Reading #1: The Nomological Network (https://conjointly.com/kb/nomological-network/)

"The basic rule for adding a new construct or relation to a theory is
that it must generate laws (nomologicals) confirmed by observation or
reduce the number of nomologicals required to predict some
observables."

This is Ockham's Razor, and my thesis adviser's statement: The day you
discover that what was formerly thought to be two things are actually
one, is a great day in science.  I have had some of those great days,
especially in my Theory of Humor (TomVeatch.com/humor) and Bliss
Theory (https://tomveatch.com/bliss/MathPsych.php).

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Reading #2: Multitrait-Multimethod Matrix (https://conjointly.com/kb/multitrait-multimethod-matrix/)

Convergent validity: multiple measures of the same thing should converge.
Discriminant validity: measures of different stuff should be uncorrelated, discriminable by the different measures.

R = COV(X,Y)/SD(X)*SD(Y): what part of the variation is covariation.

MTMA shows R values in a matrix for a number of measures ostensibly
for the same underlying concept measured in different ways and
different underlying concepts.

The matrix is symmetric since R(a,b) = R(b,a) (true?)

(A) Multiple measures of the same trait ought to be correlated strongly.
(B) Measures of one trait when applied to objects of a different trait ought to have no correlation.
(C) Measures of different traits ought to be uncorrelated.

Validity diagonals show correlations (A).
Diagonal blocks off diagonals show (B).
Off-diagonal blocks off diagonals show (C).

In single-method MTMM, skipping the Methods factor, we have ... a problem.

The Modified MTMM "does not explicitly include a methods factor as a
true MTMM would", yet it does indeed show 2 or 3 measurements ie
methods for each of two traits.

So I think the author is confused, as if reducing 3 to 2 traits makes
a conceptual difference, which it does not.  They show a (2x2) 4 block
table with symmetric above-diagonal values instead of (3x3) 9 block
table leaving the implied symmetric above diagonal values empty.  But
the proofs are the same.  Only that reliability on the main diagonal
is not used, the self-correlation is always 1.<P>

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Reading #3: Pattern Matching (https://conjointly.com/kb/construct-validity-pattern-matching/)

	"The pattern match is accomplished by a test of significance
	such as the t-test or ANOVA."

This considers the basic question, is there a real
thing/idea/abstraction/category here? (i.e., in and out of the
category are two groups, and if it is a real thing then those in
should differ in some respect from those out).

Fisher Exact Test also shows whether 2 nominal groups differ in 2
nomimal features, nearly the same idea.

This is also the Structuralist Method: which may relate underlying
feature vs observed features (at "emic" vs "etic" levels).

This shows the methodological family-relationship between
Psychology and Linguistics..

But "pattern match" is a much broader concept than a 2x2 table for
ANOVA or Fisher or the Structuralist Method, or multivariate logistic
regression, etc.

Question: What is the pattern that is matched if we show a moderating
variable has an influence on a (list of many) dependent-to-independent
variable relationship(s)?

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Reading #4: Another take on the topic: “The Validation Crisis in Psychology”
(https://replicationindex.com/category/nomological-networks/)

    Contrary to the current practices, Cronbach and Meehl assumed that
    most users of measures would be interested in a “construct
    validity coefficient.”

My question is, Could that be the same as the fraction of all the
measures that is predicted from a single factor?  (E.g., in IQ, g,
where the weighting of an unobserveable general factor in a
multivariate regression in which IQ measures for different types of
intelligence are modelled as g[p] + t[p] (p for person, t for a Type
of intelligence).  After multiple regression g may in general account
for zero or more of the total variance, if >0 would that be a
construct validity coefficient, since it is measured to that degree by
all the measures?

Finally, wow:

    "maybe the 2030s may produce the first replicable studies with
    valid measures"

Everyone likes to be a curmudgeon.