Leadership Ratings with the Island Commission

Submitted by Stephen J. Guastello and Gonzalo Zaror

The data file consists of ratings of leadership behavior that were
collected in the course of 15 games of ISLAND COMMISSION. Each
game was played with 8 players.There were 120 persons rated altogether.
The participants were business school students in Chile. 

All players within a game indicated who in their group acted most 
like the leader and who acted second-most like the leader. Two points 
were scored for most like the leader, one point for second-most, and 
zero points otherwise. Ratings of each player given by each player 
were summed, so that the final score range was 0 to 16. 

For the first analysis, it was necessary to obtain a frequency
distribution of the scores, along with the standard deviation.
The SPSS file below is the control file for producing the nonlinear
regression of the scores against the swallowtail probability
density function. The RECODE statement converts raw scores into
cumlative frequencies. COMPUTE Z translates raw scores from raw
values into Z with respect to location and scale. 

The nonlinear regression analysis was run with and without the z**4 
term. Inasmuch as z**4 is an additional correction for location it
was possible that it could be unnecessary for producing a well-defined
model with statistically significant regression weights. Indeed that
was the case. 

For further description of the underlying theory of leadership,
swallowtail probability density function, and details of the experiment,
see:

Guastello, S. J. (1998). Self-organization in leadership emergence.
Nonlinear Dynamics, Psychology, and Life Sciences, 2, 301-315.

Guastello, S. J. (2002). Managing emergent phenomena: Applications of
nonlinear dynamics to work organizations. Mahwah, NJ: Lawrence
Erlbaum Associates.

Zaror, G., & Guastello, S. J. (2000). Self-organization and leadership
emergence: A cross-cultural replication. Nonlinear Dynamics, Psychology,
and Life Sciences, 4, 113-119.



title 'island data' Chilean sample
set width=80
data list file='zarorisl.dat' records=1
 /rating 1-2 
*frequencies variables=rating 
*descriptives variables=rating 
 /statistics=all
recode rating (0 = .500) (1 = .617) (2 = .683) (3 = .725)
 (4 = .750) (5 = .775) (6 = .800) (7 = .825) (8 = .842)
 (9 = .842) (10 = .883) (11 = .933) (12 = .950) (13 = .967)
 (14 = .999) (15 = .999) (16 = .999) into pctrat
compute z = (rating - 2.908)/431.7
model program  a= -0.2 b=0.2 c=0.2 d=0.2 e=0.2
compute pred = exp(a*(z**5) + b*(z**4) + c*(z**3) + d*(z**2) + e*z)
nlr pctrat with z
model program  a= -0.2 x=0.2 c=0.2 d=0.2 e=0.2
compute pred = x*(exp(a*(z**5) + c*(z**3) + d*(z**2) + e*z))
nlr pctrat with z