COMPUTING THE PERCEIVED ENVIRONMENTAL UNCERTAINTY
FUNCTION BY RASCH MODEL.
VANESSA YANES-ESTÉVEZ 1, JUAN RAMÓN OREJA-RODRÍGUEZ 2, PEDRO ALVAREZ 3
1
Departamento de Economía y Dirección de Empresas
Fac. Ciencias Económicas y Empresariales - Universidad de La Laguna
38071-La Laguna (Canary Islands)- SPAIN
2
Departamento de Economía y Dirección de Empresas
Fac. Ciencias Económicas y Empresariales - Universidad de La Laguna
38071-La Laguna (Canary Islands)- SPAIN
3
Departamento de Economía Aplicada
Universidad de Extremadura
Avda. de Elvas s/n. 06071-Badajoz
SPAIN
Abstract: The objective of this work is to validate empirically the Perceived Environment Uncertainty (PEU) as a
function of the dynamism and complexity using Rasch model as an instrument of measurement. Complexity and
dinamism are considered latent variables, although are defined by the same set of items, they are different dimensions.
The items have been assessed by a sample of 338 managers of firms in Canary Islands (Spain). The obtained results
show how dinamism and complexity are related. PEU can be explained and determined in terms of dinamism and
complexity by the perceptions of managers.
Key words: Rasch; uncertainty; environment; dynamism; complexity; perceptions.
1 Introduction
The fact that organizations are in continual interaction
with their environment and that, it becomes one of
their key sources of opportunities and threats,
implying that knowledge about what is happening
around is a crucial resource to stay in an advantaged
position. In this way, the environmental uncertainty is
the main used dimension to study its implication.
Applying the common features of the most
widely-used definitions of environmental uncertainty
[1, 2], we could say that perceived uncertainty is the
lack of information about external events to the
organisation experienced by the individual according
to its mental models.
In our case, considering the environment as a
source of information, uncertainty is associated with
the environmental dimensions of dynamism and
complexity [3].
According to the proposals of the literature [1,4],
the environmental dynamism is identified as the
changes in the environment that are difficult to predict,
which are those that most condition the decisions [5].
It will be defined as the frequency of changes in
environmental elements and their degree of
predictability.
On the other hand, environmental complexity
seems to be synonymous with heterogeneity, or based
on it, such as in the definition of Child [6], which is
generally accepted and similar to those of other
researchers [1,7]. Thus, it is defined as the level of
knowledge necessary to understand a variable, and the
number of elements that must be taken into account to
comprehend its complexity.
In this article we give another step by proposing a
methodology to analysis the perceived uncertainty
from dynamism and complexity without introducing
any external weights. The methodology used is a
technique based on Rasch probability [8]. The core
idea of the present analysis is defining the latent
variables environmental complexity and dynamism, in
order to measure PEU, using Rasch model as an
instrument for measurement.
2 Problem formulation
2.1 Perceived environmental uncertainty
It can be said that the Perceived Environmental
Uncertainty (PEU) shows the lack of information of
the world around a firm that perceived its deciders
while enter the decision making process.
There are some dimensions that generate this lack
of information: it could be because the items are very
difficult to understand (complexity) or/and they
change frequently (dynamism).
Following this reasoning, we can say that the PEU is a
function of the dynamism and complexity perceived
for the items of that environment:
PEU = F (Di, Ci)
(1)
Mapping of perceived complexity and dynamism,
considered as two different dimensions, provide the
following graph of PEU (Figure 1).
and managers along a single line for their
measurement according to the situation whereas factor
analysis fails to construct any linear measure [9].
2.1.1 Latent variables and Rasch probability
Let Xni be a latent variable representing the
environmental complexity/dynamism. The score is
expressed by Xni = {1, 2, 3, 4, 5} in terms of the
parameter  n (the manager n) and i (item i of the
environmental complexity/dynamism).
These latent variables are conceived of as a single
dimension along the continuum where parameters n
and i are located.
The following illustrates the manner in which
managers 0 and attributes {1 , 2 , 3 , 4 } can be
thought of as located on the environmental
complexity/dynamism line.
Complexity
Environmental complexity or dynamism
PEU
low
Dynamism
Fig. 1. Complexity and dynamism vs.PEU
Any point on that line will give us the PEU
experienced by an individual according to the
complexity and dynamism perceived of the
environmental items.
2.2 Rasch model
A
way
of
measuring
the
environmental
complexity/dynamism is by means of latent variables
defined by certain items where the observations or
data are manifestation of these variables [8].
Latent trait models focus on the interaction
between the perception of a manager interviewed on
an item rather than upon test scores.
The latent variable can be conceived of as a
straight line along which the manager interviewed and
items are situated
One assumes there is a single direction implies “more”
of the variables (environmental complexity/ or
dynamism). More means more distance along the line.
This will serve as a support for forming a hierarchy of
the perception of the environmental complexity and
dynamism
Rasch measurement is more suitable than other
methods as factor analysis or factor correspondence
for reducing a complex data matrix to one dimensional
variable.The Rasch model allows us to situate items
0
-|-----|-----|-------|------|-1 2 3
4
high
(2)
The attributes 1 , 2 , 3 , in this case, are closer to
the low end than 0 and attribute 4
An even-handed way of relating the positions of
managers and attributes of the environmental
complexity or dynamism is in terms of probabilities.
If  n endorses the attribute i , then  n > i , that is
( n - i ) > 0, and the probability of being complex o
dynamic is >0.5
If
If
If
 n > i , (n - i ) >0 , then P[Xni =1] > 0.5 (3)
 n < i , (n - i ) <0 , then P[Xni =1] < 0.5 (4)
 n = i , (n - i ) =0 , then P[Xni =1] = 0.5 (5)
The difference ( n - i ) can be range from - to
+ and the probability from o to 1, that is,
0  P [Xni =1]  1
(6)
-  ( n - i )  
(7)
If we use the difference as an exponent of e, then
0  e
(n - i )
 
(8)
With a further adjustment we can bright the
expression into the interval from zero to one.
e (n - i )
0  { ----------------- }  1
1 + e (n - i )
(9)
We take this formula to be an estimate of the
probability of perceived environmental complexity or
dynamism.
The relationship can be written as:
e (n - i )
P [Xni =1 |  n , i ] = ----------------1 + e (n - i )
(10)
This is Rasch’s formulation of this development of
latent trait theory [10].
Parameters n and i are estimated by the
maximum likelihood method [11] by using the PROX
and UCON algorithms computed by the Winsteps
computer program [12].
3 Problem solution
3.1 Research methodology
This study is part of a line of research whose main
objective is to analyse the importance of the
environment for firms operating in a geographicallydifferentiated area.
The area chosen is Canary Islands, a Spanish
autonomous region located at over 2,000 km from the
mainland in the Atlantic Ocean. This geographical
feature makes it one of the most peripheral regions in
the European Union, with such consequences as the
distinctive character of business and entrepreneurial
behaviour. Because of this geographical situation,
warm weather, political stability and natural resources,
among other factors, its main industry is tourism.
We obtained the data required for this study during
the first four months of 2001 with a questionnaire
applied within a personalised interview. The valid
sample used was 338 surveys answered by the
managers.
The questionnaire was made up of closed
questions concerning perceptions of the environmental
dynamism and complexity for a total of 25 items
according to Oreja [13]. He defines the variables
relevant to the island economy in four subscales:
 Geographic subscale: insularity, physical geography,
natural resources, demography.
 Economic subscale: developmental level of the
Canaries, situation of the demand, income level of
the demand, technological resources, situation of
competitors, distance from big markets, market
segmentation, natural, financial and human
resources, physical barriers, economies of scale,
dependence on exterior, exchange rate.
 Politico-legal subscale: political situation of the
Canaries, sector legislation, labour legislation,
consumer protection.
 Socio-cultural subscale: consumer motivation,
attitude to the firm, professional training.
To find out the position of the managers in the
face of both these environmental dimensions, their
perceptions are measured on a 5-point scale, where 1
is a low level of perceived dynamism and complexity,
and 5 is a high level of perceived dynamism and
complexity.
The reliability and validity of the scales used for
the perceived uncertainty was evaluated using Rasch
model as a tool providing a measurement for managers
and items.
3.2 Results: Items measurement
The results show the item measurements which
express the location along the straight line
complexity. “Situation of the demand, situation of
the competitors”, “Income level of the demand”,
etc are the most frequent items endorsed by the
managers, and “Natural resources”, “Physical
orography”, etc are the most rare.
ITEMS STATISTICS: MEASURE ORDER
INFIT
OUTFIT
A B
C
D
E F G H I J ITEMS
||------------------------------------+----------+----------+-----+---------------------|
| 3 735 328 53.0
.2|1.24 3.1|1.22 2.7| .51| Natural Resources
| 2 752 328 52.8
.2|1.15 2.0|1.11 1.5| .48| Physical geography
|| 11 758 328 52.7 .2|1.18 2.4|1.14 1.9| .48| Natural resources
|| 18 798 328 52.3 .2|1.26 3.5|1.24 3.1| .38| Exchange rate
|| 15 862 328 51.5 .2| .99 -.2| .98 -.3| .54| Physical barriers
|| 16 896 328 51.2 .2| .86 -2.3| .87 -2.0| .52| Economies of scale
| 10 909 328 51.0 .2| .83 -2.8| .84 -2.5| .50| Market segmentat.
| 4 918 328 50.9
.2|1.15 2.1|1.13 1.8| .52| Demography
|| 19 935 328 50.7 .2|1.05 .8|1.09 1.3| .49| Political situation
| 9 1015 328 49.8 .2|1.23 3.1|1.22 2.9| .49| Distance to market
| 21 1025 328 49.7 .2| .76 -3.9| .76 -3.7| .49| Labour law
| 14 1047 328 49.5 .2| .86 -2.2| .85 -2.2| .55| Technological res. |
| 12 1051 328 49.4 .2| .83 -2.6| .83 -2.6| .50| Financial resources
| 22 1057 328 49.4 .2| .87 -1.9| .88 -1.8| .47| Consumer defence
| 24 1062 328 49.3 .2| .81 -3.0| .83 -2.6| .46| Attitude to firm
| 13 1085 328 49.0 .2| .81 -2.9| .82 -2.7| .54| Human resources
|| 17 1085 328 49.0 .2|1.46 5.8|1.47 5.7| .49| Dependence ext.
|| 5 1097 328 48.9 .2| .83 -2.7| .84 -2.4| .53| Development|
| 25 1098 328 48.9 .2| .91 -1.4| .93 -1.0| .45| Prof. training
|| 23 1102 328 48.9 .2| .92 -1.2| .92 -1.1| .51| Consumer motivat.
| 1 1111 328 48.7 .2|1.47 5.9|1.45 5.4| .48| Insularity
|| 20 1124 328 48.6 .2| .96 -.5| .96 -.6| .51| Sector legislation
|| 7 1126 328 48.6 .2| .76 -3.8| .77 -3.5| .53| Demand income
|| 8 1157 328 48.2 .2|1.10 1.3|1.09 1.2| .45| Sit.competitors |
| 6 1182 328 47.9 .2| .90 -1.4| .94 -.7| .50| Sit. of demand |
|------------------------------------+----------+----------+-----+---------------------| MEAN 999. 328. 50.0 .2|1.01 -.1|1.01 -.1| |
|| S.D. 132. 0. 1.5 .0| .21 2.9| .20 2.6| |
|
+-----------------------------------------------------------------------------------------
Table1. Complexity.
The table 2 shows the measurements of items
which define Dynamism. Their measure order is very
much alike to Table 1.
Items STATISTICS: MEASURE ORDER
INFIT
OUTFIT
A B
C
D
E F G H I J ITEMS
--------------------------------------------------------------------------------------| 2 602 326 54.2 .3|1.11 1.3|1.04 .5| .50 | Orography
| 3 660 326 53.3 .3|1.09 1.2|1.03 .4| .55 | Natural resources
|| 11 681 326 53.0 .3| .99 -.1| .95 -.7| .53 | Natural resources
|| 1 700 326 52.7 .3|1.45 5.3|1.42 4.9| .47| Insularity
|| 15 719 326 52.4 .3| .88 -1.7| .88 -1.7| .56| Physical barriers
|| 18 759 326 51.8 .3|1.45 5.5|1.44 5.2| .44| Exchange rate
|| 16 774 326 51.6 .3| .92 - 1.2| .91 -1.3| .54| Economy of scale
|| 10 826 326 50.9 .2| .86 - 2.1| .84 -2.4| .59| Market segmentat.
|| 19 855 326 50.5 .2|1.05 .7|1.08 1.0| .51| Political situation
| 9 863 326 50.4
2|1.14 1.9|1.10 1.3| .58| Dist. To market |
| 4 871 326 50.3 .2|1.12 1.6|1.11 1.5| .52| Demography
|| 17 902 326 49.9 .2|1.23 3.1|1.23 3.1| . 54|Dependence ext
|| 21 922 326 49.6 .2| .81 - 2.9| .80 -3.0| .59| Labour law
|| 24 952 326 49.2 .2| .82 - .7| .81 -2.9| . 60| Attitude to firm
|| 22 967 326 49.0 .2| .85 -2.2| .85 -2.1| .57| Consumer defence
|| 13 969 326 49.0 .2| .91 -1.3| .91 -1.3| .59| Human resources
|| 20 973 326 48.9 .2|1.09 1.3|1.07 1.0| .55| Sector legislation
|| 25 983 326 48.8 .2| .86 -2.1| .85 -2.2| .59| Profes. training
|| 12 988 326 48.7 .2| .68 -5.1| .68 -5.1| .66| Financial resourc.
|| 5 1023 326 48.3 .2| .81 -2.9| .86 -2.0| .55| Development
| 23 1040 326 48.0 .2| .94 -.9| .94 -.9| 55| Consumer motivat
|| 14 1065 326 47.7 .3|1.11 1.5|1.11 1.5| .56| Technological res.
|| 7 1066 326 47.7 .3| .72 -4.4| .74 -3.9| .56| Income of demand
|| 8 1087 326 47.4 .3|1.06 .9|1.04 .6| . 54| Competitors
| 6 1130 326 46.8 .3| .88 -1.7| .92 -1.1| .52| Situation demand
|------------------------------------+----------+----------+-----+--------------------| MEAN 895. 326. 50.0 .3| .99 -.3| .98 -.4| |
|| S.D. 144. 0. 2.0
.0| .19 2.6| .18 2.5| |
|
+-----------------------------------------------------------------------------------------
J) PTBIS: Point-biserial correlation, between the
individual item (or manager) scores and the total
manager (or item) score.
Perceived Enviromental Uncertainty Function.
Ploting the results from the table 1 and 2, we obtain
the graph of PEU (Graph 2). As we can see there is
relation (R2 = 0’848) among both dimensions and that
is what formed the PEU from the individual
perceptions. So our methodology confirms what
previous literature said but using only perceptions
[14].
It can be noticed that the items “Insularity” does
not follows the pattern. It is considered as a misfit or
item that no contributes to the model and could be
eliminated in future researches. It could be due to the
dense and vague meaning of “insularity” for people
living in islands. This is the reason why it is perceived
less dynamic than complex. Everything in an insular
economy is influenced by the idea of “insularity”.
Table 2. Dynamism.
ORO
TIPC
52,00
BARF
ECES
SEGM
POL
DEMO
51,00
complejidad
Explanation:
Columns
A) Entry number: indicator reference number
B) Raw score: raw score (computation number)
C) Count: number of managers interviewed
encountered for each item
D) Measure: environmental complexity or dynamism
estimate for item
E) Error: standard error of the estimate
INFIT: a standardized information-weighted mean
square statistics, which is more sensitive to unexpected
scores affecting computations for items near
environmental complexity/dynamism level
F) MNSQ: mean square INFIT statistics, with
expectation 1. Values substantially less than 1 indicate
dependency of data. Values substantially than 1
indicate noise.
G) ZSTD: INFIT mean –square fit static standardized
to approximate a theoretical mean 0 and variance 1.
OUTFIT: a standardized outlier-sensitive mean square
fit statistc, more sensitive to unexpected scores by
managers on item far the item’s environmental
complexity / dynamism level
H) MNSQ: Mean square OUTFIT statistics, with
expectation 1. Values substantially < 1 indicate
dependence on the data; values substantially > 1
indicate the presence of unexpected outliers.
I) ZSTD: OUTFIT mean square fit statistics
standardized to approximate a theoretical mean 0 and
variance 1
RRN
RECN
53,00
50,00
LEGL DIST.
RECN
RECT
ACTE
DEFC
DESA
MOTC RRHH DEPEX
49,00
REN.D.
INS
LEGS
COMP
SIT.D.
48,00
47,00
46,00
48,00
50,00
52,00
54,00
dinamismo
Fig. 2. Curve of perceived environmental uncertainty
If we observe the graph 2 we conclude that both,
dynamism and complexity, contribute nearly both in
the same quantity and way to PEU. This term confirms
that in those times the understanding of what it is
happening “outside” is as important as the changes of
the items for making decisions. This conclusion is
quite different from Duncan’s [1] that he found that
dynamism contributes more to uncertainty.
4 Conclusions
Complexity/dynamism can be conceptualized as a
latent variable defined by a set of items and quantified
in term of Rasch measurement. This possibility gave
us the opportunity to advance in diagnosing the
environment in a way nearer to individual mind.
The results are that the measures are related. The
Perceived Environmental Uncertainty function
obtained by the resulting computed measures
corroborates the accepted theory about the relation
between complexity and dynamism [14].
The great difference and our contribution is that
the relation is given by deciders itself not by any
objective weight that “forced” the relation. What we
have in figure 2 is the mental models of decision
makers and then, the input of the decision making
process: the perceptions. A part from that, it is also
important because the knowledge owned by
individuals is created from latent structures of
information, among others, in the brain of individuals
[15].
One of the basic problems of organizations is to
have supports of decision-making to improve the
cognitive process of deciders [16]. A previous step to
design and choose those supports would be to know
more about that cognitive process that need to be
improved. This methodology leads us also know
which environmental items are perceived more
uncertain and why: due to the complexity and/or
dynamism. Then we could identify the objectives of
our potential support systems.
In the future and from these results, we could
develop another research line considering, for example
the Strategic Reference Points with the order measure
from the Rasch model. In another hand, if we centre in
the cognitive perspective we could also analyse is
there were any difference in perceptions depending on
the sector of activity or type of firm.
Anyway, this application of Rasch probabilities
and model to business administration not only lets us
know more about environmental uncertainty, but also
open a great field of research, what it is even more
relevant.
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