...
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1answer
31 views

Understanding a “computationally convenient uniqueness condition” on loadings in factor analysis

In "Applied Multivariate Statistical Analysis" by Johnson and Wichern, the authors mention a "computationally convenient uniqueness condition" $$L^T\psi^{-1}L=\Delta,$$ where $\Delta$ is a diagonal ...
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15 views

Is it possible to conduct confirmatory factor analysis in SPSS?

I found the factor analysis of SPSS seems to only support EFA, but I am not sure. Is it possible to conduct CFA in SPSS? If not, what statistical tool can be used to conduct CFA? I especially need ...
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26 views

Should I be concerned that the correlation between factors changes sharply when I move from EFA to CFA?

I am running an EFA and CFA on the same data (I realise this would not normally be appropriate). I've found that when I do an EFA (direct oblimin rotation) with a four-factor solution there is a ...
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1answer
79 views

Why confirmatory factor analysis has more degrees of freedom?

I am reading the textbook "Multivariate Data Analysis" and I am puzzled by one statement it makes about confirmatory factor analysis, saying that CFA has more degree of freedom than EFA. The following ...
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60 views

How to compute component or factor scores when the analysis is based on polychoric/tetrachoric correlations?

[This question is modified based on suggestion from @ttnphns] I am doing linear principal component analysis (PCA) based on polychoric correlations between the variables (rather than on native ...
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10 views

Tetrachoric Correlation Between Some Columns — R Factor Analysis Smoothing

My data has a number of columns that are dichotomous (in one case I seem to have a ternary logical relationship). I have been trying to perform exploratory factor analysis on this data. I can split up ...
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14 views

Matlab FACTORAN error on line 162: a covariance matrix is not positive definite [closed]

I have a data set called Z2 that consists of 717 observations (rows) which are described by 33 variables (columns). The data is standardized by using ZSCORES. Additionally, there is no case for which ...
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15 views

SEM design on dyadic data. Please help!

I have two surveys, and one is implemented to counselors. The questions ask about they feel about their relationship with their administrator. It has have two dimensions, let's say d1 and d2. I have ...
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1answer
47 views

What does “varimax” mean in SPSS factor analysis?

In the rotation options of SPSS Factor Analysis, there is a rotation method named "Varimax". If I choose this option, does it mean the same orthogonal rotation techniques of Principal Component ...
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1answer
67 views

Strange results in parallel analysis — weird output by rstudio but not R-Fiddle

Major UPDATE based on discussion with Aleksandr Blekh's answer (thanks so much!): This MRE would run with no problem in R-Fiddle ...
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1answer
41 views

Compute component scores from principal$loadings directly in R

I am using a polychoric correlation matrix to run PCA, so I cannot obtain the scores directly from the function. I am currently manually plugging in the numbers from the ...
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16 views

Finding redundant variables

I have data of several variables (all numeric or continuous) on different subjects. I want to find out if some of these variables are highly correlated so that not all need to be determined. This will ...
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1answer
37 views

factor analysis with missing values

I have data on about 25 subjects and 30 variables with about 20 missing values. The data is missing at random. What will be the best approach to perform factor analysis. How is factor analysis versus ...
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19 views

Does biplot() function in R use rotations or loadings to plot arrows? [duplicate]

For following code performing principal component analysis: ...
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1answer
26 views

How to use factor analysis / PCA / regression for data having serial IV and DV?

I have data regarding effect of a food chemical on blood and urine levels as well as effect on blood sugar and cholesterol. So I have following variables: ...
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How to determine proportion of variance explained in factor analysis

How can I determine proportion of variation explained by 2 factors obtained in output of following code of factor analysis using pacakge "rela" in R: ...
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24 views

How many components should be used? [duplicate]

How many components should be used? I've not really used SAS or SCREE plots how many compotents should be used? Where is the elbow?
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30 views

Why do I need to estimate factor scores rather than simply derive them?

It seems to be a well-known fact, but I never got why. I want to know, why factor scores are estimated, or respectively where my mistake in the rearrangement below lies. Admittedly, matrix algebra has ...
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Rotation in PCA and Factor Analysis [duplicate]

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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1answer
28 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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1answer
61 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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1answer
33 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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2answers
59 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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31 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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24 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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2answers
146 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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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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21 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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1answer
90 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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17 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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19 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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1answer
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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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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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1answer
41 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 ...
2
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1answer
41 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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1answer
46 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 ...
2
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1answer
106 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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1answer
18 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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1answer
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 ...