chapter 17 Flashcards
what is the difference between latent and observed variables
observed are- observed and latent represent an underlying construct that is not directly measured and inferred by the observed variables
Factor analysis attempts to achieve parsimony by explaining the __________ amount of ____ ________ in a correlation matrix using the _______ _____ of explanatory constructs.
Factor analysis attempts to achieve parsimony by explaining the MAXIMUM amount of COMMON VARIANCE in a correlation matrix using the SMALLEST NUMBER of explanatory constructs.
Explanatory constructs in FA are called
factors
PCA tries to explain the maximum amount of..
total variance in a correlation matrix
How does PCA explain total variance in a correlation matrix
by transforming variables into linear components
Exploratory factor analysis will
describe and summarize
confirmatory factor analysis will
test hypothesis and structure
How many steps in FA and PCA
7
Steps in PCA and FA:
- Select and measure___ ___ ____
- Make a ________ ______
- Extract a set of _______ from the correlation matrix
- Determine the number of________
- ______ the factors
- _______ _____ _______
- Verify the ______ _______
Steps in PCA and FA:
- Select and measure A SET OF VARIABLES
- Make a CORRELATION MATRIX
- Extract a set of FACTORS from the correlation matrix
- Determine the number of FACTORS
- ROTATE the factors
- INTERPRET THE RESULTS
- Verify the FACTOR STRUCTURE
Why do we rotate the factors
to increase interpretability
IN FA AND PA we seek to ________ the R-matrix into a smaller set of ______ dimensions.
reduce the r-matrix into a smaller set of uncorrelated dimensions
True or false: The assumption f FA is that algebraic factors in a factor matrix represent real - world dimensions
True
True or false: PA CANNOT be used to solve the problem of multicollinearity
FALSE_ FA can be used to solve multicollinearity problems
Both PA and FA look for variables that correlate highly with one another but…
not with anything else.
The factor loading can be thought of as the…
Pearson correlation between a factor and a variable
So if we square a factor loading we get the
substantive importance of a particular variable
In a matrix columns represent each_________ and rows represent
factor and rows represent each variable on each factor.
Weighted average simply puts a persons scores into…
What will influence the resulting scores?
- the equation and gives you a score on those particular factors.
- scales of measurement.
If scales of measurement are different what does it mean
we cannot compare factor scores with different scales of measurement.
Recommended sample size for FA=
and minimum number of responses=
minimum correlation r value=
- at least 300
- 5 to 10
- .3
Factor analysis is usually performed on
ordinal or continuous
variables
Bartlett Method and Anderson Rubin Method are used to calculate
factor scores
Bartlett Method and Anderson Rubin Method are used to calculate factor scores instead of regression because the regression method
means the scores can correlate with other factors
If you want factor scores that are uncorrelated and standardized use the
Anderson Rubin Method
How can results of PCA be generalized to the population..
This is called
if analysis using a different sample confirms the factor structure.
cross-validation
Kaiser recommended retaining all factors with
eigenvalues greater than 1
An eigenvalue of 1 represents
a substantial amount of variation
Orthogonal means
unrelated
when we rotate something on an orthogonal axis we rotate but
keep factors independent
Oblique allows for
correlation between factors
Orthogonal rotations include
varimax
equinox
Quartmax
Direct oblivion and promax rotations are
oblique
As commonalities lower sample size
becomes of greater importance
If you have a KMO value of 0
factor analysis is inappropriate and there are a large number of semi partial correlations
KMO value below .50s are
no good
Bartlett’s test tells us whether our correlation matrix is significantly different than…
or in other words:
That the correlations between variables are …
…an identity matrix
…significantly different than zero
We want Bartlett’s test to be
significant
proportion of common variance in a variable is called
the communality
Communality of 1 =
all shared variance
Communality of 0=
zero shared.
The extraction column of the commonalities table can be multiplied by 100 and expressed as a percentage of…
shared variance or common variance
