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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

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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)

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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

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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.

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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

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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.

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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:

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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

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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

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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

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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)

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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

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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

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Two Branches of Psychometrics. Or Three?

Jones & Thissen (2007) give three branches:

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Second Part:

Psychometrics in the Low Countries

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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”

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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).

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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:

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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).

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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.

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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

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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)

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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.

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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, …

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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.

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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.

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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

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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

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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

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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.