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FACTOR ANALYSIS AND RELIABILITY - Coggle Diagram
FACTOR ANALYSIS AND RELIABILITY
RELIABILITY
It is the overall consistency of a measure. A measure is said to have high reliability if it produces simnilar results under consistent conditions. (Cronbach's alpha index)
reliability does not imply validity. If the measure is consistent does not mean that it representes what we wanted to measure.
FACTOR ANALYSIS
It is useful to
summarize information, verify the dimensional structure of multi-dimensional scale.
it is about
summarization and reduction, it helps to discover smaller number of varibles (factors) which could be explain by observed variables (latent variable)
interdependece technique: the examination of an entire set of interdependent relationship (through correlation matrix)
types
EXPLORATORY
When you do not have a pre-defined idea of the structure or number of dimension in a set of varibles
CONFIRMATORY
when you want to test specific hypothesis about the structure or number of dimension of a set of variables
Steps
correlation matrix
it is the basis for the factor analysis. The variables MUST BE CORRELATED for an appropriate factor analysis. system to test FA appropriateness:
Bartlett test < 0.05;
KMO > 0.05;
substantial number of correlations higher than 0.30
determine the method
1.principal component analysis (PCA) [when the main objective is to determine the minimum number of latent factors that will account for maximum variance]
common factor analysis
determine the number of factors to consider
several procedures
determination base on eigenvalues
it represents the amount of variance in the original variable associated with factors; >=1
determination based on the percetage of variance
the cumulative % of variance at least 60%
a priori determination
determination based on the scree plot
elbow point
problem formulation
if exploratory or confirmatory; the items to include and the right number of observations (like 5:1; 5 observations for each item)
rotate matrix
the factor matrix indicates the relationship between the factors and the individual variable. It is too complicate to analyze
ROTATION
transform the factor matrix in a simpler one through the
maximization of high saturation and minimization of low saturation
methods
orthogonal rotation (varimax)
results factors are uncorrelated. It minimzes the number of variables with high loading on factor.
Oblique rotation (oblimin)
factors are dependent (correlated)
Interpret the results
you have to identify the variables that have high loadings in the same factor
identify the items that have large loading on the same factor
reasons to removal: variable loading on several factors and variable with low loading < 0.30
IDENTITY MATRIX
Items are correlated each other and not just with themselves