Meeting 2: Chapter 4 Test Dimensionality and Factor Analysis (Three key…
Meeting 2: Chapter 4 Test Dimensionality and Factor Analysis
Three key questions of dimensionality
1.How many dimensions?
Eigenvalues, screeplot, factorloadings
Meaning of Dimensions?
Rotation method, inter factor correlations
dimensions are not correlated
dimensions are correlated
test includes items that reflect only one single attribute of a person, this means that resposnses to those items are driven by that attribute
reflect only one psychological dimension
conceptual homogeniety --> responses to each item would be a function of the same psychological attribute
has implications for its scoring evaluation, and use
all the items are combined in some way to for a composite or total score
Multidimensional tests--> test includes items reflecting more than one psychological attribute
multidimensional test with correlated dimensions/test with high order factors
test has multiple dimensions that are correlated with each other . eg. WISC-IV
Simple structure: each item loads mainly on one of the factors.
high-order factor-->at a more general level than the specific factors or attributes
multidimensional tests have a score for each subset and each subset score is evaluated with regard to it psychometric quality
Multidimensional test with uncorrelated dimensions
no total score is computed--> score is obtained for each dimesions but not combined
each dimension scores is evaluated in terms of psychometric quality
Exploratory Factor Analysis
EFA looks for factors that expain as much as variance in the items as possible.
Mathematically identifies sets of items that go together –-> have strong intercorrelations.
Rather than visually inspecting a matrix of dozens of correlations, we can use EFA to process a large set of correlations
large number of items-> large number of correlations to examine (48 items--> 1100 correlations)
Confirmatory Factor Analysis
CFA examines whether the predefined structure of relationships between items and factors fits the observed correlation matrix
used in early phases of of the development and evaluation pf psychological tests
used when there is a clear picture of dimensionality
inferential tests of parameter estimates and "goodness of fit"
Conducting and Interpreting EFA
choose extraction method
identify number of factors and extract them
item-factor associations-->clear unidimensional scale
clear multidimensional scale with correlated dimensions
Axes are rotated such that items load maximally on one of the factors
The correlation between the factors remains 0
oblique rotation (e.g.promax)
clear multidimensional scale with uncorrelated dimensions
Axes are rotated such that items load maximally on one of the rotated axes.
factors are allowed to correlate
different extraction methods
Principal Component Analysis (PCA)
Maximum likelihood factor analysis
Principal Axis Factoring (PAF)
how to extract --> 1. Theory +varience explained + eigenvalue>1+ screeeplot
eigenvalue greater than 1.0 is among the least accurate methods for selecting (Costello)
Structure matrix-->correlation between the items and the factor
Pattern Matrix-->factor loadings, the unique contribution of the factor in explaining the variance in the item, corrected for the other factors.
examining Item-factor Associations
By examining the loadings and identifying the items that are most strongly linked to each factor , we can begin to understand psychological meaning
factor loading range between -1 and 1 --> standerdized regression weights
simple structure is important in psychometrics and scale usage
occurs when each item is strongly linked to one and only one factor
factor loadings can violate simple structure
item might not load strongly on any factor
item might load strongly on more than one factor
interpreting factor loadings
size of the loading
ppl who respond with a high score on the item have a high level of that underlying factor
oblique rotation s are preferred to orthogonal -->
results produced show very clear associations between factors, easier to understand
brane Bencic 424918/ 2.5.2 Course and Practical : Psychometrics: An Introduction / Meeting 2/ Tutor: Nalleke Deijkers /Source: Furr, R.M. & Bacharach, V.R. (2014). Psychometrics: An introduction. Second Edition. Thousand Oaks, CA: Sage Publications. ISBN 9781452256801.