Seven possibly controversial but hopefully useful rules

Paul De Boeck

K.U.Leuven

Examples

• Political openness and economic openness

• Life satisfaction and cost of living

• Research performance and innovation intensity

• Socioeconomic status and intolerance

Multi-level governance structure

Link concept-operationalisation

Participation

Competition

Transparance

Accountability

Rule of law

Interfaces

Political openness

various aspects

combine subindicies

Implicit theory

X1 numerical obs

X2 numerical obs

X3 numerical obs

X4 numerical obs

the thing to be measured

test scoreglobal index

“Measurement”

X1 numerical obs

X2 numerical obs

X3 numerical obs

X4 numerical obsassignment rulee.g., sum, first component score

the thing to be measured

• Heavy vs light on meaning

Alternative

X1 numerical obs

X2 numerical obs

X3 numerical obs

X4 numerical obs

Can I explain?Which model can explain?

The data are not meant as a measurement of something, but as to be explained.

For example, responses to inventory items,how can they be explained?Do the correlations between items stem from overlap in the information used to respond?Which information is it?Why not extract the information directly?What is the origin of the information?

When explained with a quantitative theory, then measurement is a by-product

1. Not everything is worth being measured or can be measured, often the data are more interesting than the concept

Assignment of numbers

• number finding: counts, percentages

• number asking: ratings

• number construction: apply a rule on original numbers in order to obtain a derived number

“Measurement”

X1 numerical obs

X2 numerical obs

X3 numerical obs

X4 numerical obsassignment rulee.g., sum, first component score

the thing to be measured

Measurement

• A quantity

• Increasing or decreasing doesn’t change the nature

• Addition from two sources is possible

• Splitting is possible, e.g. in halves

Questions

• Why are you interested in the link between the two concepts?Why do you want to measure?Because I want to test a theorydata for the theoryWhy aren’t you interested in the data?and try to explain the data?theory for the data

• Aren’t your numerical variables of sufficient interest to keep them as they are?

Examples

• Woodworth Personal Schedule 1917 to measure psychological adaptation

Before, lists of questions were used and one would listen to the responses

• Hirsch index: the maximum obtained by selecting a number of publications with each at least the same number of citations, e.g., 15 articles with 15 or more citations

• A strong dimension does not mean the conceptual component is important.It shows there are large individual differences in the component.

2. Psychometric criteria such as reliability and validity are not theory-independent

• The underlying theory is the simple implicit theory

• Alternatives- canalization: one behavior has developed into a the dominant one and excludes the other behaviors- behavior competition: the strongest takes it all- negative feedback: showing a behavior makes it less likely to occur next- drop-out: only occasionally it is affected by

Dynamic theories

Dynamic theories

Dynamic theories

Reliability

Repetition over

• Situations

• Behaviors

• Time

Questions

• Do you have the simple theory for your data that they are a direct and linear reflection of the concept?

• What is your theory of stability?Stability over?

3. Always reflect on which type of covariation is meant when speaking about the link between two concepts

The case of shame and guilt

• Covariation over situations guilt vs shame is one of two dimensions

• Covariation over personsguilt & shame define a dimension together with fear and anger

• Covariation over culturesguilt and shame define their own common dimension

Negative emotions

• Fear and anger are positively correlated over persons

• Fear and anger cannot co-occur because they rely on opposite action tendencies (flight and fight)

Guilt

• Experienced norm violation

• Self-reproach

• Tendency to restitute

Unidimensional in the sense of individual-differences, and they each contribute separately to the probability of feeling guilty

Questions

• Are you interested in individual differences?Are you ready to find traits?

• Components of?Meaning – semanticIndividual differencesSituational differencesTime differencesProbability of occurence

4. Measurement, reliability, validity, hypothesis testing don’t need to be sequential steps

Hypothesis:

link between concept A and B

• Step 1: construct a measurement for A, B

• Step 2: test reliability measurements

• Step 3: test validity measurements

• Step 4: test hypothesis

measurement

measurement reliability

validity measurement

measurement hypothesis testing

validity measurement reliability hypothesis testing

Questions

• Do you want to construct a test?

• ?Meaning – semanticIndividual differencesSituational differencesTime differencesProbability of occurence

5. Always do a PCA

• PCA tells you about the sources of differences between the row elements

• PCA tells you whether there is interaction and where it is

• PCA is a quite robust way to check multidimensionality

• PCA shows the main interactions in a repeated measures data matrix- unidimensional & equal loadings- unidimensional & unequal positive loadings- unidimensional bipolar- multidimensional

Questions

• Show me your PCA before we continue, especially when complex methods are going to be used, such as SEMs

6. One does not necessarily have to care about the scale of the data

• Common concern:“what is the scale level?”“are parametric statistics permissible?”

• Scale level only matters when - numbers are taken for an index of something else, how does the index relate to the “something else”?

• Transformations are interesting when a simpler and better structure can be found

Representations of relations

Example

P(Xpi=1)/(1-P(Xpi=1)) = p / i

p and i are on a ratio scale,as far as they represent odds ratios

Questions

• Suppose you forget about the scale level and you find an interesting relationship

• Do you want to generalize over other number assignment procedures?

• How meaningful are the numerical variables as they are?

7. Don’t construct indices of concepts, unless for descriptive summaries

Problems

• The global index depends on the components, and hence, on the definition.

• Often definitions are arbitrary or they are mainly semantic

• Perhaps the relationships of the index follow from the relationships of the components

Questions

• What is the definition?

• What do others say?

• Aren’t you interested in the components?