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A catastrophe model of construction conflict behavior
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Building and Environment 41 (2006) 438–447 www.elsevier.com/locate/buildenv
A catastrophe model of construction conflict behavior Kenneth T.W. Yiu, Sai On Cheung Construction Dispute Resolution Research Unit, Department of Building and Construction, City University of Hong Kong, 83 Tat Chee Avenue, Hong Kong Received 18 November 2004; received in revised form 5 January 2005; accepted 12 January 2005
Abstract Buildings are part of the built environment in which many activities are performed. One of the critical part of a development process is the physical construction of the proposed facility. As such an efficient construction process is invaluable. Moreover, due to the inherent divergence in interest, conflict among the contracting parties appears inevitable. Escalating conflict level may turn into psychological struggles between the contracting parties and manifests as dispute. The unfortunate outcomes are loss of productivity and increase in cost of construction. This paper describes the dynamic change in construction conflict behavior based on the catastrophe theory. How conflict behavior is affected by conflict level is first discussed. As such a catastrophe model of construction conflict behavior with tension level, behavioral flexibility as control variables is proposed. It is suggested that conflict is positively correlated to the tension level among the project team and subject to the moderating effect of the behavioral flexibility displayed by the project team members. The model suggests a sudden jump in conflict level will occur when tension reaches a threshold. Once this happens the conflict level will not subside even the tension level returns to the threshold just reached. The proposed model was tested by an empirical study that affirms: (1) The appropriateness of the use of tension and behavioral flexibility as control variables; (2) catastrophe model is a better fit to describe construction conflict behavior than the linear and logistic model; and (3) the bimodal nature of construction conflict behavior. The model reinforces the conventional wisdom of ‘prevention is better than cure’ as far as construction conflict resolution is concerned. r 2005 Elsevier Ltd. All rights reserved. Keywords: Catastrophe theory; Conflict; Tension; Construction conflict behavior
1. Introduction Buildings are part of the built environment in which many activities are performed. In many countries, the building industry is a major economic driver. As such, facilities need to be constructed efficiently while meeting the aesthetic and functional requirements. One of the key factors affecting the successful delivery of construction projects is enabling a cooperative working environment [1]. Traditional construction contracting methods are considered as one of the major sources of adversarial attitude within the project team. This confrontational culture often leads to loss of productivity and cost increases [2]. Maintaining a cooperative environment is Corresponding author. Tel.: +852 2788 7603; fax: +852 2788 7612.
E-mail address: [email protected] (S.O. Cheung). 0360-1323/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.buildenv.2005.01.007
not an easy task for the very fact that conflicts are inherent in all construction projects [3–6]. Conflict can be defined as a serious difference between two or more beliefs, ideas or interests [7]. It can have detrimental effects on the performance of the project resulting from the adversarial and mistrust environment so developed [1]. In recent years, partnering as a means to alleviate conflict, has gained tremendous interest of the construction community [8–11]. Notwithstanding, conflict remains a major concern and total elimination appears daunting [12–14]. Improvement may be more readily achieved should effort be directed to reduce its magnitude and/or keeping it under control [15]. Reported researches in construction conflicts have examined its causation [16–19], prevention [1] and management [12,15,20,21]. These are important references for the study of construction conflict. However,
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these are often discussed within a contractual and legal context. It is believed that equal importance should be aligned with the human factors involved [17]. Conflict is somehow stemmed from and handled by the people involved [22], the role of human factor, in particular behavior, must be an integral part of conflict management. Previous study suggested that conflicts, if not handled properly, will escalate [14]. This escalation occurs when emotional and psychological reasons are involved [16]. Hence, the change in conflict level may turn into psychological struggles between the contracting parties [23]. In construction, confliction described as the creation of conflict by Burton [24], persists during the construction processes [3–6]. Previous studies in human behavior suggested that a continuous change of behavior often displays a discontinuous lapse [25,26]. In the study of construction conflict behavior, taken as the behavior in response to conflict in construction, such change is dynamically associated with the magnitude of conflict. This suggests that there exists a threshold of conflict level beyond which a sudden change in conflict behavior will occur. The theoretical explanation of such behavior pattern can be found on the catastrophe theory developed by Thom [27]. This theory accords a grounded approach for modeling conflict behavior in construction, and the mathematical treatment allows the examination of the dynamics among interacting variables analytically.
2. An overview of catastrophe theory Catastrophe theory is a well-established approach with applications in different research areas such as physics [28–30], chemistry [31], biology [32,33], finance [34] and social sciences [35,36]. Furthermore, catastrophe theory has widely been applied in management studies such as employee turnover [37,38], organizational management [39,40], forecasting and decision making [41,42], competitive strategies [43] and customer behavior [44,45]. Applications to attitude-based analysis were also reported in studies on multi-stable perception [46], child development [47], perception of an apparent motion [48], cognitive development [49] and sudden transitions in attitudes [50]. In view of the above, catastrophe theory offers exciting prospect in analyzing construction conflict behavior. This paper discusses the relationship between conflict and its respective behavior. A catastrophe model on construction conflict behavior is proposed. The validity of the model was tested by an empirical study.
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discontinuous effect on a dependent variable. It is a mathematical model devised by French Rene Thom [27] and then popularized by Zeeman [26,51,52]. A catastrophe model in its simplest form includes a dependent variable and two independent variables. The dependent variable shall have two or more extreme forms. While the two independent variables have different qualitative meanings: One of the independent variable is called normal factor and the other is called splitting factor [53]. The normal factor is related to the dependent variable in a consistent pattern. The splitting factor is the key variable as it is described as ‘‘a moderator variable which specifies conditions under which the normal factor will affect the dependent variable in a continuous fashion, and other circumstances under which the normal factor will produce discontinuous changes in the dependent variableyit is the splitting factor that determines the ‘‘breaking point’’ or threshold of change in the dependent variabley’’[53]. In a catastrophe framework, when the intensities of the normal factor and splitting factor reach a critical point, the dependent variable will change suddenly and radically.
4. The model Fig. 1 shows the hypothesized catastrophe model that describes the change in conflict level, hence the conflict behavior, as a result from the interaction between tension level and behavioral flexibility. Conflict behaviors ranging from avoidance to aggression as depicted in the behavior surface (B) are governed by the conflict level as shown in the vertical axis. For any combination of avoidance and aggression, and thus for any point on the control surface, there is at least one likely form of behavior, indicated as a point above the corresponding point on the control surface and at the appropriate height on the behavior axis. The set of all such points makes up the behavior surface. In most cases there is only one probable mode of behavior. However, where avoidance and aggression are roughly equal, in the middle of the graph there are two sheets representing likely behavior. These are connected by a third sheet to make a continuous pleated surface. This third sheet represents the least likely behavior, in this case, neutrality. Towards the origin, the pleat in the behavior surface becomes narrower and eventually vanishes. The line defining the edges of the pleat is called the fold curve and its projection onto the control surface is a cuspshaped curve. 4.1. Model descriptions
3. A catastrophe model for construction conflict behavior Catastrophe theory describes how small and continuous changes in independent variables can have sudden,
4.1.1. Conflict as the dependent variable As discussed, the role of human behavior is an integral part of conflict resolution. There is a need to
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B Aggress Neutral
D
G
F A Conflict Behavior Surface (B)
High
E
Avoid Conflict Level (Z)
C
Low
Tension Level (X)
High
High Control Space (C)
Behavioral flexibilityconcern for self/other (Y) Low
Fig. 1. A catastrophe model of construction conflict behavior.
better understand the relationship between conflict level and its respective behavior. It has been suggested that conflict is one of the major influences on conflict behavior [24,54,55]. When conflict level is high, feeling of frustration surfaces and manifests as aggressive behavior [24,56–59]. The parties are, therefore, more likely to adopt an aggressive approach to resolve their disputes. This type of behavior is supported by the study of Chen et al. [56], which showed that the existence of conflict significantly correlated with aggressive behavior. 4.1.2. Tension as normal factor Tension affects conflict level. The intensity of tension tends to increase with decrease in the social distance between the groups and with the increases in the amount of energy behind them [24]. In a project team, tension may result from the inconsistent demands from team members; identity crises, uncertainty or extra-organizational pressures [21]. If these incompatible groups are in close contact, as in the case of project team, the tension will be great [24]. Another source of tension derives from the time pressure on the team. Completion by the due date is one of the most frequently used project success measures [60]. Dealing with the time pressure sometimes implies that the project team members have to work overtime. As such, this stressor intensifies tension.
4.1.3. Behavioral flexibility as the splitting factor Behavioral flexibility is the ability to act differently and appropriately in different situation [61,62]. In fact, this personality trait has been reported to have implication on conflict level [63]. Most relationships within a project team involve mixed motives, and demand high behavioral flexibility if they are to be managed optimally [21]. Behavioral flexibility is demonstrated when individuals are both able and willing to react (and presumably, appropriate) responsive to the contexts [61,65]. It is a type of adjustment in one’s behavior to his/her surroundings. Hence, it implies that a flexible individual shall have the knowledge and perceptiveness to match their behavior to situational demands. In the study of conflict behavior, those having a narrower range of behavioral flexibility are less likely to exploit the integrative potential fully [63]. They may engage in negotiation to the exclusion of collaborative problem solving, become passive or even withdraw [64]. On the other hand, flexible individuals will adjust their own conflict resolution styles in response to the situation seeking to maximize potential collaboration [66]. For example, they will accommodate both the concerns of their own and the others in resolving conflicts. This behavior can best be illustrated by the model of conflict handling styles suggested by Rahim et al. [67] and
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CONCERN FOR SELF
HIGH
LOW
INTEGRATING
OBLIGING
COMPROMISING LOW
CONCERN FOR OTHERS
HIGH
DOMINATING
AVOIDING
Fig. 2. A conflict handling model (adopted from Rahim [68]).
Behavioral flexibility- (concern for self/other) High Avoiding
Dominating
Compromising
Obliging
Integrating
Low
Fig. 3. The splitting factor–behavioral flexibility.
Rahim [68]. This model adopted the conflict handling style classifications suggested by Blake and Mouton [69]. The styles described are: integrating, obliging, compromising, dominating and avoiding. For the purpose of this study, two dimensions were added to Rahim’s model (Fig. 2 refers). The first dimension explains the degree to which a person attempts to satisfy his own concern. The second dimension explains the degree to which a person wants to satisfy the concern for the others. In summary, when dealing with conflict, those who have high behavioral flexibility, will adopt a resolution style contingent to their/the other’s need. As such, the conflict level can be controlled or even reduced. However, with low behavioral flexibility, it will be difficult to accommodate the concern of the opposing party, the conflict level will likely to escalate. Adopting the style model developed by Rahim [68], Fig. 3 shows the measurement framework for behavioral flexibility.
5. Model implications Having introduced the model components, this section gives the implications suggested by the catastrophe model. According to the model, the changes in
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the conflict level as a result of the moderating effect of behavioral flexibility on tension level influence the conflcit behavior. Cases of low, moderate and high degree of behavioral flexibility are elaborated. When the degree of behavioral flexibility is high, the parties can be at high concern for self as well as the other party. At this position, the conflict behavior can be described as problem solving, collaboration, cooperation, solution-orientation, win-win, or positive-sum and is relatively constrained, i.e. the change from avoidance to aggression is relatively unlikely. The parties are more accommodating and willing to adjust their responses to situational demands. Hence, in the presence of these integrating approaches, there is a higher chance to reach a win-win solution. This situation is reflected in Fig. 1 by the movement between A and B within the high degree of behavioral flexibility region. Note that changes in tension level are translated relatively directly to differences in conflict level, but at a slow rate and within modest levels of conflict. Thus, if the tension level is relatively low, a fairly large increase in tension level is necessary to increase the conflict level. The trajectory between points A and B in Fig. 1 represents such behaviors. As the degree of behavioral flexibility becomes moderate, the parties become less adaptive. The capability of matching situational demands becomes weaker over different tension level. They may, therefore, exhibit higher or lower level of conflict than he would at the same tension level when the degree of behavioral flexibility is high. At this moment, the parties are in moderate concern for self as well as for the other parties, it is often described as the mixed motive style in game theory and equivalent to the compromising style as suggested by Raham [68]. This style involves give-andtake or sharing, whereby both parties give up something to make a mutually acceptable decision [70]. The degree of scarification of a compromising individual is greater than the other styles. A small change in the tension level can result in fairly substantial changes in conflict level. The transition in conflict level is smooth. There is no discontinuous shift from high conflict level to low conflict level as the tension level moves from high to low. If the degree of behavioral flexibility decreases beyond moderate, the behavioral responses move out to C, D, E and become bimodal. The graphical representations are given in Figs. 3 and 4. Bimodal means that the conflict level will be either low or high and will not be achieved in moderated level due to the existence of inaccessible region, even if the tension level is moderate. If the degree of behavioral flexibility is low, the conflict level tends to resist change until the tension levels take on an opposite extreme value. The thresholds of low or high tension level, which demarcate the switching points from low conflict level to high conflict level and vice versa, emerge.
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and
Conflict Level
b ¼ b0 þ b1 x1 þ b2 x2 þ ::: þ bn xn . D
High
Moderate E
C Low
Low
Moderate
High
Tension Level Fig. 4. Movement at low degree of behavioral inflexibility.
Consider a situation in which a party with low degree of behavioral flexibility (point C in Figs. 1 and 4), the parties are not flexible enough to cope with the mixed motives. They focus on their own concerns only. Neutrality is unlikely, instead a sudden increase in conflict level will occur if the tension level reaches the threshold. This change will occur only when the tension level reaches position D as shown in Figs. 1 and 4. The catastrophe model further suggests that once this happens conflict will remain at a high level even if the tension level subsides until the point E where a sudden drop will occur.
6. Model fitting This stage of the study seeks to test empirically the fitness of the catastrophe model. Cobb [71–74] and Cobb et al. [74–76] developed a catastrophe fitting technique that is based on the stochastic differential equations to estimate model parameters from the data. As such, Cobb [72] proved that there is a family of probability density function, which a stable equilibrium corresponds to a mode and an unstable equilibrium corresponds to an anti-mode [48]. A stable equilibrium state is a point of high probability. By examining the probability density functions of the catastrophe model, the control variables can be estimated by using maximum likelihood estimation. The form of the behavioral surface in raw score form can be expressed by Eq. (1) [75–77] 1 1 f ðzjabÞ exp ay þ by2 y4 , (1) 2 4 where y ¼ ðz lÞ=s; l and s scale the observed behavioral variable z to y. a and b are linear functions of the independent variables x1 to xn ; with a ¼ a0 þ a1 x1 þ a2 x2 þ ::: þ an xn
(2)
(3)
The maximum likelihood method of Cobb [71–74] is considered as the most elegant and statistically satisfactory method for fitting the cusp catastrophe model [78]. Based on this algorithm, a flexible and robust program called Cuspfit was developed by Hartelman [77]. Cuspfit, with a more reliable optimization routine, is also equipped with additional functions such as comparison with logistic and linear models. These enable the algorithms to distinguish an arbitrarily fast acceleration from a catastrophical change [48]. Two fit measures, Akaike’s Information Criterion (AIC) and Bayesian Information Criterion (BIC) are also provided by the program. AIC [79] is a goodness-of-fit index that takes into account the number of parameter [80], which defined as minus twice the log-likelihood plus twice the number of parameters. The model with smallest AIC is the best fit. BIC [81], is also a goodness-of-fit indicator that takes into account the number of data points, which implements Occam’s razor by quantifying the trade-off between goodness-of-fit and parsimony, models with lower BIC values are preferred [81–83]. Hence, the model with the lowest AIC and BIC shall be selected. Furthermore, to test the presence of bifurcations the fit of the cusp model is compared to the fit of both a linear model and the logistic growth model. If the AIC and BIC values of the catastrophe model is lower than that of logistic and linear models, the catastrophe model has the best fit [48]. In addition to these improvements, another notable feature of Hartelman’s program is the possibility of introducing restrictions to parameters to test specific hypotheses. For example, by restricting some of the parameters (a0 . . . an and b0 . . . bn ) to 0 and then compare the AIC and BIC values with the unrestricted catastrophe model [50], the appropriate independent variables to act as the normal and the splitting variables of the proposed model can be identified. The above testing method has been successfully applied in the recent studies of Ruhland [84], Ploeger et al. [48] and van der Maas [50]. 6.1. Data collection A questionnaire was designed to collect data in respect of the measurements of dependent and control variables. The targeted respondents were construction professionals such as project managers, architects and quantity surveyors, who had at least 5 years experience in project management. They were asked to report the significance of each of the variables with reference to one of their recent project. A five-point Likert scale was employed to measure the dependent variable (conflict level) and the normal factor (tension level). The scale used was least significant (1) and most significant (5).
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The same approach was also adopted by van de Maas et al. [50] to measure the variables on attitude changes. Regarding the measurements of the splitting factor (behavioral flexibility), the Rahim [68]’s model was reduced to a five-point scale, represented as low concern for self and other (1) to high concern for self and other (5). As discussed, since behavioral flexibility is demonstrated when individuals are both able to make different responses in different social contexts [61,65], parties shall have the knowledge and perceptiveness to match their behavior to situational demands. The parties will attempt to satisfy their own/the other’s concern such that their styles will change contingently.
7. Results and discussions A total of 83 sets of data were collected and analyzed by the Cuspfit program [72,77]. Three steps were involved: 1. to test the appropriateness of the control variables (Tension level as normal factor and behavioral flexibility as splitting factor) for the proposed catastrophe model (Fig. 1 refers). 2. to investigate the statistical fitness of the model, and, 3. to identify the bimodality of construction conflict behavior. These steps were widely adopted by previous studies of catastrophe theory using Cuspfit program [46,48,50,85,86]. Step 1: The appropriateness of the proposed control variables: The Cuspfit program fits the catastrophe model with the control variables a; b; and behavior variable z to cross-sectional data, using the maximum likelihood method. Hence, with reference to Eqs. (2) and (3), the linear function, a (the normal factor) and b (the splitting factor), for the two control variables, (x1 ¼ tension level) and (x2 ¼ behavioral flexibility) can be written: a ¼ a0 þ a1 x1 þ a2 x2 ; b ¼ b0 þ b1 x1 þ b2 x2 :
(4)
In the model of construction conflict behavior, tension level and behavioral flexibility are defined as normal and splitting variables respectively; According to the algorithm of Cobb et al. [76], Hartelman [77] and Cobb et al. [75], the setting of these control variables can be considered as the a2 and b1 of equations (4) are zero. Hence, the linear function of a (the normal factor) and b (the splitting factor) can be devised as a ¼ a0 þ a1 x1 ; b ¼ b0 þ b2 x2 :
(5)
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To demonstrate the appropriateness of this setting, a total of 16 catastrophe models were constructed by substituting the four parameters a1, a2, b1 and b2 randomly with zero and then compared (by AIC and BIC) with the unrestricted model [48,50,77]. In this connection, it is possible to construct and calculate the fit of these catastrophe models. The fit measures thus show which of the 16 models is the most appropriate and which of the independent variables fit to act as the normal and the splitting factor. Table 1 presents the results of the analysis. The parameter values, the fit measures of the 16 models as well as the fit measures of the unconstrained linear and logistic models are listed. From Table 1, three models, 9, 10 and 11, show better fit (as they have a lower AIC and BIC values). Model 10 is consistent with the setting of control variables in the catastrophe model of construction conflict behavior, i.e. tension level only loads on the normal factor, and behavioral flexibility only loads on the splitting factor, as defined in the Eq. (5). Hence, the finding shows that the setting of the model, the tension level as normal factor and behavioral flexibility as splitting factor, is statistically fit. Step 2: The statistical fitness of the proposed model Having confirmed the statistical fitness of the normal and splitting factors, the Cuspfit program was also employed to examine the statistical fitness of the proposed model. Cuspfit is able to test three types of models (linear, logistic and catastrophe). Cobb’s [72] algorithm calculates whether the catastrophe model or the linear model gives the better description of its relationship between the independent and the dependent variables. In addition, the improvement done by Hartelman [77] enables the comparison of the catastrophe model with a logistic model. The comparison is to distinguish an arbitrarily fast acceleration from a catastrophical change [48]. When the AIC and the BIC of the catastrophe model are lower than the AIC and the BIC of the logistic and the linear models, the catastrophe model gives the better fit (Hartelman[77]). This assessment method was successfully applied recently in research studies in psychology [48,50]. In this connection, with reference to Table 1, model 10 gives the lowest AIC and BIC values when compared with the linear and logistic models, hence, the data of the study is better described by the proposed catastrophe model than the linear and logistic models. Step 3: The identification of bimodality of construction conflict behavior Based on the results obtained in the above steps, Model 10 is the best model with the tension level as normal factor and behavioral flexibility as splitting factor. This step demonstrates the bimodality of conflict behavior. The Cuspfit program gives a bifurcation diagram which shows how the data fit into the bifurcated region. This diagram can be used to confirm
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Table 1 Results of catastrophe analysis (Adopted from Ploeger et al. [48]) Model
a0
a1
a2
b0
b1
b2
l
s
Log likelihood
Parameters
AIC
BIC
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Linear* Logistic*
.50 .50 .33 .31 .50 .50 .30 .31 .64 .65 .57 .58 .64 .64 .57 .57
0 0 0 0 0 0 0 0 .68 .68 .69 .69 .68 .68 .69 .69
0 0 0 0 .46 .10 .18 .26 0 .0 0 0 .10 .59 .93 .67
.88 .88 .10 .50 .87 .88 .50 .50 .49 .49 .42 .43 .48 .49 .42 .43
0 0 .28 .21 0 0 .28 .21 0 .0 .46 .43 0 0 .45 .44
0 .16 0 .17 0 .15 0 .14 0 .20 0 .16 0 16 0 .13
.51 .52 .33 1.26 .51 .51 1.25 1.25 .49 .50 .34 .36 .49 .49 .35 .35
1.07 1.07 1.00 2.16 1.07 1.07 2.15 2.15 1.07 1.07 1.04 1.04 1.07 1.07 1.04 1.04
.11E+03 .11E+03 .11E+03 .10E+03 .11E+03 .11E+03 .10E+03 .10E+03 .99E+02 .13E+03 .97E+02 .97E+02 .98E+02 .98E+02 .97E+02 .97E+02 .13E+03 .11E+03
4 5 5 6 5 6 6 7 5 4 6 7 6 7 7 8 4 5
.23E+03 .23E+03 .23E+03 .22E+03 .23E+03 .23E+03 .22E+03 .22E+03 .21E+03 .21E+03 .21E+03 .21E+03 .21E+03 .21E+03 .21E+03 .21E+03 .27E+03 .22E+03
.24E+03 .24E+03 .24E+03 .24E+03 .24E+03 .25E+03 .23E+03 .24E+03 .22E+03 .22E+03 .22E+03 .23E+03 .22E+03 .23E+03 .23E+03 .23E+03 .28E+03 .23E+03
*Unconstrained linear and logistic models; Model 1–16:cusp models. Note: a1 and b1 are parameters for tension level; a2 and b2 are parameters for behavioral flexibility; l, location; s, scale; log likelihood value; AIC, Akaike’s information criterion; BIC, Bayes’s information criterion. Zeros are fixed parameters.
5
High D
4 3
Splitting Axis
2
Tension Level
Bifurcation Lines (Bimodal Zone) Behavioral Flexibility
Aggress
E B
Data Points
F
1
A
Low 0
C
High -1 Tension Level
-3
Low
Fig. 6. Behavioral surface of catastrophe model of construction conflict behavior.
-4 -5 -5
Avoid
Behavioral Flexibility
-2
-4
-3
-2
-1
0 1 Normal Axis
2
3
4
5
Fig. 5. Location of the data in the catastrophe control plane (modified from van der Maas et al. [50]).
the bimodality of the behavior [48,50]. If the data points are located in the bifurcation set, the area between the bifurcation lines, the behavior is bimodal in nature. Fig. 5 shows the location of data points in the control plane. Tension level is related to the normal axis, and behavioral flexibility is related to the splitting axis. A reasonable portion of the data falls within the bifurcation set, which shows that under a range of tension level and behavior flexibility, conflict behavior is
bimodal. The bimodality nature of conflict behavior means that for identical combination of tension level and behavioral flexibility, different behaviors with different directional flows can occur (Fig. 6 refers). Within the bimodal zone, i.e. within the area of bifurcation line, there exists a choice of two points, one residing in the aggressive state and the other residing in the avoidance state. As a point in the bimodal zone can be in either state, without additional information one cannot predict the outcome of further movement from such a point. However, if past history is available, that is, prior movements are known, then one
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can predict an eventual state for the next movement from that point [87]. For example, for the same bimodal point, the previous point was from the avoidance behavior, then if the tension level continues to increase, a jump from avoidance behavior to aggressive behavior is forthcoming (path AB). If a point resides on the avoidance state and tension level decreases, a smooth movement should occur (path AC). However, if the point resides on the aggressive state, sufficient decrease in tension level will cause a behavioral jump to the avoidance behavior (DEF), this is the so called hysteresis effect. Hence, for the prediction which state of behavior will occur, both the present point on the curve and the recent history of both the control variables and behavioral state are needed.
8. Conclusion Confliction persists in all building and construction projects. If conflict is not handled properly, it will escalate. The change in conflict level may turn into psychological struggles between the contracting parties. Previous studies in human behavior suggested that a continuous change of behavior often displays a discontinuous lapse. In the study of conflict behavior in construction, such behavioral change is dynamically associated with the magnitude of conflict. This paper describes a conflict behavior found on the catastrophe theory. The catastrophe model describes a construction conflict behavior under the influence of conflict level that depends on the control variables of tension and behavioral flexibility. The model was empirically tested employing the Cuspfit programme. The empirical study affirms the appropriateness of employing tension level and behavioral flexibility as the normal factor and splitting factor, respectively. The result also supports the statistical fitness of the catastrophe model that displayed a bimodal conflict behavior within a range of control variables. This model provides construction practitioners an analytical method to analyze the conflict behavior that a disputant will take basing on the information/data of the control variables. Most significantly the model suggests the need to evaluate the hysteresis effect in such analyses.
Acknowledgements The authors would like to thank Prof. Dr. Han L.J. van der Maas, University of Amsterdam, Amsterdam, Netherlands, for his helpful comments on the use of the Cuspfit programme. The work described in the paper was fully supported by a CityU Project (No. 7001597).
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Building and Environment 41 (2006) 438–447 www.elsevier.com/locate/buildenv
A catastrophe model of construction conflict behavior Kenneth T.W. Yiu, Sai On Cheung Construction Dispute Resolution Research Unit, Department of Building and Construction, City University of Hong Kong, 83 Tat Chee Avenue, Hong Kong Received 18 November 2004; received in revised form 5 January 2005; accepted 12 January 2005
Abstract Buildings are part of the built environment in which many activities are performed. One of the critical part of a development process is the physical construction of the proposed facility. As such an efficient construction process is invaluable. Moreover, due to the inherent divergence in interest, conflict among the contracting parties appears inevitable. Escalating conflict level may turn into psychological struggles between the contracting parties and manifests as dispute. The unfortunate outcomes are loss of productivity and increase in cost of construction. This paper describes the dynamic change in construction conflict behavior based on the catastrophe theory. How conflict behavior is affected by conflict level is first discussed. As such a catastrophe model of construction conflict behavior with tension level, behavioral flexibility as control variables is proposed. It is suggested that conflict is positively correlated to the tension level among the project team and subject to the moderating effect of the behavioral flexibility displayed by the project team members. The model suggests a sudden jump in conflict level will occur when tension reaches a threshold. Once this happens the conflict level will not subside even the tension level returns to the threshold just reached. The proposed model was tested by an empirical study that affirms: (1) The appropriateness of the use of tension and behavioral flexibility as control variables; (2) catastrophe model is a better fit to describe construction conflict behavior than the linear and logistic model; and (3) the bimodal nature of construction conflict behavior. The model reinforces the conventional wisdom of ‘prevention is better than cure’ as far as construction conflict resolution is concerned. r 2005 Elsevier Ltd. All rights reserved. Keywords: Catastrophe theory; Conflict; Tension; Construction conflict behavior
1. Introduction Buildings are part of the built environment in which many activities are performed. In many countries, the building industry is a major economic driver. As such, facilities need to be constructed efficiently while meeting the aesthetic and functional requirements. One of the key factors affecting the successful delivery of construction projects is enabling a cooperative working environment [1]. Traditional construction contracting methods are considered as one of the major sources of adversarial attitude within the project team. This confrontational culture often leads to loss of productivity and cost increases [2]. Maintaining a cooperative environment is Corresponding author. Tel.: +852 2788 7603; fax: +852 2788 7612.
E-mail address: [email protected] (S.O. Cheung). 0360-1323/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.buildenv.2005.01.007
not an easy task for the very fact that conflicts are inherent in all construction projects [3–6]. Conflict can be defined as a serious difference between two or more beliefs, ideas or interests [7]. It can have detrimental effects on the performance of the project resulting from the adversarial and mistrust environment so developed [1]. In recent years, partnering as a means to alleviate conflict, has gained tremendous interest of the construction community [8–11]. Notwithstanding, conflict remains a major concern and total elimination appears daunting [12–14]. Improvement may be more readily achieved should effort be directed to reduce its magnitude and/or keeping it under control [15]. Reported researches in construction conflicts have examined its causation [16–19], prevention [1] and management [12,15,20,21]. These are important references for the study of construction conflict. However,
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these are often discussed within a contractual and legal context. It is believed that equal importance should be aligned with the human factors involved [17]. Conflict is somehow stemmed from and handled by the people involved [22], the role of human factor, in particular behavior, must be an integral part of conflict management. Previous study suggested that conflicts, if not handled properly, will escalate [14]. This escalation occurs when emotional and psychological reasons are involved [16]. Hence, the change in conflict level may turn into psychological struggles between the contracting parties [23]. In construction, confliction described as the creation of conflict by Burton [24], persists during the construction processes [3–6]. Previous studies in human behavior suggested that a continuous change of behavior often displays a discontinuous lapse [25,26]. In the study of construction conflict behavior, taken as the behavior in response to conflict in construction, such change is dynamically associated with the magnitude of conflict. This suggests that there exists a threshold of conflict level beyond which a sudden change in conflict behavior will occur. The theoretical explanation of such behavior pattern can be found on the catastrophe theory developed by Thom [27]. This theory accords a grounded approach for modeling conflict behavior in construction, and the mathematical treatment allows the examination of the dynamics among interacting variables analytically.
2. An overview of catastrophe theory Catastrophe theory is a well-established approach with applications in different research areas such as physics [28–30], chemistry [31], biology [32,33], finance [34] and social sciences [35,36]. Furthermore, catastrophe theory has widely been applied in management studies such as employee turnover [37,38], organizational management [39,40], forecasting and decision making [41,42], competitive strategies [43] and customer behavior [44,45]. Applications to attitude-based analysis were also reported in studies on multi-stable perception [46], child development [47], perception of an apparent motion [48], cognitive development [49] and sudden transitions in attitudes [50]. In view of the above, catastrophe theory offers exciting prospect in analyzing construction conflict behavior. This paper discusses the relationship between conflict and its respective behavior. A catastrophe model on construction conflict behavior is proposed. The validity of the model was tested by an empirical study.
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discontinuous effect on a dependent variable. It is a mathematical model devised by French Rene Thom [27] and then popularized by Zeeman [26,51,52]. A catastrophe model in its simplest form includes a dependent variable and two independent variables. The dependent variable shall have two or more extreme forms. While the two independent variables have different qualitative meanings: One of the independent variable is called normal factor and the other is called splitting factor [53]. The normal factor is related to the dependent variable in a consistent pattern. The splitting factor is the key variable as it is described as ‘‘a moderator variable which specifies conditions under which the normal factor will affect the dependent variable in a continuous fashion, and other circumstances under which the normal factor will produce discontinuous changes in the dependent variableyit is the splitting factor that determines the ‘‘breaking point’’ or threshold of change in the dependent variabley’’[53]. In a catastrophe framework, when the intensities of the normal factor and splitting factor reach a critical point, the dependent variable will change suddenly and radically.
4. The model Fig. 1 shows the hypothesized catastrophe model that describes the change in conflict level, hence the conflict behavior, as a result from the interaction between tension level and behavioral flexibility. Conflict behaviors ranging from avoidance to aggression as depicted in the behavior surface (B) are governed by the conflict level as shown in the vertical axis. For any combination of avoidance and aggression, and thus for any point on the control surface, there is at least one likely form of behavior, indicated as a point above the corresponding point on the control surface and at the appropriate height on the behavior axis. The set of all such points makes up the behavior surface. In most cases there is only one probable mode of behavior. However, where avoidance and aggression are roughly equal, in the middle of the graph there are two sheets representing likely behavior. These are connected by a third sheet to make a continuous pleated surface. This third sheet represents the least likely behavior, in this case, neutrality. Towards the origin, the pleat in the behavior surface becomes narrower and eventually vanishes. The line defining the edges of the pleat is called the fold curve and its projection onto the control surface is a cuspshaped curve. 4.1. Model descriptions
3. A catastrophe model for construction conflict behavior Catastrophe theory describes how small and continuous changes in independent variables can have sudden,
4.1.1. Conflict as the dependent variable As discussed, the role of human behavior is an integral part of conflict resolution. There is a need to
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B Aggress Neutral
D
G
F A Conflict Behavior Surface (B)
High
E
Avoid Conflict Level (Z)
C
Low
Tension Level (X)
High
High Control Space (C)
Behavioral flexibilityconcern for self/other (Y) Low
Fig. 1. A catastrophe model of construction conflict behavior.
better understand the relationship between conflict level and its respective behavior. It has been suggested that conflict is one of the major influences on conflict behavior [24,54,55]. When conflict level is high, feeling of frustration surfaces and manifests as aggressive behavior [24,56–59]. The parties are, therefore, more likely to adopt an aggressive approach to resolve their disputes. This type of behavior is supported by the study of Chen et al. [56], which showed that the existence of conflict significantly correlated with aggressive behavior. 4.1.2. Tension as normal factor Tension affects conflict level. The intensity of tension tends to increase with decrease in the social distance between the groups and with the increases in the amount of energy behind them [24]. In a project team, tension may result from the inconsistent demands from team members; identity crises, uncertainty or extra-organizational pressures [21]. If these incompatible groups are in close contact, as in the case of project team, the tension will be great [24]. Another source of tension derives from the time pressure on the team. Completion by the due date is one of the most frequently used project success measures [60]. Dealing with the time pressure sometimes implies that the project team members have to work overtime. As such, this stressor intensifies tension.
4.1.3. Behavioral flexibility as the splitting factor Behavioral flexibility is the ability to act differently and appropriately in different situation [61,62]. In fact, this personality trait has been reported to have implication on conflict level [63]. Most relationships within a project team involve mixed motives, and demand high behavioral flexibility if they are to be managed optimally [21]. Behavioral flexibility is demonstrated when individuals are both able and willing to react (and presumably, appropriate) responsive to the contexts [61,65]. It is a type of adjustment in one’s behavior to his/her surroundings. Hence, it implies that a flexible individual shall have the knowledge and perceptiveness to match their behavior to situational demands. In the study of conflict behavior, those having a narrower range of behavioral flexibility are less likely to exploit the integrative potential fully [63]. They may engage in negotiation to the exclusion of collaborative problem solving, become passive or even withdraw [64]. On the other hand, flexible individuals will adjust their own conflict resolution styles in response to the situation seeking to maximize potential collaboration [66]. For example, they will accommodate both the concerns of their own and the others in resolving conflicts. This behavior can best be illustrated by the model of conflict handling styles suggested by Rahim et al. [67] and
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CONCERN FOR SELF
HIGH
LOW
INTEGRATING
OBLIGING
COMPROMISING LOW
CONCERN FOR OTHERS
HIGH
DOMINATING
AVOIDING
Fig. 2. A conflict handling model (adopted from Rahim [68]).
Behavioral flexibility- (concern for self/other) High Avoiding
Dominating
Compromising
Obliging
Integrating
Low
Fig. 3. The splitting factor–behavioral flexibility.
Rahim [68]. This model adopted the conflict handling style classifications suggested by Blake and Mouton [69]. The styles described are: integrating, obliging, compromising, dominating and avoiding. For the purpose of this study, two dimensions were added to Rahim’s model (Fig. 2 refers). The first dimension explains the degree to which a person attempts to satisfy his own concern. The second dimension explains the degree to which a person wants to satisfy the concern for the others. In summary, when dealing with conflict, those who have high behavioral flexibility, will adopt a resolution style contingent to their/the other’s need. As such, the conflict level can be controlled or even reduced. However, with low behavioral flexibility, it will be difficult to accommodate the concern of the opposing party, the conflict level will likely to escalate. Adopting the style model developed by Rahim [68], Fig. 3 shows the measurement framework for behavioral flexibility.
5. Model implications Having introduced the model components, this section gives the implications suggested by the catastrophe model. According to the model, the changes in
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the conflict level as a result of the moderating effect of behavioral flexibility on tension level influence the conflcit behavior. Cases of low, moderate and high degree of behavioral flexibility are elaborated. When the degree of behavioral flexibility is high, the parties can be at high concern for self as well as the other party. At this position, the conflict behavior can be described as problem solving, collaboration, cooperation, solution-orientation, win-win, or positive-sum and is relatively constrained, i.e. the change from avoidance to aggression is relatively unlikely. The parties are more accommodating and willing to adjust their responses to situational demands. Hence, in the presence of these integrating approaches, there is a higher chance to reach a win-win solution. This situation is reflected in Fig. 1 by the movement between A and B within the high degree of behavioral flexibility region. Note that changes in tension level are translated relatively directly to differences in conflict level, but at a slow rate and within modest levels of conflict. Thus, if the tension level is relatively low, a fairly large increase in tension level is necessary to increase the conflict level. The trajectory between points A and B in Fig. 1 represents such behaviors. As the degree of behavioral flexibility becomes moderate, the parties become less adaptive. The capability of matching situational demands becomes weaker over different tension level. They may, therefore, exhibit higher or lower level of conflict than he would at the same tension level when the degree of behavioral flexibility is high. At this moment, the parties are in moderate concern for self as well as for the other parties, it is often described as the mixed motive style in game theory and equivalent to the compromising style as suggested by Raham [68]. This style involves give-andtake or sharing, whereby both parties give up something to make a mutually acceptable decision [70]. The degree of scarification of a compromising individual is greater than the other styles. A small change in the tension level can result in fairly substantial changes in conflict level. The transition in conflict level is smooth. There is no discontinuous shift from high conflict level to low conflict level as the tension level moves from high to low. If the degree of behavioral flexibility decreases beyond moderate, the behavioral responses move out to C, D, E and become bimodal. The graphical representations are given in Figs. 3 and 4. Bimodal means that the conflict level will be either low or high and will not be achieved in moderated level due to the existence of inaccessible region, even if the tension level is moderate. If the degree of behavioral flexibility is low, the conflict level tends to resist change until the tension levels take on an opposite extreme value. The thresholds of low or high tension level, which demarcate the switching points from low conflict level to high conflict level and vice versa, emerge.
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and
Conflict Level
b ¼ b0 þ b1 x1 þ b2 x2 þ ::: þ bn xn . D
High
Moderate E
C Low
Low
Moderate
High
Tension Level Fig. 4. Movement at low degree of behavioral inflexibility.
Consider a situation in which a party with low degree of behavioral flexibility (point C in Figs. 1 and 4), the parties are not flexible enough to cope with the mixed motives. They focus on their own concerns only. Neutrality is unlikely, instead a sudden increase in conflict level will occur if the tension level reaches the threshold. This change will occur only when the tension level reaches position D as shown in Figs. 1 and 4. The catastrophe model further suggests that once this happens conflict will remain at a high level even if the tension level subsides until the point E where a sudden drop will occur.
6. Model fitting This stage of the study seeks to test empirically the fitness of the catastrophe model. Cobb [71–74] and Cobb et al. [74–76] developed a catastrophe fitting technique that is based on the stochastic differential equations to estimate model parameters from the data. As such, Cobb [72] proved that there is a family of probability density function, which a stable equilibrium corresponds to a mode and an unstable equilibrium corresponds to an anti-mode [48]. A stable equilibrium state is a point of high probability. By examining the probability density functions of the catastrophe model, the control variables can be estimated by using maximum likelihood estimation. The form of the behavioral surface in raw score form can be expressed by Eq. (1) [75–77] 1 1 f ðzjabÞ exp ay þ by2 y4 , (1) 2 4 where y ¼ ðz lÞ=s; l and s scale the observed behavioral variable z to y. a and b are linear functions of the independent variables x1 to xn ; with a ¼ a0 þ a1 x1 þ a2 x2 þ ::: þ an xn
(2)
(3)
The maximum likelihood method of Cobb [71–74] is considered as the most elegant and statistically satisfactory method for fitting the cusp catastrophe model [78]. Based on this algorithm, a flexible and robust program called Cuspfit was developed by Hartelman [77]. Cuspfit, with a more reliable optimization routine, is also equipped with additional functions such as comparison with logistic and linear models. These enable the algorithms to distinguish an arbitrarily fast acceleration from a catastrophical change [48]. Two fit measures, Akaike’s Information Criterion (AIC) and Bayesian Information Criterion (BIC) are also provided by the program. AIC [79] is a goodness-of-fit index that takes into account the number of parameter [80], which defined as minus twice the log-likelihood plus twice the number of parameters. The model with smallest AIC is the best fit. BIC [81], is also a goodness-of-fit indicator that takes into account the number of data points, which implements Occam’s razor by quantifying the trade-off between goodness-of-fit and parsimony, models with lower BIC values are preferred [81–83]. Hence, the model with the lowest AIC and BIC shall be selected. Furthermore, to test the presence of bifurcations the fit of the cusp model is compared to the fit of both a linear model and the logistic growth model. If the AIC and BIC values of the catastrophe model is lower than that of logistic and linear models, the catastrophe model has the best fit [48]. In addition to these improvements, another notable feature of Hartelman’s program is the possibility of introducing restrictions to parameters to test specific hypotheses. For example, by restricting some of the parameters (a0 . . . an and b0 . . . bn ) to 0 and then compare the AIC and BIC values with the unrestricted catastrophe model [50], the appropriate independent variables to act as the normal and the splitting variables of the proposed model can be identified. The above testing method has been successfully applied in the recent studies of Ruhland [84], Ploeger et al. [48] and van der Maas [50]. 6.1. Data collection A questionnaire was designed to collect data in respect of the measurements of dependent and control variables. The targeted respondents were construction professionals such as project managers, architects and quantity surveyors, who had at least 5 years experience in project management. They were asked to report the significance of each of the variables with reference to one of their recent project. A five-point Likert scale was employed to measure the dependent variable (conflict level) and the normal factor (tension level). The scale used was least significant (1) and most significant (5).
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The same approach was also adopted by van de Maas et al. [50] to measure the variables on attitude changes. Regarding the measurements of the splitting factor (behavioral flexibility), the Rahim [68]’s model was reduced to a five-point scale, represented as low concern for self and other (1) to high concern for self and other (5). As discussed, since behavioral flexibility is demonstrated when individuals are both able to make different responses in different social contexts [61,65], parties shall have the knowledge and perceptiveness to match their behavior to situational demands. The parties will attempt to satisfy their own/the other’s concern such that their styles will change contingently.
7. Results and discussions A total of 83 sets of data were collected and analyzed by the Cuspfit program [72,77]. Three steps were involved: 1. to test the appropriateness of the control variables (Tension level as normal factor and behavioral flexibility as splitting factor) for the proposed catastrophe model (Fig. 1 refers). 2. to investigate the statistical fitness of the model, and, 3. to identify the bimodality of construction conflict behavior. These steps were widely adopted by previous studies of catastrophe theory using Cuspfit program [46,48,50,85,86]. Step 1: The appropriateness of the proposed control variables: The Cuspfit program fits the catastrophe model with the control variables a; b; and behavior variable z to cross-sectional data, using the maximum likelihood method. Hence, with reference to Eqs. (2) and (3), the linear function, a (the normal factor) and b (the splitting factor), for the two control variables, (x1 ¼ tension level) and (x2 ¼ behavioral flexibility) can be written: a ¼ a0 þ a1 x1 þ a2 x2 ; b ¼ b0 þ b1 x1 þ b2 x2 :
(4)
In the model of construction conflict behavior, tension level and behavioral flexibility are defined as normal and splitting variables respectively; According to the algorithm of Cobb et al. [76], Hartelman [77] and Cobb et al. [75], the setting of these control variables can be considered as the a2 and b1 of equations (4) are zero. Hence, the linear function of a (the normal factor) and b (the splitting factor) can be devised as a ¼ a0 þ a1 x1 ; b ¼ b0 þ b2 x2 :
(5)
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To demonstrate the appropriateness of this setting, a total of 16 catastrophe models were constructed by substituting the four parameters a1, a2, b1 and b2 randomly with zero and then compared (by AIC and BIC) with the unrestricted model [48,50,77]. In this connection, it is possible to construct and calculate the fit of these catastrophe models. The fit measures thus show which of the 16 models is the most appropriate and which of the independent variables fit to act as the normal and the splitting factor. Table 1 presents the results of the analysis. The parameter values, the fit measures of the 16 models as well as the fit measures of the unconstrained linear and logistic models are listed. From Table 1, three models, 9, 10 and 11, show better fit (as they have a lower AIC and BIC values). Model 10 is consistent with the setting of control variables in the catastrophe model of construction conflict behavior, i.e. tension level only loads on the normal factor, and behavioral flexibility only loads on the splitting factor, as defined in the Eq. (5). Hence, the finding shows that the setting of the model, the tension level as normal factor and behavioral flexibility as splitting factor, is statistically fit. Step 2: The statistical fitness of the proposed model Having confirmed the statistical fitness of the normal and splitting factors, the Cuspfit program was also employed to examine the statistical fitness of the proposed model. Cuspfit is able to test three types of models (linear, logistic and catastrophe). Cobb’s [72] algorithm calculates whether the catastrophe model or the linear model gives the better description of its relationship between the independent and the dependent variables. In addition, the improvement done by Hartelman [77] enables the comparison of the catastrophe model with a logistic model. The comparison is to distinguish an arbitrarily fast acceleration from a catastrophical change [48]. When the AIC and the BIC of the catastrophe model are lower than the AIC and the BIC of the logistic and the linear models, the catastrophe model gives the better fit (Hartelman[77]). This assessment method was successfully applied recently in research studies in psychology [48,50]. In this connection, with reference to Table 1, model 10 gives the lowest AIC and BIC values when compared with the linear and logistic models, hence, the data of the study is better described by the proposed catastrophe model than the linear and logistic models. Step 3: The identification of bimodality of construction conflict behavior Based on the results obtained in the above steps, Model 10 is the best model with the tension level as normal factor and behavioral flexibility as splitting factor. This step demonstrates the bimodality of conflict behavior. The Cuspfit program gives a bifurcation diagram which shows how the data fit into the bifurcated region. This diagram can be used to confirm
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Table 1 Results of catastrophe analysis (Adopted from Ploeger et al. [48]) Model
a0
a1
a2
b0
b1
b2
l
s
Log likelihood
Parameters
AIC
BIC
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Linear* Logistic*
.50 .50 .33 .31 .50 .50 .30 .31 .64 .65 .57 .58 .64 .64 .57 .57
0 0 0 0 0 0 0 0 .68 .68 .69 .69 .68 .68 .69 .69
0 0 0 0 .46 .10 .18 .26 0 .0 0 0 .10 .59 .93 .67
.88 .88 .10 .50 .87 .88 .50 .50 .49 .49 .42 .43 .48 .49 .42 .43
0 0 .28 .21 0 0 .28 .21 0 .0 .46 .43 0 0 .45 .44
0 .16 0 .17 0 .15 0 .14 0 .20 0 .16 0 16 0 .13
.51 .52 .33 1.26 .51 .51 1.25 1.25 .49 .50 .34 .36 .49 .49 .35 .35
1.07 1.07 1.00 2.16 1.07 1.07 2.15 2.15 1.07 1.07 1.04 1.04 1.07 1.07 1.04 1.04
.11E+03 .11E+03 .11E+03 .10E+03 .11E+03 .11E+03 .10E+03 .10E+03 .99E+02 .13E+03 .97E+02 .97E+02 .98E+02 .98E+02 .97E+02 .97E+02 .13E+03 .11E+03
4 5 5 6 5 6 6 7 5 4 6 7 6 7 7 8 4 5
.23E+03 .23E+03 .23E+03 .22E+03 .23E+03 .23E+03 .22E+03 .22E+03 .21E+03 .21E+03 .21E+03 .21E+03 .21E+03 .21E+03 .21E+03 .21E+03 .27E+03 .22E+03
.24E+03 .24E+03 .24E+03 .24E+03 .24E+03 .25E+03 .23E+03 .24E+03 .22E+03 .22E+03 .22E+03 .23E+03 .22E+03 .23E+03 .23E+03 .23E+03 .28E+03 .23E+03
*Unconstrained linear and logistic models; Model 1–16:cusp models. Note: a1 and b1 are parameters for tension level; a2 and b2 are parameters for behavioral flexibility; l, location; s, scale; log likelihood value; AIC, Akaike’s information criterion; BIC, Bayes’s information criterion. Zeros are fixed parameters.
5
High D
4 3
Splitting Axis
2
Tension Level
Bifurcation Lines (Bimodal Zone) Behavioral Flexibility
Aggress
E B
Data Points
F
1
A
Low 0
C
High -1 Tension Level
-3
Low
Fig. 6. Behavioral surface of catastrophe model of construction conflict behavior.
-4 -5 -5
Avoid
Behavioral Flexibility
-2
-4
-3
-2
-1
0 1 Normal Axis
2
3
4
5
Fig. 5. Location of the data in the catastrophe control plane (modified from van der Maas et al. [50]).
the bimodality of the behavior [48,50]. If the data points are located in the bifurcation set, the area between the bifurcation lines, the behavior is bimodal in nature. Fig. 5 shows the location of data points in the control plane. Tension level is related to the normal axis, and behavioral flexibility is related to the splitting axis. A reasonable portion of the data falls within the bifurcation set, which shows that under a range of tension level and behavior flexibility, conflict behavior is
bimodal. The bimodality nature of conflict behavior means that for identical combination of tension level and behavioral flexibility, different behaviors with different directional flows can occur (Fig. 6 refers). Within the bimodal zone, i.e. within the area of bifurcation line, there exists a choice of two points, one residing in the aggressive state and the other residing in the avoidance state. As a point in the bimodal zone can be in either state, without additional information one cannot predict the outcome of further movement from such a point. However, if past history is available, that is, prior movements are known, then one
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can predict an eventual state for the next movement from that point [87]. For example, for the same bimodal point, the previous point was from the avoidance behavior, then if the tension level continues to increase, a jump from avoidance behavior to aggressive behavior is forthcoming (path AB). If a point resides on the avoidance state and tension level decreases, a smooth movement should occur (path AC). However, if the point resides on the aggressive state, sufficient decrease in tension level will cause a behavioral jump to the avoidance behavior (DEF), this is the so called hysteresis effect. Hence, for the prediction which state of behavior will occur, both the present point on the curve and the recent history of both the control variables and behavioral state are needed.
8. Conclusion Confliction persists in all building and construction projects. If conflict is not handled properly, it will escalate. The change in conflict level may turn into psychological struggles between the contracting parties. Previous studies in human behavior suggested that a continuous change of behavior often displays a discontinuous lapse. In the study of conflict behavior in construction, such behavioral change is dynamically associated with the magnitude of conflict. This paper describes a conflict behavior found on the catastrophe theory. The catastrophe model describes a construction conflict behavior under the influence of conflict level that depends on the control variables of tension and behavioral flexibility. The model was empirically tested employing the Cuspfit programme. The empirical study affirms the appropriateness of employing tension level and behavioral flexibility as the normal factor and splitting factor, respectively. The result also supports the statistical fitness of the catastrophe model that displayed a bimodal conflict behavior within a range of control variables. This model provides construction practitioners an analytical method to analyze the conflict behavior that a disputant will take basing on the information/data of the control variables. Most significantly the model suggests the need to evaluate the hysteresis effect in such analyses.
Acknowledgements The authors would like to thank Prof. Dr. Han L.J. van der Maas, University of Amsterdam, Amsterdam, Netherlands, for his helpful comments on the use of the Cuspfit programme. The work described in the paper was fully supported by a CityU Project (No. 7001597).
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