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.

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.

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

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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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