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20/02/2015 1
THE EVOLUTION OF PSYCHOMETRICS
Willem Heiser
Institute of Psychology
& Mathematical Institute
Leiden University
February 2015
1. Historical Dilemmas about the Role of Chance & Variability
2. Driving Forces in the Evolution of the Statistical Sciences
3. Two Branches of Psychometrics, or Three?
4. Two Dutch Pioneers: Gerard Heymans & John van de Geer
5. Four Genealogical Trees in Dutch/Flemish Psychometrics
20/02/2015 2
Fortuna versus Sapientia
Symbolize two opposite ways
to knowledge:
Fortuna consults the
Wheel of Fortune, sitting on a
Sphere Uncertainty
Sapientia consults the
Speculum, sitting on a
Cube Certainty
(source: Petrarca, 1524)
20/02/2015 3
Prudentia (Wisdom Applied to Practice – Bocchi 1574)
The Renaissance starts imagining that
chance processes are not messages from
God, but man must decide for himself by
discerning systematic & incidental causes
On the stormy sea of life, or changing
circumstances, Prudentia is carefully
weighting and balancing the cube
of wisdom and the sphere of chance.
Second symbol of chance is Occasio:
Opportunity instead of
Fate
20/02/2015 4
Practical Solutions for Measurement Problems
Measurement is counting of units, but how to obtain a measurement
unit that is stable and also
hard to dismiss?
Legal definition of “foot”
as the average of 16
randomly chosen
individual feet.
Again and again it turns out
that measurement problems
can be solved statistically.
20/02/2015 5
Empirical Footsteps Always Precede Theoretical Footsteps
1657 Huygens: Expected value
1710 Arbuthnott: Significance test
Mortality registers: Graunt 1662
1e Control group: Lind 1747 (scurvey)
1669 Huygens: Plot of survival
probability
Triangulation Holland: Snellius 1617
(angle measurements) 1628 Galilei: First error theory
Gambles: Pascal & Fermat 1654
1733 de Moivre: Normal distribu- tion as an approximation
1774-1814 Laplace en Gauss: Foundation of theory of statistics
1764 Bayes: Inductive inference
Political anatomy: Petty 1672
(Ireland)
Triangulation of the Pacific:
Captain Cook 1770
Demography: Süssmilch 1741
20/02/2015 6
John Graunt’s Mortality Registers (1662)
After an outbreak of the plague in 1538, the city of London had begun
to keep track of mortality figures & cause of death on a regular basis.
20/02/2015 7
Analysis of Graunt’s Mortality Registers
by Lodewijk & Christiaan Huygens (1669)
Lodewijk had extracted a new table from Graunt’s data containing the
expected number of years being still alive for 10 age groups.
Survival
Probability
Age
AC = Median
remaining years
alive for a
20-year old
Christiaan came up with this curve:
20/02/2015 8
Evolutionary Forces Drive Development of Science
Evolution is characterized by:
1. Phylogenetic trees (Tree-of-Life Hypothesis)
2. Natural selection (Survival of the Fittest)
Darwin’s vision of the
Tree-of-Life:
What are the genes of
scientific knowledge?
There are two types of
evolutionary processes
20/02/2015 9
Statistical Sciences as a Multidisciplinary Drainage Basin
We saw that applications very often precede theoretical justifications.
Solutions to new problems in different disciplines originate upstream
and can become mainstream.
So I think:
Epidemiology
Demography
Geodesy
Psychometrics Mainstream
Statistics
20/02/2015 10
Similar Problems Similar Solutions
In biological evolution, unrelated species can obtain the same
biological function or feature by selective pressure of the environment:
this is called convergent evolution. Best solutions survive.
Statistics also shows this phenomenon
20/02/2015 11
19th Century: Birth of Moral and Mental Measurement
History of social measurement starts from the empiricist’s idea that
averaging parallels the way the mind forms generic concepts.
Concept of average man: Adolphe Quetelet, Treatise on Man and
the Development of his Faculties (1842);
Concept of correlation: Francis Galton, Hereditary Genius: An
Inquiry into its Laws and Consequences (1869);
Concept of systematic variance as distinct from error variance:
Karl Pearson, moment of inertia and standard deviation.
History of mental measurement shows development along
two relatively independent lines (see Guilford, 1936, Chap. 1):
1. Psychophysical tradition (experimental psychology);
2. Mental-test tradition (evolutionary biology)
20/02/2015 12
Joint Display of the Two Lines, the First Hundred Years
1833: first large scale testing in the
UK, to send soldiers to India
Probability as unit of measurement,
Method right/wrong cases: Fechner 1860
Just noticeable difference: Weber 1846
Estimation of Psychophysical function:
Müller 1878 1st Psychological Laboratory: Wundt 1879
Estimation for Constant method: Urban 1909
Ph.D. of Wundt: Cattell 1886
Law of comparative judgment:
Thurstone 1927 1934 Thurstone: Vectors of the mind
1844 Verhulst: derives the logistic function
1869 Galton: Hereditary Genius
1879 Galton:”Psychometric exp.” in Brain
1888 Edgeworth: Statistics of examinations
1910 Spearman: test length & reliability
1925 Thurstone: Method of scaling P&E tests
1905 Binet: 1st IQ test
1889 Cattell: 1st US professor of Psychology
1904 Spearman: Factor analysis
Psychophysics Mental Testing
Personal equation: Bessel, Gauss 1823
20/02/2015 13
Post-World War-II Consolidation (?) of Psychometrics
Logistic choice model: Luce 1959
Scaling without a unit of measurement:
Coombs 1950
Coombs 1950
Ordinal Analysis of Proximities: Shepard 1962 Mathematical Psychology leaves
the Psychometric Society 1964
Multidimensional Scaling: Kruskal 1964
Judgment & Choice: Bock & Jones 1968
INDSCAL: Carroll & Chang 1970 1970 Jöreskog: Analysis of Covariance Struct
1941 Guttman: optimal scaling of
multivariate categorical data
1950 Lazarsfeld: Latent class analysis
1953 Lord: Relation of test score to the trait…
1960 Rasch: One-parameter logistic model
1966 Bock: Estimating multinomial resp…
1968 Lord & Novick: ST Mental Test Scores
1969 Samejima: Graded response model
1957 Birnbaum: Two-parameter logistic model
Psycho(physics) Mental Testing
Quantifying paired comparisons
and rank order: Guttman 1946
Multidimensional Scaling: Torgerson 1952
20/02/2015 14
Two Branches of Psychometrics. Or Three?
Jones & Thissen (2007) give three branches:
20/02/2015 15
Second Part:
Psychometrics in the Low Countries
20/02/2015 16
Pioneers in the Netherlands
Gerard Heymans (1857-1930)
PhD from Leiden (1880) and Freiburg
(1881)
1890: professor History of Philosophy,
Logic, Metaphysics and Psychology
1892: first Lab of experimental psycho-
logy in the Netherlands (at home)
1905: Einführung in die Metaphysik auf
Grundlage der Erfahrung
1909: as rector of Groningen University,
announces “Century of Psychology”
20/02/2015 17
Embedding Types in Multivariate Space
He not only founded an experimental laboratory with Wundt-type
apparatus, but also studied individual differences with questionnaires.
Type emotional active secondary
nervous + − −
sentimental + − +
*sanguine − + −
*phlegmatic − + +
*choleric + + −
passionate + + +
amorphous − − −
apathic − − +
*Humorous types (Hippocrates, Galen)
melancholic is missing
The Heymans cube shows that you can express types as extreme
points in a space of fewer dimensions. It is the way most
psychologists still conceive clusters (in relation to latent variables).
20/02/2015 18
Multidimensional Contingency Table Analysis
Heymans & Wiersma (1906-1909) tried to validate the cube and to
determine heritability on a sample of 437 families from which they
obtained 2415 character descriptions, as assessed by family doctors all
over the Netherlands. One example, of impulsivity:
20/02/2015 19
Searching for g
Inspired by Spearman (1904), Heymans & Brugmans (1914) were
interested in “an experimental determination of the degree to which
different simple intellectual functions cooperate”.
Note the ”positive manifold”, indication of g. Heymans’ work is
quoted several times very favorably in Spearman’s monumental work
“The Abilities of Man: Their Nature and Measurement” (1927).
20/02/2015 20
Why Did I Choose Heymans and not A.D. de Groot as
Pioneer of Psychometrics in the Netherlands?
As mentioned by Van der Heijden & Sijtsma (1996), A.D. de Groot
started his career as head of the psychology section at Philips company
In 1927, when Heymans retired, his chair was split into two chairs:
(1) Philosophy: Leo Polak (freethinker & humanist)
(2) Psychology: Henri Brugmans (already lecturer in Educ. Psych.)
Brugmans (PhD student of H.) was founder of the first Personnel
Assessment Institute of the Netherlands (Dr. Bos Foundation,
Groningen, 1920), together with Jacob Luning Prak (also PhD of H.).
Luning Prak went in 1924 to Philips company, and wrote a book
together with A.D. de Groot, who became professor in applied
psychology in 1950:
De moderne Onderneming en haar Personeel: Een Inleiding tot de
Psychotechniek. Amsterdam: Kosmos, 1947.
20/02/2015 21
John van de Geer (1926-2008)
Together with Jos Jaspars, wrote first systematic Annual Review
paper about the emerging cognitive revolution (in 1966)
Annual Review of Psychology, 17 (1966), 145-176
20/02/2015 22
Career
1947: started study Psychology in Leiden (professor Chorus 1st chair)
1949: teaching assistant in statistics, learning, perception & thinking
1957: Ph.D. “A Psychological Study of Problem Solving”
1963: Chair in experimental psychology and statistics (Leiden)
1970: Chair in data theory & mathematical psychology (Leiden)
1987: retired
Some Additional Affiliations:
• Institute for Perception TNO Soesterberg
(1960-1970)
• Shelter Home for Female Juveniles
(1953-1963)
• Center for Advanced Study in the
Behavioral Sciences, Stanford (1968)
20/02/2015 23
Work
Apart form a wide range of papers in many areas of psychology,
John van de Geer wrote four books:
De Mening van de Psycholoog, 1961.
Inleiding in de Multivariate Analyse, 1967.
Introduction to Multivariate Analysis for the Social Sciences, 1971.
Multivariate Analysis of Categorical Data, 1993.
Also co-author of Albert Gifi, Nonlinear Multivariate Analysis, 1990.
20/02/2015 24
Van de Geer’s Ideas about Consulting and Teaching
a) Discovery goes by trial and error: the hypothetical-deductive
process that scientists use to learn about nature is also valid in
applied psychology, psychological counseling and consultation;
b) Learning must be contextualized: instruction is more efficient if
interactive and personalized—Van de Geer started programmed
instruction for teaching statistics to psychology students;
c) Formalization helps: often many names exist for the same
concepts and methods switch to the language of mathematics;
d) Cross-fertilization: what we have learned to use in one context
(e.g., psychology) should have good application in other contexts
(e.g., political science). Same for biology psychology, …
20/02/2015 25
Evolution of Psychometrics in the Netherlands
We are now going to show the academic ancestry of current key
psychometricians in IOPS, by looking at their scientific family trees.
1. Sociocultural evolution (Dissertation supervision relations)
2. Natural selection (Survival of the Fittest: only full professors)
Darwin’s vision of the
Tree-of-Life:
Therefore, we need to look at
pedigrees of PhDs and their
supervisors.
20/02/2015 26
Indication of Impact: Genealogical Trees of PhD students
One way to see structure in a group of scientists, and to get an idea of
the evolution of an area of research, is to build genealogical trees, in
which nodes are connected between PhDs and supervisors
(intellectual gene transfer), starting from a the root node (ancestor).
Trees of IOPS psychometricians and some sociometricians in the
nodes will only show descendants who have become professor
themselves, because they are the only nodes that can produce further
progeny (survival of the fittest).
The Mathematics Genealogy Project is a web-based database for the
academic genealogy of mathematicians with ancestors & descendants
(see http://www.genealogy.ams.org/). It contains records of 158.844
individuals. Some IOPS members are in the database, but not all.
It turns out almost all IOPS professors are grouped in 4 trees.
20/02/2015 27
Wilhelm Wundt Tree: Leuven/Leiden/Tilburg/Groningen
Wundt 1856
Külpe 1887
Michotte 1900
Nuttin 1941
Roels 1913
I. Molenaar 1970
Oldendorff 1940
Rutten 1929
Chorus 1940
Van de Geer 1957 Claeys
De Boeck
Van Mechelen Tuerlinckx
Roskam 1968
Van der Kamp 74 De Leeuw 1973 Ten Berge 1977
v.d. Heijden 1987
Kroonenberg 1983
Meulman 1986
Heiser 1981
Kiers 1989
Mooijaart 1978
Groenen 1993 Van Buuren 1990
Stouthard 1965
Hagenaars 1985
Vermunt 1996 Knops
Delbeke
Verhelst
Eggen
20/02/2015 28
Johannes Müller Tree: Amsterdam (psychology)
Müller 1873
Révész 1905
de Groot 1946
E. de Leeuw 1992
van der Linden 1980
Sanders 1992
Oort 1996 Borsboom 2003
Van Naerssen 1962
Mellenbergh 1971
Hox 1986 Kelderman 1987
Glas 1989
20/02/2015 29
Van der Waerden Tree: Amsterdam/Groningen (statistics)
+ Tree 4 (longitudinal data) Calvijn 1529
Van der Waerden 1926
Hemelrijk 1950
Van Dantzig 1931
Jan Tinbergen 1929
I. Molenaar 1970 Mokken 1970
Stokman 1977 Saris 1979
Dalmulder 1936
Ehrenfest 1904
Ten Berge 1977
Sijtsma 1988
Hoijtink 1990 Meijer 1994
Kiers 1989
Stobberingh 1972
P. Molenaar 1981
Dolan 1992
V.d. Maas 1993
20/02/2015 30
Conclusions
1. Psychometrics has had two independent lines of development:
psychophysics & mental testing.
2. Shared elements of these two subfields are: binary data and the
cumulative normal or logistic, probability as a unit of measure-
ment, pair-wise and other specific designs of data collection,
such as ranking and rating, often with within-subject factors.
3. Psychometrics has produced lots of results that are now part of the
mainstream of social & bio-statistics, or even statistics in general.
4. Pioneers of psychometrics tend to be generalists: they have often
contributed new results and/or synthetic knowledge in both
subfields. But the field could not move forward without specialists.
5. All key psychometricians in the Netherlands & Belgium are
members of a small number of families. They fit almost perfectly
into one of only 4 pedigrees.