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Results tagged with factor-analysis
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user 9162
Factor analysis is a dimensionality reduction latent variable technique which replaces inter-correlating variables with 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 the tag 'confirmatory-factor'. Also, the term "factor" of factor analysis should not be confused with "factor" as categorical predictor of a regression/ANOVA.]
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EFA: interpreting negative factor loadings [duplicate]
I've run an exploratory factor analysis with oblique rotation, and specifying three factors.
The first two factors are correlated at almost zero with one another, while there's a negative correlation …
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28
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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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In the context of factor analysis, are the terms 'factor' and 'latent variable' synonymous?
I realise that the term factor has additional applications in other areas (e.g. in ANOVA), but it seems to me that in factor analysis the two terms are used synonymously.
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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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What is $X$ in the fundamental equation of factor analysis?
Mulaik (2009) p. 135-136 writes that
Let Y be an $n \times 1$ random vector of random variables whose
variables are the observed random variables $Y_{1}, ... , Y_{n}$.
Assume that $E(Y) = 0$ …
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When is it incorrect to compute factor scores by summing (or averaging) raw variable scores?
I understand that a problem will be inevitable if the variables have different scales of measurement.
My inclination is to think that even if the variables have the same scale of measurement it would …
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answer
262
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Correlation between factors vs correlation between error terms of items measured by each factor
Say there is a CFA model where there are 2+ factors, and the correlation between factors is freely estimated.
A change is made to the model such that an error term connected to an item on one factor i …
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Relationship between overall KMO and variance explained by factors
The Wikipedia page for the Kaiser–Meyer–Olkin test says that KMO "is a measure of the proportion of variance among variables that might be common variance."
So you will see people get an overall KMO o …
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What is the intuition behind the KMO formula?
In answer to a different question about data assumptions of factor analysis rolando2 writes:
There is another condition that is sometimes treated as an "assumption": that the zero-order (vanilla) …
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How are inter-factor correlations calculated?
I understand from this answer (near the end) that whether factor scores will reproduce interfactor correlations depends on the method of factor score estimation, and thus that it is not in general tru …
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Why does PCA's failure "to explicitly model error variance" make it difficult to interpret c...
I've heard statements like this many times over the years, and it's perhaps expressed most clearly by Preacher & MacCullum (2003), which is a popular paper on stats.stackexchange.com (e.g. mentioned t …
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Feasible to do hierarchical CFA with only two first-order factors?
Kline (2011) p249 writes:
To identify a hierarchical CFA model, there must be at least three
first-order factors. Otherwise, the direct effects of the second-order
factor on the first-order fa …
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Cluster analysis vs Factor analysis as a means for "grouping" variables or cases
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.
peo …
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655
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Will CFA produce the same loadings as an obliquely rotated EFA under these conditions?
I have in mind figures like the following, which purport to explain the difference between EFA (left) and a 'standard' CFA (right). I guess in this picture one loading per factor should be fixed, and …
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Scree plot: $m$ vs $m-1$ components/factors
@ttnphns comments here that
there exist two expositions of the Cattell scree-plot rule: If the "elbow" is the m-th eigenvalue, (1) choose to extract m components; or (2) choose to extract m-1 compone …