what are latent variables?
they are factors that cant be observed and measured so we use observed variables to measure them
what are observed variables?
they are items in a questionnaire, factors that can be directly measured
why should items on a scale not correlate too weakly or too highly?
too weak = the items are not measuring the same construct/latent variable
too high = items are measuring the same thing so the scale is not capturing all aspects of a construct
why do people use factor analysis?
to understand the structure of a set of variables (whether they have good level of correlation)
to reduce a large set of variables to a smaller subset of factors
what are the elements of performing factor analysis?
- understanding communalities: each item’s total variance (1) is made up of unique variance (1-h2) and common variance (h2). one way to estimate the communality is to use squared multiple correlation (r2)
- eigenvalues and factor extraction
extraction = deciding how many factors best capture our data - we want to explain as much variance with as little factors as possible. this is based on eigenvalues
eigenvalues = the variance in al the variables explained by a particular factor. if eigenvalue is low = doesn’t explain much = can get rid of it
what are the extraction methods ordered worst to best?
kaiser’s criterion: retain factors with eigenvalues >1
scree plot: extract factors on the left side of inflection point
parallel analysis: retain factors if their eigenvalue from the actual data is greater than eigenvalue from random data
what does ‘factor loading’ mean?
how much each item contributes to a certain factor
what does factor rotation mean?
a technique used to clarify the relationships between items and factors. it optimises how the items load onto a factor and equalises the importance of each factor
when do you use orthogonal rotation?
when the underlying factors are independent
what type of rotation would you use when underlying factors are correlated?
oblique rotation
