Lions, Foxes and St. Bernards

Bi-polar psychological constructs, such as Jung's introversion- extraversion, can be expressed as measures on a unidimensional variable of "differential amount of". Multi-polar constructs are more of a challenge to report in an easily understood way.

According to Porter's (1973) Relationship Awareness Theory, there are three motivational patterns exhibited by team members. The assertive- directing pattern, symbolized by a lion, is exhibited by individuals who seek gratification through leading others. These individuals organize team resources, and expect to benefit from team success. The analytic-autonomizing pattern, symbolized by a fox, works towards logical order and meaning in action. These individuals focus on data collection and analysis. They expect to be paid for their work. The altruistic-nurturing pattern, symbolized by a St. Bernard dog, helps others with little interest in their own material advancement. When participating in a team, every team member exhibits more or less of all three patterns, but how much?

To investigate Porter's theory, I constructed a 15 item self- administered "team member inventory". Each item has a stem and three options, one for each pattern. For instance, one item is:

If someone were to describe what role you tend to play in a group, would it be
a) fact-finding analyzer?
b) supportive hard-worker?
c) driven decision-maker?

The respondent chooses one option. The key for this item (unknown to the respondent) is a=(F)ox, b=St. (B)ernard, c=(L)ion. Each item is answered twice: once for a safe and secure team environment, and again for a dangerous, risky environment. The resulting data set consists of 30 data points per respondent, with each response coded L, F or B.

In order to understand what my respondents are telling me about themselves, I decompose the tri-polar theory into three bi-polar constructs. Each pair of patterns (animals) represents opposite ends of a latent variable on which each respondent can be located. Thus, to locate respondents on the Lion-Fox construct, any response coded "L" indicates more lion-ness. Any response coded "F" indicates more fox-ness, i.e., less lion-ness, and any response coded "B" is treated as missing data. Rasch analysis of the three bi-polar constructs yields three measures for each respondent: a Lion/Fox measure, a Fox/St. Bernard measure, and a St. Bernard/Lion measure.

A useful communication device for these three measures is an equilateral triangle. Each bipolar variable is rescaled and centered on one of the sides. In my examples, the vertices are 8 logits apart. The three Figures illustrate three actual profiles. Figure 1 depicts a typical respondent whose moderate behavior is somewhat lion-like. The measures are Fox/St.Bernard, 0.24 logits; Lion/Fox, 0.10; and St.Bernard/Lion, -0.60. To place these measures in the triangular diagram, each measure is located on its side, and a line perpendicular to the side is drawn from that point. The intersection of the lines forms a smaller equilateral triangle. The center of this triangle summarizes the respondent's tri-polar behavior.

Moderate Lion

Figure 2 shows a conspicuously St. Bernard-like profile. Figure 3 shows someone whose placement, while somewhat indefinite, avoids Lion- like behavior.

There is more information in the responses, but these Figures provide a quick initial summary and classification, informative to the team manager.

Solid St. Bernard

Foxy St. Bernard?

Lions, foxes and St. Bernards. Williams, Evelyn. … Rasch Measurement Transactions, 1994, 8:2 p.351

Rasch Publications
Rasch Measurement Transactions (free, online) Rasch Measurement research papers (free, online) Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch Applying the Rasch Model 3rd. Ed., Bond & Fox Best Test Design, Wright & Stone
Rating Scale Analysis, Wright & Masters Introduction to Rasch Measurement, E. Smith & R. Smith Introduction to Many-Facet Rasch Measurement, Thomas Eckes Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, George Engelhard, Jr. Statistical Analyses for Language Testers, Rita Green
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar Journal of Applied Measurement Rasch models for measurement, David Andrich Constructing Measures, Mark Wilson Rasch Analysis in the Human Sciences, Boone, Stave, Yale
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