# PSYCH 2B03 Lecture Notes - Confirmatory Factor Analysis, Correlation And Dependence, Factor Analysis

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18 Mar 2013
School
Department
Factor Analytic Trait Theories
History
- Looking for non-orthogonal factors, developed first theory which used factor analysis. Modelled personality using 16
factors developed a test called 16PF (personality factor) to measure these factors - often used as an independent
variable (i.e. how would we describe these individuals who perform differently in these tasks give them 16PF)
- Problem: factor analysis doesn’t name what the factors are
- Eynseck: orthogonal, found 2 and then 3
- 1960s, number of people began generating data based on factor analysis, which suggested 5, which contains 2 of 3
Eynseck’s factors began generating data suggesting that 5 collections of traits underlies most. By early 1980s, more
data consistent with this 5 factor model. It was not as popular before because MIschel critiqued the trait approach
saying that there’s not enough consistency between an individuals behaviour from one situation to another, against
trait theory.
- Dominated trait theory, this approach to personality still well supported so popular because it’s measurable, these
traits are much easier to measure compared to psychoanalytic approach etc.
- 2 people who are mostly associated with the 5 factor model are costa and mcprey? worked in field of aging, became
best known for contributions to factor analytic trait
Factor analysis
- almost all trait theories today are factor analytic trait theories
- note: understand what it is that factor analysis does vs. does not do
and how you understand results
- understanding the relationship between inter-correlated variables
- sample correlation matrix
o e.g. 0.8 correlation between A and C
- correlation coefficient (r) = 0 to 1 reflects degree of relatedness, the closer to 1,the better we are at predicating one
variable by knowing the value of the other variable. If it’s at 1, you can perfectly predict.
- High inter-correlation reflects the ability to predict one from other but why are we able to do this? Reason why it’s
predictable is because of causation (one causing the other) or because there’s some underlying variable which is
influencing the values of both
- E.g. heat stroke and ice cream sales correlated (inter-correlated variables)
o Not causal relationship
o Tempature, 3rd underlying variable, influencing both
- Factor analysis takes a correlation matrix, looks for highly inter correlated values, takes a group and hypothesize that
underneath these variables there’s a hidden variable affecting all of them to some degree (underlying factor)
o Underlying factor influencing all of the values (in the box)
o Underlying factor especially influencing D and G high inter-correlation
- Factor analysis builds mathematical model: what would be model look like/what would the variables be?
- The first factor
o E.g. factor 1 which influences the different variables to a different extent
- Second non-orthogonal factor
o Take another group
o Another weighted combination of the factors
- Underneath matrix of inter-correlated values, there’s 2 underlying factors which are causing the matrix of inter-
correlation can be expressed in two equations, each factor has a different impact on the measured variables
- Factor analysis does not tell us what the factor is how do we know what it is then?
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- Look at what the variables are: e.g
o C = likes to party
o D= seeks out sensations
o E= likes to take risks
o F= learns more slowly
- What’s the common thread behind these? E.g. it’s extroversion/introversion factor 1
- Produces a mathematical model- if we assume a small number of underlying factors are responsible for inter-
correlations, what would these factors look like and how would they be reflected?? (For eynseck, he came up with 2,
and then psychoticism)
- What factor analysis does
o Does not find real things
It’s a hypothetical model (factors are hypothetical constructs)
o Does not identify factors
If there are underlying factors what would they look like? He did not find them, just produced a
model for it
o Not necessarily traits
Can be anything, doesn’t have to be factors e.g. it’s ego vs. id or something
Traits are not the only thing you can discover, just that these people were trait-theorists
o It’s a set of methods depending on how you decide to do it, you may get different results
o Results depend on parameters
Orthogonal vs. non-orthogonal
do you want factors to be inter-correlated?
Do not want factors to be correlated set analysis up that way and you get orthogonal factors
(uncorrelated factors)- this is the focus, will get smaller number of factors
Can also set up factor analysis where you don’t care whether factors themselves are correlated or not
look for non-orthogonal factors (factors themselves are intercorrelated to some degree)
Eynseck’s model is orthogonal factors (stability arousal and introvert/extroversion dimension)
there actually might be a correlation (higher extroversion, lower neuroticism)- still under debate
o Results depend on measures
What kind of data are you collecting
- Mathematical model produced based on assumption that inter-correlated measures reflects underlying processes
o Do not identify traits! Just produces a model for them
o Only used by trait theorists, though they are not just looking for traits can be used by others
o If we were to assume there’s a smaller set of underlying factors, this is what the factors would look like
doesn’t find anything, just identifies constructs (small set of hypothetical constructs which could be used to
explain the constructs) not identifying anything concrete
- exploratory vs. confirmatory
o exploratory: begins with no assumptions about what you are going to find in the data and then model will
identify some number of underlying factors if they exist/can be modelled (no preconceptions about what
you’re going to see)
o confirmatory: set up analysis where it’s looking for the same factors in another set of data trying to confirm
that hypothesis, want to see whether the same number and kind of factors can be located/identified, could
adequately describe a new set of data
o currently, only doing confirmatory factor analysis in trait theory (no longer exploring)
What makes a factor “Basic”
- Reliable: stable over time and observers
o Relatively unchanging, consistently reported
o Wouldn’t expect measures to be stable in other theories (e.g. Rogers and constant move to self-actualization)
o Trait/type theory, expect temporal stability because it’s unchanging for the most part
- Used by both theorists and laypersons (people who aren’t in the field of research)
o Something that’s meaningful for everyone
- Appear across culture
o Because there’s a physiological/genetic basis it should be everywhere
o There are many aspects of psychology which are different from place to place, but personality is not, if we
assume that it’s based on underlying factors
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- Must have some biological basis
The Big Five
- there are only 5 collections of traits/underlying factors, and with those 5, can adequately capture the essence of
anyone’s personality
- testing instrument that goes along with it: NEOPI (NEO personality inventory revised)
- NEO: first 3 factors/dimensions identified
- Represents a set of 6 underlying/correlated traits, there are various names for each dimension, since factor analysis
doesn’t tell you the name
- Dimension 1: Extroversion/introversion
o Social adaptability, assertiveness, sociability and ambition, positive emotionality, interpersonal involvement
- Dimension 2: Friendliness-Hostility
o Agreeableness, conformity, likeability, friendly compliance, sociability, love, level of socialization
o Encapsulates the following subtraits: trust, straight forwardness, compliance, modesty, tender-minded
- Dimension 3: Conscientiousness-Will
o Will to achieve, dependability, task interest, prudence, impulsivity, self-control
o Conscientiousness: staying with, sticking with something, fulfilling one’s responsibilities
o Will: impulsivity, doing whatever you want to do regardless of obligations
o Underlying traits correlated in this dimension: competence, dutifulness, achievement striving, self-discipline,
deliberation
- Dimension 4: Neuroticism-Emotional Stability
o Emotional control, emotionality, adjustment, emotional stability
o Underlying traits: anxiety, depression, hostility, self-consciousness, impulsiveness
- Dimension 5: Intellect (Openness)
o Fantasy, aesthetics, feelings, actions, ideas and values
o Reflective of intelligence, cognitive activity
o Openness to experience, ideas, curiosity (cost and mccray?)
- 240 statements, say whether you strongly agree, disagree etc.
o Accuracy depends on what people report so need to be conscious in interpreting NEOPI
- Underlying factors/traits are biologically given, present at birth to the same extent/degree that they will be throughout
life
o There are changes, environment makes impact but the impact of experience is very limited
o Biology giving a range along trait dimensions within which you can possibly move
o If you believe in strong genetic determination range is small
o Within that range, experiences depend where you fall
- However, clear from data, that our personalities do change over time
o social dominance (sub-trait of extroversion) goes up over time, especially between ages of 20-40- in general,
populations increase in social dominance
o conscientiousness goes up, between same age group
o emotional stability goes up (neuroticism) goes up, same age group
o social vitality (sub trait of extroversion) goes up in adolescence, goes down in old age
o openness/intellect: up in adolescence, down in old age
o agreeableness goes up in old age
o don’t know what causes the changes trait theorists may argue that it’s biological
o genes that are active in our genome change over time, genes which may be active and easily produce products
when we’re young may no longer be active when we are an adult. Genes which we’re doing anything when we
were young may become active at middle or old age thus biology is changing. if this underlies personality,
should not be surprised that personality is changing as well
- Cultural differences in Big 5
o General level of these traits slightly different, gene pool is different expect differences across the world
o Clear difference: in European/north American vs. African/asian countries Europeans/north Americans are
more extroverted
o Goes along with general collectiveness nature of asian culture values which de-emphasizes individuality and
outgoingness, and emphasize the value of quietness etc.
o Openness higher in Europe/north America
o Agreeableness is lower in Europe/N America- ability to get along with others is lower
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## Document Summary

Looking for non-orthogonal factors, developed first theory which used factor analysis. Problem: factor analysis doesn"t name what the factors are. 1960s, number of people began generating data based on factor analysis, which suggested 5, which contains 2 of 3. Eynseck"s factors began generating data suggesting that 5 collections of traits underlies most. By early 1980s, more data consistent with this 5 factor model. It was not as popular before because mischel critiqued the trait approach saying that there"s not enough consistency between an individuals behaviour from one situation to another, against trait theory. Dominated trait theory, this approach to personality still well supported so popular because it"s measurable, these traits are much easier to measure compared to psychoanalytic approach etc. Worked in field of aging, became best known for contributions to factor analytic trait. If it"s at 1, you can perfectly predict.

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