lecture 6 factor analysis Flashcards
What is Intelligence?
Intelligence as defined by the lay public (Sternberg et al 1980s)
Reasons logically and well”, “reads widely”, “displays common sense”, “keeps an open mind”, “reads with high comprehension”
Differences between laypeople & experts:
Motivation & narrower (experts)
Interpersonal aspects & broader (lay people)
laypersons & expert common factors
Common factors: problem-solving, verbal-ability, & social-competence
Intelligence as defined by the lay public (Seigler & Richards, 1980)
&intelligence in infants (lay def)
Developmental psychology students listed behaviours associated with intelligence in infancy, childhood, and adulthood.
Motor co-ordination
Awareness of people
Awareness of the environment
Verbal output
Intelligence as defined by the lay public (Seigler & Richards, 1980) cont.
children and adults
Children Motor co-ordination Understanding Learning Ability Verbal Facility
Adults Use of logic Problem solving Learning ability Verbal ability
lay construct changes over course of development
increase in “cognitive” component over time
verbal ability consistent, but developing
Intelligence as defined by children (Yussen & Kane, 1980)
Notions of intelligence emerge as early as first grade.
Younger children: tended to emphasise interpersonal skills
e.g., being nice, helpful, polite
Older Children: emphasised academic skills
e.g., reading well, doing well in class
Developmental progression in understanding of intelligence, differs from adults
Intelligence as defined cross-culturally
Culture provides a model for thinking, acting, & feeling
Differing values -> different views of what constitutes intelligence
-Can differ in sub-cultures too
Greater emphasis on {{{social}}} aspects of intelligence in both African and Asian cultures compared to Western
Adults in Zambia (Serpell, 1974, 1996) Social responsibilities, cooperativeness & obedience Intelligent children expected to be respectful to adults
Taiwanese Chinese conceptions of intelligence (Yang & Steinberg, 1997)
(i) general cognitive factor
(ii) interpersonal intelligence
(iii) intrapersonal intelligence
(iii) intellectual self-assertion (knowing when to show you are smart)
(iv) intellectual self-effacement (knowing when to not show you are smart)
Summary of Lay Theories
Lay or everyday theories of intelligence reflect personal definitions and assumptions about IQ:
Structure
Underlying mechanisms
Developmental processes
That are affected by:
Age of person
Background
Culture
And that differ from expert theories
Constructed by
psychologists, empirically- tested and/or derived
Intelligence as defined by the experts:
Galton (
1883): more intelligent = higher sensory abilities
Thus, advocated that tests of visual acuity or hearing ability are measurements of intelligence.
Galton developed many sensorimotor and perception-related tests by which he attempted to measure his definition of intelligence.
Intelligence as defined by the experts
Binet
did not define explicitly, but described various components of intelligence, including reasoning, judgment, memory, and abstraction.
Criticised Galton’s approach & called for more complex measurements
Viewed intelligence as inseparable abilities that required complex measurements to determine.
Intelligence as defined by the experts
Wechsler (1958) conceptualised intelligence as,
“the aggregate…capacity of the individual to act purposefully, to think rationally, and to deal effectively with his environment. It [is] composed of elements or abilities which…are qualitatively differentiable” (p. 7).
Advocated measuring several “qualitatively differentiable” abilities, which were verbal- or performance-based in nature.
Intelligence as defined by the experts
Piaget
focused his research on the development of cognitive abilities in children (i.e., how children think, and how they understand themselves and the world around them).
Defined intelligence as an evolving biological adaptation to the outside world;
As a consequence of interaction with the environment, psychological structures become reorganised.
General Definition of Intelligence
Intelligence: a multifaceted capacity that includes the abilities to:
- Acquire and apply knowledge
- Reason logically, plan effectively, and infer perceptively
- Grasp and visualise concepts
- Find the right words and thoughts with facility
- Cope with and adjust to novel situations
General definition of interactionalism
complex concept by which heredity & environment are presumed to interact and influence the development of intelligence
Major theme in theories of Binet, Wechler, & Piaget.
Factor-analytic theories of intelligence do…..what?
focus on identifying the ability or groups of abilities deemed to constitute intelligence.
need to know the structure of intelligence in order to:
Need knowledge of structure of intelligence to:
devise appropriate measures
evaluate measures
ensure assessment covers construct sufficiently
Factor Analysis
what is it?
Family of statistical techniques used to examine correlations among variables (items or tests)
-Used in theory validation
-Used in test construction and validation
Invented by Pearson in 1901
Further developed by Spearman in 1904
Applied by Spearman to cognitive abilities in 1927
Factor Analysis part 2
simple vs complex
what does it do?
Simple theory is generally better than a complicated theory
Factor analysis helps us discover the smallest number of psychological dimensions (or factors) that can account for various behaviours, symptoms, and test scores we observe.
2 Two main types
of factor analysis
Exploratory Factor Analysis (EFA)
Confirmatory Factor Analysis (CFA)
Exploratory Factor Analysis
Identifies or finds underlying dimensions/ clusters/ factors/ components in data, used for:
- theory development (e.g., structure of personality)
- test construction/ validation
Types of Psychometric Questions
As related to EFA?
Personality
How many personality factors are there?
2, 3, 5, 16?
e.g., the “Big 5”? (Neuroticism, Extraversion, Agreeableness, Openness, Conscientiousness)
Intelligence
Does intelligence consist of separate factors:
e.g., Verbal, Performance, Interpersonal, etc?
..or is it one global factor (“g”)?
…is it hierarchically structured?
Exploratory Factor Analysis
what does it do
Summarises large amount of items or information into fewer scores
Based on correlations among items
Identifies clusters of highly correlated items
Common variance among items might reflect central underlying theme
Also identifies items that are not captured by these clusters
And items that are complex- fall equally into two or more different clusters
Exploratory Factor Analysis
within factor correlations
factors represent?
Within-factor correlations will/should be higher than cross-factor correlations
Each factor represents items with “shared variance”
Each factor represents single relatively homogeneous underlying dimension
Data Reduction with Factor Analysis
E.g., Questionnaire about child behaviour with hundreds of items
Instructions: On a scale of 1-5, compared to other children, my child… gets into fights frequently at school is defiant to adults is very impulsive has stomach aches frequently is anxious about many things appears sad much of the time
example about child behaviour
slide 32 & 33
Look at the correlations between scales, which ones are correlated with each other?
How many factors does this suggest?
Factor Loadings
Need to label factors meaningfully
Thoughts?
Factors correlate .46 -> higher order overall factor
Correlations between Factors
Factors produced from items are called 1st order factors
A correlation matrix of factor scores can also be factor analysed to examine presence of 2nd order factors
Can also examine for 3rd order factor (global factor- e.g., overall ‘g’ in IQ)
Rare to go beyond that
Factor Structure Example with 1st, 2nd, and 3rd Order Factors (BASC-II)
hyperactivity««
Note
on neatness
Neatness is rare
Especially in EFA in test construction
May be left with items that don’t fit on a factor or that fit on multiple
Naming/interpreting factors can be hard!
Confirmatory Factor Analysis
Confirmation Factor Analysis (CFA)
-Conducted after EFA with a different sample during test construction
-Evidence of validity (i.e.,
structural or factorial validity)
–Tests hypotheses about underlying structure of tests/items
—-i.e., tests if specified relationships / correlations exist in data
Confirmatory Factor Analysis part 2(whats it do)
Confirms structure suggested by EFA (or theory or literature)
E.g., EFA asks what is the underlying structure of personality items whereas CFA asks whether a 3-, 5-, or 6-factor structure of personality fits best
Model-testing function
Factor Analysis and the Structure of Intelligence
(historical)/g
Factor analysis played a powerful role in shaping 20th Century developments in understanding of the structure of intelligence
Spearman – g factor (1903 +)
Based on extensive study of correlations between tests of intellectual and sensory ability
Proposed that intelligence consisted of two kinds of factors – general factor (g) and numerous specific factors (s1, s2, s3 etc).
Factor Analysis and the Structure of Intelligence
part 2
Spearman argued examinee’s performance on any test was determined mainly by two influences (g and s)
Most interested in g and sought to study it
likened to ‘energy’ or ‘power’ – common in the whole brain
Proposed that some tests were heavily loaded with g factor
Although largely dismissed – idea of a general factor is still very much alive (dismissed?? wtf - listen to this part of lecture!)
Two-Factor Theory of Intelligence (Spearman, 1927)
g represents the portion of variance that all intelligence tests have in common and the remaining portions of the variance being accounted for either by specific components (s) , or by error components (e) of this general factor.
Multifactor Theories
PMA
What are the seven corroborated factors?
Thurstone (1931) – Primary Mental Abilities (PMA)
Concluded that several factors (not a single g) could best explain empirical results
Proposed approximately a dozen factors
Seven frequently corroborated:
Verbal comprehension, word fluency, number (mental arithmetic), space (mental rotation), associative memory (rote memory), perceptual speed, inductive reasoning
Developed a test (PMAT) to assess each of these factors – however acknowledged the inter- relationships between subtests
Later acknowledged underlying ‘g’ factor
Vernon 1950 (multifactor theories)
Vernon (1950) – provided link between theories by Thurston and Spearman
Proposed a hierarchical group structure that included an over-arching factor (like “g”), two grouping factors (verbal/spatial abilities), and minor factors (like Thurston’s Primary Mental Factors) and specific factors (like Spearman’s “s”)
Multifactor Theories - Cattal and Horn (40s-70s+)
Again used factor analysis to study the structure of intelligence – no single factor or group of factors – Two major factors:
Fluid Intelligence: largely non-verbal and culture reduced form of mental efficiency
Related to a person’s inherent capacity to learn and problem solve
Used when a person needs to adapt to a new situation
Crystallised Intelligence: highly culturally dependent and used for tasks that require a learned for habitual response
Acquired skills and knowledge
Related to formal and informal education
Cattell’s original theory 1941 – 1965
g was “reflected” in Gf and Gc
Gf = fluid
Gc - crystalized
Horn & Cattell’s Extended Gf-Gc Theory
Extended number of 2nd tier factors
But no g
Full list broad factors included:
Ranked in order of strength of association with g
(10 factors)
Ranked in order of strength of association with g
“Gf” – fluid intelligence
“Gq” – quantitative knowledge “Gc” – crystallised intelligence “Grw” – reading and writing ability “Gsm” – short-term memory “Gv” – visual processing “Ga” – auditory processing “Glr” – long-term retrieval “Gs” – processing speed “CDS” – correct decision speed
Bringing g back
John Carrol
John Carroll (1916- 2003) Carroll reviewed all of the factor analytic research since Spearman
Re-analysed > 460 data sets (1500 references!)
Revised Cattell and Horn’s model to hierarchical 3-strata model
Main difference is inclusion of g as over-arching factor
Three-Stratum Theory of Cognitive Abilities (Carroll, 1997)
The first stratum is g, followed by a level constituted of eight abilities and processes (e.g., Gf, Gc, general memory and learning (Y), and processing speed (T)), followed by a stratum containing varying “level factors” and “speed factors.”
CHC Theory of Intelligence
(Kevin McGrew
Kevin McGrew (1997; Schneider & McGrew, 2012) integrated Cattell-Horn’s Gf-Gc Model and Carroll’s 3-strata model to produce the CHC Theory of Intelligence
The CHC Model integrates
the Cattell-Horn and Carroll models, featuring ten “broad-stratum” abilities and over seventy “narrow-stratum” abilities.
–Each broad-stratum ability subsumes two or more narrow-stratum abilities.
chc theory part 2
added what factors, clustered what associated abilities?
Added Stratum II Broad Factors ‘Gkn’—domain specific knowledge ‘Gps’—psychomotor speed ‘Go’—olfactory abilities ‘Gh’—tactile abilities ‘Gk’—kinaesthetic abilities ‘Gp’—psychomotor abilities
Clustered associated abilities
- Domain-independent general abilities
- Acquired knowledge systems
- -Sensory-motor linked abilities
- 74 Stratum I Specific abilities
CHC Model
Part 3
what is used for, reffered to as?
CHC model is now accepted as the most-empirically supported working taxonomy of human cognitive abilities
Used to guide research into intelligence
Used as the basis for test development and assessment practice
Referred to as, “periodic table of human cognitive ability”
