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 X 1 numerical obs X 2 numerical obs X 3 numerical obs X 4 numerical obs the thing to be measured test score global index

“Measurement” X 1 numerical obs X 2 numerical obs X 3 numerical obs X 4 numerical obs assignment rule e.g., sum, first component score the thing to be measured

Heavy vs light on meaning

Alternative X 1 numerical obs X 2 numerical obs X 3 numerical obs X 4 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” X 1 numerical obs X 2 numerical obs X 3 numerical obs X 4 numerical obs assignment rule e.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 theory data for the theory Why 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

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 persons guilt & shame define a dimension together with fear and anger Covariation over cultures guilt 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 – semantic Individual differences Situational differences Time differences Probability 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 – semantic Individual differences Situational differences Time differences Probability 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(X pi =1)/(1-P(X pi =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?