PSYCH 2B03 Lecture Notes - Lecture 8: Correlation And Dependence, Factor Analysis, Trait Theory
10 Jun 2018
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Factor Analytic Trait Theories
Lecture 8
Introduction
• Factor analysis – a set of complex mathematical calculations performed on data.
Designed to measure patterns of traits that are intercorrelated
o Some people high in conscientiousness are also high in honesty, low in
neuroticism, etc. These things are correlated even if they’re separate trait
measures
o This is because it’s measuring a common factor in the individual’s personality
o It is able to measure non-orthogonal factors, meaning they are correlated and
knowing where one falls in a certain dimension, might determine where they
would fall in another dimension
Correlation Matrix – Factor Analysis
• We begin w/ a correlation matrix containing values from any kind of research study (e.g.
test scores, responses to ratings on trait dimensions, etc.). Numbers in the matrix
represent the correlation between various items in the study
• Correlation b/w A and C is 0.80, meaning it’s very likely if you’re rated high in A, you’ll
be high in C (high correlation)
• Correlations of 0 or anything close to 0 = no correlation/very low correlation (they have
been removed in the matrix)
• Numbers in red are highly correlated and we can assume there is a common underlying
factor → there is something in the individual’s personality that is shaping all of these
responses
• Factor equation – estimates the extent to which the hypothesized factor is reflected in
the value of each intercorrelated variable
o Factor 1/F1 (some one thing/factor) influences item C to 0.8 extent, influences
item D to 0.6, etc.
▪ It influences item C more than item E but it influences all items to some
degree
o These numbers are called the factor loadings – the degree to which items in the
correlation matrix is affected by the factor
o Factor 2/F2 could be some other factor that might be responsible for correlations
of other items
o These factors are non-orthogonal factors – scores on factor 1 and factor 2 will be
correlated b/c they contain some of the same items. High score on factor 1 = high
score on factor 2
▪ Orthogonal factors are independent of each other, while non-orthogonal
factors are related
Naming Our First Factor
• We will never leave our factors named F1 or F2; we have to give them names and
describe them
• We look at the items to see what they are:
o C = likes to party
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o D = seeks out sensations
o E = likes to take risks
o F = learns more slowly
o G = has leadership skills
• Find out how to describe someone who has values in all of these dimensions in common
→ F1 = extroverted
What Factor Analysis Does
• Does not find ‘real’ things – these factors (extroversion, introversion, etc.) are
hypothetical constructs; they do not have real, physical existence
• Does not identify factors – factor analysis is not specific to trait factors only; it works
with all theories depending on what you’re studying. It is not specific to trait theory
• Not necessarily traits
• Results depend on parameters – different researchers can find different results depending
on how they do their factor analysis
• Results depend on measures – depends on what input we put into the program (trait
measures, psychodynamic measures, cognitive response measures, etc.) it all depends on
how you interpret and see the data. Depends on judgment of the examiner
What Makes a Factor ‘Basic’?
• There are several characteristics that make a characteristic a “factor of personality”.
Costa & McCrae (1992) developed this, as well as the big five factor model
• Reliable/stable aspect of one’s personality – the factor should be stable over time to
observers, it should be a stable aspect of one’s personality. Traits are biologically
determined so they shouldn’t change over time
• Used by both theorists & laypersons – factors should make sense to everyone (everyone
understands emotional stability, extroversion, introversion, etc.)
• Appear across cultures – should be true of all human beings because it’s determined by
evolution
• Must have some biological basis – factor must have some underlying genetic basis,
should be able to show high heritability
Exploratory vs. Confirmatory Factor Analysis
• Exploratory factor analysis – you go in w/ no preconceptions of what you’ll find, how
many factors will be found, what they’ll look like, etc. Several of these factor analysis
may be done on different populations or different data sets
• Confirmatory factor analysis – after you have a good sense of the factors, you will try
to replicate the same factors with new population/sample to confirm the same set of
underlying factors found in the exploratory factor analysis
Early Factor Analytic Theories
• Raymond Cattell (1930) – the first person to use factor analysis to try to understand
personality
o He found 16 non-orthogonal personality factors
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
Introduction: factor analysis a set of complex mathematical calculations performed on data. Designed to measure patterns of traits that are intercorrelated: some people high in conscientiousness are also high in honesty, low in neuroticism, etc. Correlation matrix factor analysis: we begin w/ a correlation matrix containing values from any kind of research study (e. g. test scores, responses to ratings on trait dimensions, etc. ). High score on factor 1 = high score on factor 2: orthogonal factors are independent of each other, while non-orthogonal factors are related. What makes a factor basic": there are several characteristics that make a characteristic a factor of personality . Costa & mccrae (1992) developed this, as well as the big five factor model: reliable/stable aspect of one"s personality the factor should be stable over time to observers, it should be a stable aspect of one"s personality.
