Factor Analysis Flashcards
Factor Analysis
A procedure for reducing scores on many variables to scores on a smaller number of ‘factors’
Purpose is to explore underlying variance structure of set of correlation coefficients
Thus, factor analysis is useful for exploring & verifying patterns in set of correlation coefficients
Model representation
Factor analysis based on linear algebra
Vectors should produce other vectors & be linearly independent (any combination between vectors should generate a null vector)
F= common factor X= observable variable U= specific factors a/d= weights (factor loadings)
Observable variables
Can be described in terms of some statistical parameters
Individually by mean & variance
Grouped by covariance (correlation)
Continuous
Covariance
Covariance measures relationship between 2 distinct variables
Variance depends on single variable
Since covariance can assume infinitesimal values, correlation is needed to delimit relationship degree of variables
Properties of the observable variables in relation to the other factors
1st property- covariance between observable & the factors is the loading of this variable on the respective factor
2nd property- the variance of the observable variable is the sum of squares of its loading in the common & the specific factors
3rd property- the covariance between the observed variables themselves in terms of the factors is expressed by the product if they’d factor loadings
Factorial components of variance
The variance of the observed variables in relation to their factors can be divided into several parts
A= specific variance B= common variance C= error variance
Common variance
Covariance between items & factors
The percentage of communality (common variance) defines the quality of the behavioural representation of the latent trait from the observable variables (test items)
Communality= the sum of squared factor loadings in all factors- the proportion of each variables variance that can be explained by the factors
True variance
Reliability-> true variance
True variance= communality + specificity
Uniqueness= complement of communality, corresponds to difference between total variance & value of communality
Sample size
5-10 subjects for each variable (item)
Ideal sample is over 200 pp
A psychometric validation with less than 200 subjects may be considered inadequate as it doesn’t provide the desired variability
Level of measurement
In conventional factor analysis, all variables must be quantitative
Important to test normality of variables, seeking to control large deviations of normality
FA analysis
Most used technique for validation of psych instruments
Reduces large number of variables to manageable item pool
FA disadvantages
Usefulness depends on ability of the researchers to develop a set of conditions that make the technique viable
And
Subjectivity of factors
Traditional FA assumes that the relations between the variables are typically linear
