Symposium
PSYCHOMETRIC ISSUES
IN THE DEVELOPMENT AND USE OF SPORT PSYCHOLOGY INVENTORIES
CHAIR: Dr. Robert W. SCHUTZ
LATENT VARIABLES:
THE IDENTIFICATION OF THEORETICAL
CONCEPTS IN SPORT PSYCHOLOGY
Petr BLAHUŠ
Charles University, Prague
- Concept formation
in sport psychology
- Is theory building in this
science in principle "worse"
than in other sciences ?
- Can the statistical models with
latent variables solve the
correspondence problem ?
THEORETICAL AND EMPIRICAL
ATTRIBUTES:
CONCEPTS AND INDICATORS
Schutz & Gessaroli 1992:
"theory driven" inventories and
empirical measures
Explaining theory :
theoretical concepts, "constructs"
abstract and generic attributes
intermediating the scientific
explanation
For example:
- attitudes to physical education,
- psychomotor abilities,
- sport performance anxiety traits
...
Identification of concepts:
"concept formation"
possibly via their measurement
Theoretical vs. empirical level:
the "correspondence problem"
E.g.: battery of psychomotor tests
vs.
level of coordination ability
rules of correspondence
Fig. 1
ATTRIBUTES -
- RESEARCH VARIABLES -
- RANDOM VARIABLES
SEMANTIC vs. SYNTACTIC level:
"measurement problem"
or
modeling problem
Fundamental assumption of
statistical modeling:
DATA have to be identified with
VALUES of random variable.
-----------------------------------------------------------------
Empirical states or
attribute alternatives
Research
variable categories, data
Random
variable values
-----------------------------------------------------------------
MEASUREMENT
of
MANIFEST and LATENT VARIABLES
DIRECT measurement:
empirical attributes - manifest variables
manifest values - "operational representations"
INDIRECT ASSOCIATIVE measurement:
theoretical concepts - latent (random) variables
latent values -
- "generated-by-model
representations"
Formalized rules of correspondence:
mathematical axioms and derivations
ASSOCIATIVE MEASUREMENT in physics:
- deterministic mathematical
functions
(e.g. measurement of temperature)
CONCEPT MEASUREMENT in psychology:
- statistical regression modeling
function
s.-c. "measurement model"
(Assumed: that the axioms of
the model hold in
the real world)
AND
- impossibility to replicate
- "unobservability" of the latent
- mixture of unreliability with
specificity
MATHEMATICAL FORMULAE OF A MODEL
AS CORRESPONDENCE RULES
Mathematical formulae - formalized correspondence rules
Two basic mathematical formulae:
(i) model equation and its axioms
(ii) axiom of local independence
Additional mathematical conditions
- measurement scale assumptions
- statistical assumptions
- identifiability of parameters
...
SCIENTIFIC NATURALISM
AND
CONCEPT MEASUREMENT
Schwager, 1991:
"naturalism" - methodological unity
of natural and social sciences
Similar problem in physics as in
psychology temperature as a latent variable:
- latent variable model
- linear common factor model
- true score model
- parallel tests model
- classical gaussian
measurement-error model
No specificity of indicators:
different indicators = replications
Estimate of true temperature:
averaging the three values of
mercury, alcohol, and bimetallic
thermometers
... a consequence:
measurement "by fiat"
or "by convention" in psychology
and
the associative measurement
in physics
are just special cases of the
WEAK ASSOCIATIVE MEASUREMENT
where
(i) the associating relationship
is statistical
(ii) indicators contain
specific components
(iii) its results exhibit
lower stability
Some aspects of the
STABILITY OF CONCEPTS:
Longitudinal stability
Stability, specificity, and
generalizability
Stability over samples
Cross-culture stability,
transferability
Discriminant vs. convergent
validity
Stability of a model
CONCLUSIONS
A paradigm of generalized concept
measurement has been defined, namely the WEAK ASSOCIATIVE
MEASUREMENT, following the intentions of
unifying conception in natural and
social sciences.
Two fundamental principles are to
be theory-laden prior the modeling:
- form of the modeling - measurement
function
- pattern of conditional structure
Too, some additional conditions and
different aspects of stability of
the concepts and the models have to
be considered.
Latent variable modeling is fully
recognizable methodological device
for concept formation in behavioral
sciences including sport psychology.