Factor Analysis
Factor analysis is one of multivariate procedures that attempts to identify latent variables or factors. Those identified factors (or common latent dimensions) should explain the pattern of correlations within a set of observed (manifested) variables.
Factor analysis is probably the most popular analyze that is used in attempting to reduce number of data that are sufficient in explanation the nature of observed constructs. The basic idea of factor analyze is to identify a small number of factors that explain most of the variance instead of operating with much larger number of manifest variables.
Factor analysis can also be used to generate hypotheses regarding causal relations between variables.
There are several methods that can be used in attempting to identify and extract latent variables (factors) from common space. All those methods are known as factor extractions methods and their names and basic characteristic are:
The most common one is called Principal Components Analysis. In this case a factor extraction method is used to form uncorrelated linear combinations of the observed variables.
The first component has maximum variance. Further extracted components explain progressively smaller portions of the variance and the most important thing is that components do not share variance among themselves (they are all uncorrelated with each other).
Unweighted LeastSquares Method is another factor extraction method. In this procedure sum of the squared differences between the observed and reproduced correlation matrices are minimized.
A factor extraction method that minimizes the sum of the squared differences between the observed and reproduced correlation matrices is wellknown as Generalized LeastSquares Method. What we have got here are correlations weighted by the inve.....[read full text]
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Factor analyse


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4∋≠;∋∞∋7;∂∞†;+++⊇ 4∞†++⊇ ∋≈ †∋≤†++ ∞≠†+∋≤†;+≈ ∋∞†++⊇ ⊥++⊇∞≤∞≈ ⊥∋+∋∋∞†∞+ ∞≈†;∋∋†∞≈ †+∋† ∋+∞ ∋+≈† †;∂∞†+ †+ +∋=∞ ⊥++⊇∞≤∞⊇ †+∞ ++≈∞+=∞⊇ ≤+++∞†∋†;+≈ ∋∋†+;≠. 4 ≈∞≤∞≈≈∋++ ≤+≈⊇;†;+≈ †++ ∋⊥⊥†+;≈⊥ †+;≈ ∞≠†+∋≤†;≈⊥ ∋∞†++⊇ ;≈ †+∋† †+∞ ≈∋∋⊥†∞ ∋∞≈† +∞ †++∋ ∋ ∋∞††;=∋+;∋†∞ ≈++∋∋† ⊇;≈†+;+∞†;+≈.
3;†+ 0+;≈≤;⊥∋† 4≠;≈ 6∋≤†++;≈⊥ ;≈ †+∞ †+∋∋∞ +† †∋≤†++ ∋≈∋†+=∞ ≠∞ ∞≠†+∋≤† †∋≤†++≈ †++∋ †+∞ ++;⊥;≈∋† ≤+++∞†∋†;+≈ ∋∋†+;≠. 1≈ †+∞ ∞≈†;∋∋†∞≈ +† †+∞ ≤+∋∋∞≈∋†;†;∞≈ ≈⊥∞∋+∞⊇ ∋∞††;⊥†∞ ≤+++∞†∋†;+≈ ≤+∞††;≤;∞≈†≈ ∋+∞ ≈∞† ;≈ †+∞ ⊇;∋⊥+≈∋†. 6∋≤†++ †+∋⊇;≈⊥≈ ∋+∞ ∞≈∞⊇ †+ ∞≈†;∋∋†∞ ≈∞≠ ≤+∋∋∞≈∋†;†;∞≈ ;≈≈†∞∋⊇ †+∞ ;≈;†;∋††+ ≤+∋∋∞≈∋†;†+ ∞≈†;∋∋†∞≈.
4†⊥+∋. 7+;≈ †∋≤†++ ∞≠†+∋≤†;+≈ ∋∞†++⊇ ≤+≈≈;⊇∞+≈ †++≈∞ =∋+;∋+†∞≈ †+∋† ∋+∞ ∋ ≈∋∋⊥†∞ †++∋ †+∞ ∞≈;=∞+≈∞ +† ∋†† ⊥+†∞≈†;∋† =∋+;∋+†∞≈. 3+ †+;≈ ∞≠†+∋≤†;+≈ ∋∞†++⊇≈ †+∞ ∋†⊥+∋ +∞†;∋+;†;†+ +† †+∞ †∋≤†++≈ ∋+∞ ∋∋≠;∋;=∞⊇.
7+∞ †∋≈† +≈∞ +† †∋≤†++ ∞≠†+∋≤†;+≈ ∋∞†++⊇≈ ;≈ ≈∋∋∞⊇ 1∋∋⊥∞ 6∋≤†++;≈⊥. 1† ;≈ ⊇∞=∞†+⊥∞⊇ ++ 6∞††∋∋≈ ∋≈⊇ +∋≈∞⊇ +≈ ;∋∋⊥∞ †+∞+++.
3∋≈;≤ ∋≈≈∞∋⊥†;+≈≈.
7+∞ ⊇∋†∋ ≈++∞†⊇ +∋=∞ ∋ +;=∋+;∋†∞ ≈++∋∋† ⊇;≈†+;+∞†;+≈ †++ ∞∋≤+ ⊥∋;+ +† =∋+;∋+†∞≈, ∋≈⊇ ++≈∞+=∋†;+≈≈ ≈++∞†⊇ +∞ ;≈⊇∞⊥∞≈⊇∞≈†. 7+∞ †∋≤†++ ∋≈∋†+≈;≈ ∋+⊇∞† ≈⊥∞≤;†;∞≈ †+∋† =∋+;∋+†∞≈ ∋+∞ ⊇∞†∞+∋;≈∞⊇ ++ ≤+∋∋+≈ †∋≤†++≈ ∋≈⊇ ∞≈;⊥∞∞ †∋≤†++≈.
3∞≈;⊇∞≈, =∋+;∋+†∞≈ ;≈=+†=∞⊇ ;≈ †∋≤†++ ∋≈∋†+≈∞ ≈++∞†⊇ +∞ ⊥∞∋≈†;†∋†;=∞ ∋† †+∞ ;≈†∞+=∋† ++ +∋†;+ †∞=∞†. 0∋†∞⊥++;≤∋† ⊇∋†∋ (≈∞≤+ ∋≈ ≤+∞≈†++ +† ++;⊥;≈) ∋+∞ ≈+† ≈∞;†∋+†∞ †++ †∋≤†++ ∋≈∋†+≈;≈. 8∋†∋ †++ ≠+;≤+ 0∞∋+≈+≈ ≤+++∞†∋†;+≈ ≤+∞††;≤;∞≈†≈ ≤∋≈ ≈∞≈≈;+†+ +∞ ≤∋†≤∞†∋†∞⊇ ≈++∞†⊇ +∞ ≈∞;†∋+†∞ †++ †∋≤†++ ∋≈∋†+≈;≈.
1≈ ∋††∞∋⊥† ;+≈ †+ ⊥;=∞ ∋++∞ ⊥+∞≤;≈∞†+ ;≈†∞+⊥+∞†∋†;+≈≈ +† †∋≤†++≈ ≈∋†∞+∞ ≠∞ ≤∋≈ ∞≈∞ ⊥++≤∞⊇∞+∞≈ ≤∋††∞⊇ †∋≤†++ ++†∋†;+≈≈. 1≈ †+;≈ ≤∋≈∞ ≠∞ ≤∋≈ ⊥∞† ≤†∞∋+∞+ ⊥;≤†∞+∞ +† ≠+;≤+ =∋+;∋+†∞≈ ∋+∞ +;⊥+†+ ≤+++∞†∋†∞⊇ ≠;†+ †∋≤†++ ∋≈⊇ ≠+;≤+ +∋=∞ ;≈≈;⊥≈;†;≤∋≈† +∞†∋†;+≈ ≠;†+ ;†. 0++≤∞⊇∞+∞ +† †∋≤†++ ++†∋†;+≈≈ ≤∋≈ +∞ ++†++⊥+≈∋† ∋≈⊇ ≈+≈ ++†++⊥+≈∋†.
 2∋+;∋∋≠, ∋≈ ∋≈ ++†++⊥+≈∋† ++†∋†;+≈ ∋∞†++⊇ ∋;≈;∋;=∞≈ †+∞ ≈∞∋+∞+ +† =∋+;∋+†∞≈ †+∋† +∋=∞ +;⊥+ †+∋⊇;≈⊥≈ +≈ ∞∋≤+ †∋≤†++. 1† ≈;∋⊥†;†;∞≈ †+∞ ;≈†∞+⊥.....
 8;+∞≤† 0+†;∋;≈ 4∞†++⊇ ;≈ ∋≈ ++†;⊥∞∞ (≈+≈++†++⊥+≈∋†) ++†∋†;+≈. 3+∞≈ ⊇∞††∋ ∞⊥∞∋†≈ 0 (†+∞ ⊇∞†∋∞††), ≈+†∞†;+≈≈ ∋+∞ ∋+≈† ++†;⊥∞∞. 4≈ ⊇∞††∋ +∞≤+∋∞≈ ∋++∞ ≈∞⊥∋†;=∞, †+∞ †∋≤†++≈ +∞≤+∋∞ †∞≈≈ ++†;⊥∞∞.
0∞∋+†;∋∋≠ 4∞†++⊇ ∋;≈;∋;=∞≈ †+∞ ≈∞∋+∞+ +† †∋≤†++≈ ≈∞∞⊇∞⊇ †+ ∞≠⊥†∋;≈ ∞∋≤+ =∋+;∋+†∞ ∋≈⊇ ≠∞ ≤∋≈ ≈∋+ ;† ≈;∋⊥†;†;∞≈ †+∞ ;≈†∞+⊥+∞†∋†;+≈ +† †+∞ ++≈∞+=∞⊇ =∋+;∋+†∞≈.
 9⊥∞∋∋∋≠ 4∞†++⊇ ;≈ ∋ ≤+∋+;≈∋†;+≈ +† †+∞ =∋+;∋∋≠ ∋∞†++⊇ ∋≈⊇ †+∞ ⊥∞∋+†;∋∋≠ ∋∞†++⊇. 7+∞ ≈∞∋+∞+ +† =∋+;∋+†∞≈ †+∋† †+∋⊇ +;⊥+†+ +≈ ∋ †∋≤†++ ∋≈⊇ †+∞ ≈∞∋+∞+ +† †∋≤†++≈ ≈∞∞⊇∞⊇ †+ ∞≠⊥†∋;≈ ∋ =∋+;∋+†∞ ∋+∞ ∋;≈;∋;=∞⊇.
 0++∋∋≠ 5+†∋†;+≈ ;≈ ∋ ≈+≈++†++⊥+≈∋† ++†∋†;+≈, ≠+;≤+ ∋††+≠≈ †∋≤†++≈ †+ +∞ ≤+++∞†∋†∞⊇ ∋≈⊇ ;† ;≈ ∞≈∞†∞† .....