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Confirmatory factor analysis - Coggle Diagram
Confirmatory factor analysis
Terminology
Communality (h^2)
indicates how much a variable/item has in common with the extracted factors
depends on the sample
ranges from 0 to 1
STANDARDS
h^2<0.20
items have
very little in commo
n with factors extracted
h^2>0.80
there are
redundant items
. strong overlap between variances of extracted factors.
Factor Loadings
indicate the degree to which each factor relates to each variable.
depends on the sample, ranges from -1 to 1, 0 lack of relationship.
STANDARDS
>0.40 or 0.30 retained and considered to be meaningful
Squared Multiple Correlations (from a reliability analysis) R^2
cronbach's alpha estimated for uni-dimensional construct
R^2 for each item predicted by the rest of the items
sample dependent, ranges from 0 to 1.
used to identify items that have very little in common with THIS particular dimension.
Goodness of Fit Indices
Absolute
Chi-square (x^2)
: small value indicate non-statistical difference between actual and implied matrix, hence no discrepancy between the hypothesized model and the data. Sensitive to sample size.
Small value means the theory fits well with the observed value
"Normed"x^2
: relative to df, X^2/df.
< 2 are considered to indicate good fit.
the goodness of Fit index (GFI)
: indicates whether proposed model is no better than null. **
> 0.90 and >0.95 are considered acceptable and good fits respectively. **
Relative
The Tucker-Lewis Index (TLI): how much better the fitted model is compared to some baseline model.
> 0.90 or >0.95 are considered to reflect acceptable and good fits respectively.
Approximate goodness of model fit in the population
The root mean square error of approximation (RMSEA) and its 90% confidence interval.
< 0.05 and a narrower confidence interval suggest a good fit.
EFA vs CFA
reduce large number of variables to a smaller and related set (bottom up)
exploration of how many factors there may be, this is done by investigating the communalities in items/variables to determine clusters/.
identify aberrant items and redundant items using communalities
can have factor loadings on different factors
loadings differ because of sample
seek evidence for a particular theory of organising factor structures (Top down)
restrictions are used to examine a theory.
number of factors
factor loadings
uniqueness of each item
only allowed to have factor loadings on the set factors.
loadings differ because of sample.
Increasing reliability
Decreasing error
Minimize the effects of external events
standardise testing conditions
standardise instructions
maintain consistent scoring procedures
Good sample size (not a solution of unreliability problems)
Work with items
eliminate unclear question
are there biased questions?
use a diverse range of questions
examine latency in the observed data
increase number of questions.