Neural networks and organizational systems: Modeling non-linear relationships

European Journal of Operational Research 181 (2007) 939–955 www.elsevier.com/locate/ejor

Interfaces with Other Disciplines

Neural networks and organizational systems: Modeling non-linear relationships John Grznar a, Sameer Prasad

b,*

, Jasmine Tata

c,1

a b

University of Illinois at Springfield, College of Business and Management, One University Plaza, Springfield, IL 62703, United States University of Wisconsin – Whitewater, Management Department, College of Business and Economics, Whitewater, WI 53190, United States c Loyola University Chicago, School of Business Administration, 820 N. Michigan Avenue, Chicago, IL 60611, United States Received 23 September 2005; accepted 29 December 2005 Available online 11 September 2006

Abstract For decades, organizational researchers have employed standard statistical methods to uncover relationships among variables and constructs. However, in complex organization systems, the prevalence of non-linearity and outliers is to be expected. Under such circumstances, the use of standard statistical methods becomes unreliable and, correspondingly, results in degraded predictions of the relationships within the organizational systems. We describe the use of neural network analyses to model team effectiveness so as to provide more accurate predictions for managers.  2006 Elsevier B.V. All rights reserved. Keywords: Organization theory; Neural networks; Group; Outliers

1. Introduction Researchers in organizational behavior have commonly employed standard regression methods to map out relationships between a set of independent variables and one or more dependent variables. Using such methods researchers are able to state, given a significance threshold level, if the relationship is strong, its direction, and the role of the intervening moderator variables. Examples of most commonly used statistical methods include linear * Corresponding author. Tel.: +1 262 472 5440; fax: +1 262 472 4863. E-mail addresses: [email protected] (J. Grznar), prasads @uww.edu (S. Prasad), [email protected] (J. Tata). 1 Tel.: +1 312 915 6543.

regression, path analysis and, more recently, structural equations modeling. Time series methods have also been used when the data set has a time element within it. Results from these methods are often reported in terms of significance levels (p or t-values), weights (b) and correlations (R2s). From such results, we can arrive at certain conclusions about the types of relationships between sets of dependent and independent variables. Also, given the estimated weights, one can then predict (forecast) the expected values for a set of given independent variables. Some researchers in organizational behavior, however, are frustrated with the results (or lack of significant results) that they obtain via standard statistical methods while testing for relationships among organizational constructs. Often the

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problem lies not in the data collection methods or the definitions of constructs, but rather in the way these complex relationships are defined and the statistical techniques used to test them. Researchers may be unaware of the assumptions that many of the common statistical procedures such as time series methods, linear regression, path analysis, and structural equations may carry. For example, are the observations truly independent of each other? Are the relationships actually linear in form? What about extreme observations (outliers)? It has been well documented that such patterns in the data may play havoc with standard statistical procedures. In this research, we identify a new way to model the complexity of organizational variables through robust neural network analysis. This technique, when used in modeling organizational systems, may help overcome some of the limitations of standard statistical procedures and may be particularly suited to understanding and learning about organization behavior. Organizational behavior literature and theory is, often, built upon methods that assume linear relationships. However, the complexity of organizations begs a reexamination of the relationships via a non-linear approach such as neural networks. In addition, the ability to account for outliers would greatly add to the accuracy in predicting organizational outcomes. We demonstrate the value of neural network by applying them in the context of teams, a popular and complex intervention in organizations today. Partisans of teamwork claim that all organizations need teams to compete in the marketplace, and the proliferation of work groups and teams in US organizations (Tata and Prasad, 2004) suggests that managers appear to agree with those partisans. In addition, research on teams suggests that teams do appear to be critical to organizational effectiveness (Langfred, 2000). A number of studies have identified direct relationships between team effectiveness and work team characteristics such as the organizational context of teams, intra-team processes, interteam processes, and team size (Campion et al., 1993, 1996). It would be naive to assume that the problems associated by traditional statistical techniques, such as auto-correlation, non-linearity, and outliers do not exist in the analyses of teams. In fact, studies suggest that teams, especially self-managed teams, are not always effective in practice (Wall et al., 1986), a finding that may be attributed to the statis-

tical techniques used to measure team processes and team effectiveness. For example, it is quite possible that within a particular team an individual’s decision is partly influenced by peers within the same group. Also, team members may vary in terms of their tenure in the team and in the amount of team-related training that they receive. This could result in a large variation in team processes, such that newer or untrained team members could perform extremely poorly (outliers), distorting findings of team effectiveness. In addition, non-linear patterns have also been noticed in the literature. For example, it has been reported that the optimal size of teams ranges between four and seven individuals (Brightman, 1988; Ray and Bronstein, 1995), suggesting a non-linear relationship between team size and effectiveness, yet studies (e.g., Alexander et al., 1996; Stoel, 2002) still examine linear patterns between these two variables. Thus, employing standard statistical methods risks the possibility of obtaining p-values indicating relationships that may not exist or, perhaps, missing out on some important complex relationships. Such misidentification and misinterpretation of the relationships between work team characteristics and team effectiveness could result in problems with team implementation in organizational settings. Although the literature on neural network applications has been connected to the production/ operations, finance, marketing/distribution, and information systems areas (Hu et al., 1999; Wong et al., 2000), studies that apply neural networks to behavioral patterns in organizational systems are largely non-existent (Wong et al., 2000). Hence, in this study we use a data set collected from actual teams in real business settings to examined the relationships between team effectiveness and a number of independent variables such as inter and intra team processes, organizational context, and team size. We run our analyses using: (1) standard regression models, (2) robust regression techniques, and (3) robust neural network analyses. We believe that this study should be of use to both academicians and practitioners. Researchers can gain by having a more accurate tool to map relationships and possibly uncover important relationships that had previously been undetected. Because research, theory, and practice are never completely detached from each other, the findings of organizational researchers are also relevant to practitioners interested in improving the performance of teams at work. Hence, the ability to

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identify true relationships between work team processes and team effectiveness through significant results is crucial to both researchers and practitioners. If such relationships are not identified, or worse, incorrectly identified, this could have both direct and indirect implications. Incorrect relationships identified during organizational evaluation research or impact studies could result in the organization incurring unnecessary expenses or missing potential benefits. For example, if an organization that has implemented self-managing teams incorrectly identifies such teams as ineffective, then it might disband such teams and, thus, lose out on the benefits that could accrue had it continued team implementation. In addition to direct implications, the incorrect identification of relationships among team constructs could also have indirect implications because inaccurate information would be disseminated to the scholarly and practitioner community. Such inaccurate information could have a major effect on the practices adopted by organizations and practitioners and on the techniques used for solving organizational problems, ultimately decreasing organizational effectiveness. Hence, it is important to examine statistical techniques that help us correctly identify and interpret organizational relationships. Increased accuracy also benefits practitioners because it helps improve predictions about the impact of policies on complex organizational variables. In large organizations, even small improvements in predictions can yield benefits in the millions of dollars. Next, the literature on the limitations of the standard statistical methods for complex organizational systems is explored. Following this review, the salient literature on neural networks is discussed. In addition, a demonstration of the efficacy of neural network analyses is presented based on data from organizational teams. Finally, in the discussion section, the advantages and disadvantage of using neural networks for such applications are analyzed. 2. Limitations of standard statistical procedures Organizations are rarely simple to examine. On the contrary, any organizational problem can often be traced to numerous causes, many of which are interrelated. Examining such problems and constructs requires us to be cognizant of outliers, and the non-linear nature of the factors involved. These inherent patterns in data emanating from complex systems play havoc with standard statistical proce-

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dures. The following discusses some of the effects of these problems of standard statistical procedures. We illustrate these effects using the example of a company implementing a move toward self-managed teams with the goal of improving productivity and decreasing product development time. 2.1. Outliers One difficulty that researchers in organizational systems might face is the occurrence of outliers. Grubbs (1969) stated, ‘‘An outlying observation, or outlier is one that appears to deviate markedly from the other members of the sample in which it occurs.’’ (p. 3). A number of authors have used the term ‘outlier’ to indicate any observation that does not come from the target population (Beckman and Cook, 1983). In our example, many teams in the organization are likely to undergo some level of turnover, as team members leave to be replaced by newer members. This turnover could result in newer team members being unfamiliar with team processes such as decision making or creative problem-solving. Measuring the team’s processes without accounting for the outlier values originating from the newer team members could result in a distorted picture of team processes and effectiveness. Outliers can distort the computation of means and variances. Thus, procedures (such as standard regression) that are not robust to the influence of outliers would be susceptible to type II errors or to the possibility of overlooking an important relationship within a complex system. The classical least squares regression revolves around minimizing the sum of the squared residuals. This model is specified as follows: y i ¼ xi1 bi þ    þ xip bp þ ei

ði ¼ 1; . . . nÞ;

where the errors ei are assumed to be normal distributed with a mean of zero. The estimates for ei can be determined from the data. The most common way to obtain these estimates is by using the Least Squares (LS) Method Minimize ^ b

n X

r2i ;

i¼1

where residuals (ri) are obtained as follows: ^i      xip b ^p : ri ¼ y i  xi1 b However, outliers can easily distort the estimates for b.

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Outliers can be accommodated in standard regression procedures by minimizing the effects of extreme observations through the use of robust regression. One simple method is to replace the mean value in the least squares function with the median (Rousseeuw, 1984; Rousseeuw and Leroy, 1987). As such the Least Median of Squares estimator can be specified as follows: Minimize median r2i : ^ b

i

This method is very robust to data sets that may be populated with outliers (Rousseeuw, 1984). In the business literature, robust regression has been applied to a number of areas including operations management (Khouja and Booth, 1991) and accounting (Booth et al., 1989). A field such as organizational behavior is ripe with possible outliers. Extreme values can be present in either the independent or dependant variables. For example, one of the critical influences on team effectiveness is their size. Although organizations tend to limit team size in the range of two to 15, it is possible for the organization in our example to have team sizes that run in the hundreds. Such extreme values would certainly skew the estimates and hence the conclusions. Surprisingly, few studies in organizational behavior apply robust regression techniques. Perhaps the lack of use might be due to unfamiliarity with this technique or, quite possibly, due to confounding effects from non-linear patterns in organizations. 2.2. Non-linearity In modeling simpler organizational settings it is possible to use linear methods without compromising significantly. However, as systems get more complex (e.g., team-based organizational systems), the likelihood of linear patterns explaining the relationships among variables diminishes. In our example of self-managed teams, the connection between individual self-management and team effectiveness may be non-linear. The literature (e.g., Uhl-Bien and Graen, 1998) suggests that moderate levels of individual self-management may increase intrinsic motivation and performance in teams. High levels, however, may result in amounts of independent decision-making that interfere with the interdependent behavior necessary for effective team functioning. Thus, there may be an ‘‘inverted U’’ relationship between individual self-management and team effectiveness, such that team effectiveness will be high when team

members have moderate levels of individual selfmanagement, and low when members have low or high levels of individual self-management. Given such non-linear behavior in complex organizational settings, it is likely that even robust regression or robust time series methods would be unable to model the underlying patterns and make accurate predictions. Researchers studying organizational systems have long recognized this issue and have used procedures such as log transformations to collapse the data into linear functions. However, such techniques are inherently limited by their inability to recognize the non-linear pattern and transform it. Simple non-linear patterns such as squared functions and exponentials are easier to detect, but higher level cubed functions found in complex organizational systems might be impossible to recognize. Proper data transformation only occurs in exceptional cases (Bunke and Bunke, 1989). Thus, trying to fit a linear model on non-linear or inappropriately transformed data may be a recipe for disaster, resulting in estimates of relationships that are dramatically inaccurate. In this research we suggest the use of neural network analyses to predict relationships among organizational variables so as to overcome the potential difficulties arising due to outliers and non-linear patterns. We believe that standard statistical procedures may be based on a paradigm of piecemeal (as opposed to systems) thinking, and do not sufficiently account for the complexity of organizational constructs. Neural networks, in contrast, involve quantitative techniques that are particularly suited to examining complex systems. The potential of neural network analysis lies in its ability to model complex relationships better than standard techniques and identify relationships that have remained hidden so far. Next, we will examine neural networks and explain why they are particularly suited to model non-linear patterns. 3. Neural networks Neural networks first became popular in the late 1980s and, more recently, in the 1990s. Compared to traditional statistical methods, neural network analysis has been found to be very useful in diverse, real-world applications. Neural networks have been applied to model complex problems in the sciences, engineering and other business applications that have proven to be difficult to deal with using

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standard statistical procedures (Wong et al., 2000). In addition, they have been used for pattern matching, function approximation, cluster analysis, and dimension reduction. For example, neural network analyses significantly improved Chase Manhattan’s credit card fraud detection rates over standard regression models (Rochester, 1990). One of the reasons why neural networks have proven to be so useful is that they are distribution and assumption free. They are capable of recognizing patterns and discovering relationships in the data, whereas regression models require a priori knowledge of the nature of the underlying relationships. Neural networks also perform well with missing or incomplete data. Furthermore, they are more robust and less sensitive to changes in sample size, number of variables, and data distribution. In neural networks the data itself determines the model form. Thus, given sufficient computational power and data, any pattern (linear or non-linear) found in complex organizational systems can be modeled. The basic idea behind neural networks is to mimic the neural activities with the human brain (Rumelhart et al., 1986). In the brain there are extensively interconnected units (neurons) that make up a vast network capable of complex pattern recognition. Similarly, neural networks consist of many computational elements operating in parallel and arranged in layers. A number of types of neural networks are available. Three of the most common ones include multilayered feedforward neural networks, Hopfield neural networks, and self-organizing neural networks (Smith and Gupta, 2000). Most researchers in the business field have used multilayered feedforward neural network analysis with back-propagation learning (Wong et al., 1997) given its relevance to business issues. This technique involves learning relationships between a set of inputs and known outputs; it is considered a supervised learning technique because a set of training data (independent and dependent variables) is necessary to learn the relationship. Hopfield networks are generally used to solve constraint satisfaction problems, such as those found in operations research, while self-organizing networks can be used for cluster analysis. Hence, in this research, we will focus on multilayered feedforward neural networks with back-propagation learning. In multilayered feedforward neural networks, organizational systems can be abstracted into the tasks of approximation of unknown functions from

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a training set of input–output pairs. For example, in modeling team behavior the input vectors would be variables such as the organizational context of teams, inter-team processes, intra-team processes, and team size. The output vector would be team effectiveness. The input and the output vectors are related via an unknown function. A residual vector is also generated as a result of an imperfect relationship between the input and output vectors which occurs because of outliers and/or unexplained variance. In linear regression, the input and output pairs are connected via direct connections. In neural network analyses the connections with output pairs are not direct, but travel via one or more intermediary nodes. In standard regression we obtain a vector of weights (bs) for the connection between the input and output pairs. With neural networks, we obtain a matrix of weights. Hence, neural networks are more complex than standard regression, but allow for greater flexibility. Neural networks consists of a number of components, including (1) a number of layers and nodes, (2) connections between the nodes among the various layers, (3) propagation rules to aggregate the signals emanating from the previous layers, (4) activation functions, and (5) learning algorithms (Zhu et al., 2001). In Fig. 1, we show a simple three-layered neural network with one output, one input and one hidden or intermediary layer. A three-layer configuration is considered to be sufficiently powerful to model most business applications (Warner and Misra, 1996). In this figure one set of weights (Tij) connects two input nodes with the hidden layer and the other set of weights (kj) connects the four hidden nodes with the one output node. Data is propagated between two connected nodes of the network as the product of the output of the sending node and the value of the weight which connects the nodes. Thus, the input of each intermediary and output layer node is a weighted sum of the outputs of all the nodes in the corresponding lower layer of nodes. To identify the value of the weights, data might travel through various routes in trying to establish a best fit between a set of input and output nodes; an activation function (gj) guards the signal and only allows it to go though if it exceeds a certain threshold or activation level (Warner and Misra, 1996). A learning algorithm adjusts the weights among the nodes by iteratively reducing the residuals emanating from the difference between the actual outputs and the expected outputs. The neural network

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Output layer

λ1

g1

w11

λ2

λ3

g2

w12

w13

g3

w22

w23

w21 x1

x2

Hidden layer Activation signal g1, g3, g3, . ., gj Weights λ1, λ1, λ1, . . . ,λ j

Input layer Input nodes x1, x2, x3 . . . xi. Weights w11, w12, w13, w21, w31. . . wij.

Fig. 1. A simple three layer neural network.

attempts to minimize this error; reaching a convergence can take millions of iterations. When we explore the use of neural network analyses for complex organizational relationships, the greater the complexity of the system, the larger the number of nodes and layers that have to be employed. Also, given the uncertainty with the type of distribution assumed in the data a distribution free model associated with backpropagation is preferred. 3.1. Backpropagation The term ‘‘backpropagation’’ (BP) indicates that the error correction signal/search direction goes backwards from the output layer to the input layer (Chen and Jain, 1994; Werbos, 1994). When the computed neural network output (predicted result) is compared with the target output (expected results based on actual data), any errors detected are propagated back through the network by sending signals to adjust the weights. The basic idea is that the sum of squared errors (the errors are the difference between the desired target values and the computed neural network outputs) is minimized by an iterative error correction mechanism that adjusts the weights between the neural network nodes until a stopping criterion is successfully reached (Chen and Jain, 1994; Bishop, 1995). Therefore, this algorithm is often viewed as an optimization procedure for min-

imizing a sum of squared error objective function. The backpropagation algorithm makes an error adjustment by making a weight adjustment propagated through the network; it does this by following a minimizing rule such as gradient descent. The iterative process continues until the error change reaches a certain threshold, stabilizes, or some other stopping criterion is reached. A similar, but simple analogy for regression can be made. Most regression methods are based on least squares or sum of squared errors. Least squares adjust the weights so as to minimize this squared error. However, a closed form solution for the least squares regression method is known; in regression, there is only one direct path and, therefore, only one iteration. No such closed form solution has been discovered for neural network analyses which use iterative methods to find a solution. Unfortunately, backpropagation algorithms and standard regression methods are dependent on the type of training data available, and become of limited use when gross errors (outliers) are present. Under such circumstances, the performance of the BP algorithm becomes unsatisfactory as the approximated function can oscillate badly attempting to interpolate outliers (Chen and Jain, 1994). This leads to inaccurate approximation (Chen and Jain, 1994), and hence poorer predictions. Next, we describe how to account for those outliers in neural networks.

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3.2. Robust backpropagation Backpropagation makes use of the sum of square errors as a learning mechanism to guide the flows and weights within the neural network. However, the sum of squared errors tends to be affected by extreme observations. In Fig. 2a, we notice that given the U-shaped function extreme values would inflate the mean squared error. For example, if the residual difference ri increases from point a to point b its effect is exaggerated by the squared function. To deal with such distortions, a number of robust linear techniques are available (Booth, 1982; Hampel, 1974; Hampel et al., 1981; Huber, 1981; Denby and Martain, 1979). One of the most common methods is Hampel’s estimator function which provides a different response to the residuals at different ranges. For example, in Fig. 2b, we can see that the extreme values do not have an unusually large effect; when the residual difference increases from point a to point b, its effect is not exaggerated by a squared function. Neural networks can also be effectively employed to account for the influence of outliers. Chen and Jain (1994) devised a robust backpropagation algorithm to downweigh the effect of these extreme

a

a

b

ri Fig. 2a. Least squares function.

b

a

b

ri Fig. 2b. Different response to residual in different ranges via Hampel’s function.

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observations in a manner similar to Hampel’s function. In this robust BP algorithm the weights change in proportion to the product of the residual error under the redescent Hampel’s transformation and the inputs, whereas for the BP algorithm the changes in the weights are simply proportional to the residuals. Relative to BP, the robust BP offers three advantages: (1) it approximates the underlying mapping rather than interpolating, (2) robustness to outliers, and (3) the convergence rate is faster given the influence of outliers is suppressed (Chen and Jain, 1994). We employ this robust BP developed by Chen and Jain (1994) for our analyses. 4. Method In this research, we examine the relative impact of using (1) standard regression models, (2) robust regression techniques, and (3) neural network analyses by analyzing data collected from organizational teams. A number of studies have examined direct relationships between work team characteristics (organizational context of teams, intra-team processes, inter-team processes, and team size) and team effectiveness. Team effectiveness refers to the extent to which teams are productive, satisfy customers, and result in team member satisfaction (Campion et al., 1993, 1996); this construct can be influenced by the organizational context of teams, intra-team processes, inter-team processes, and team size. The organizational context of teams concerns the overarching structures and systems external to a team that facilitate or inhibit its work; it refers to the extent to which the organization and top management support teams by providing resources (e.g., space, time, training, information) to teams and by integrating teams in other organizational systems (e.g., selection systems, training systems). The construct of intra-team processes has been extensively examined in the literature and refers to processes internal to a team that influence its outcomes. This construct includes both task-related aspects (e.g., establishing team goals, action planning) and interpersonal aspects (e.g., communication, conflict management, decision making). Inter-team processes refer to the interaction of the team with other entities in the organization such as other teams and top management; it refers to aspects of coordination and communication with these other entities (Ancona, 1990; McIntosh-Fletcher, 1996). Many studies in the literature (e.g., Campion et al., 1993, 1996) assume linear relationships

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between team effectiveness and the other constructs discussed above. However, these assumptions of linearity might not hold true, and the data might display outliers and possibly conceal non-linear behavior. In this research we attempt to estimate team effectiveness more accurately by not being bounded by the assumptions of linear models. 4.1. Data collection techniques The data set was collected through structured interviews. A sample of 102 teams was interviewed using a questionnaire with items based on previous research (e.g., Campion et al., 1993, 1996; Tata and Prasad, 2004). The teams were from several different organizations and included a variety of ongoing work teams such as customer product teams and safety teams. The organizations varied in size from only 7 to over 10,000 employees. The team size ranged from 2 to 30 with its members having an average age of 38.7 years; 41% were female. The average length of tenure at the present employer was 8.6 years, with 2.3 years of average tenure with the team. Each participant was asked to complete a packet of materials that included measures of the independent variables and to rate only their primary team in cases where they belonged to more than one team. Five-point Likert-type scales were used to collect responses and Cronbach’s alpha (a) was calculated to examine the reliability of the scales. Cronbach’s alpha is a coefficient of internal consistency reliability that measures how well a set of items in a scale measures a single unidimensional construct, as opposed to several multidimensional constructs. It is a function of the number of items in the scale and the average inter-correlation among the items. Alpha coefficients range in value from 0 to 1 and may be used to describe the reliability of factors extracted from multi-point formatted scales. The higher the score, the more reliable is the scale. In general, 0.7 is considered to be an acceptable lower threshold for Cronbach’s alpha (Nunnally, 1978). The dependent variable, team effectiveness was measured by a five-item scale. This scale asked participants to identify the extent to which teams were productive, the extent to which teams satisfied customers, and the extent to which team members were satisfied (a = 0.91). The organizational context of teams was measured by a 13-item scale measuring how receptive top management was to team suggestions, whether the organization generally accepted team improved work methods, how much effort

the organization put into improving conditions of teams, whether the equipment and resources available for the team were adequate, the extent to which resources (space, time, training, etc.) were provided for teams, and the extent to which teams were included in human resources polices (selection/ recruitment, performance evaluation, reward, working conditions, etc.) (a = 0.83). The intra-team processes scale measured the extent to which team members trusted and supported each other, provided feedback to each other, managed conflict effectively, specified goals and objectives, developed action plans, and communicated effectively (a = 0.93). Inter-team processes was measured through five items that examined the extent to which teams coordinated, shared information, and interacted with upper management (a = 0.82). All the scales had Cronbach’s alpha (a) well over 0.7, the acceptable lower threshold as identified by Nunnally (1978). Thus, all scales had good internal consistency reliabilities. 4.2. Analyses In this research we examined the performance of three statistical procedures (standard regression, robust regression, and neural network analyses) in estimating functions from data that were suspected to be non-linear in nature and populated with outliers. One of the established methods of comparing various types of estimation functions is to split the data into two sets: one set for training and the one set for testing. The estimates are computed from the training set and then are used to obtain expected values for the dependent variables given the independent values from the testing set. The proportion of observations falling within the two sets can vary. In this research we followed a standard approach and used the first two-thirds of the observations for training and the remaining one-third for testing. Having both the actual and expected values for the dependent variable in the testing set allows us to gauge the closeness of fit by computing a Mean Squared Error (MSE). Finally, having a measure of the overall variability of the dependent variable and the amount of variability which remained unexplained, it was possible to compute Sum of Squared Errors (SSE), R2 and F-statistics. We employed three different procedures to estimate the function between the independent variables (organizational context, intra-team processes, interteam processes, and team size) and the dependent

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variable (team effectiveness). The first procedure uses the standard least squares regression function (Fig. 2a). This procedure is commonly used in most statistical analyses in organizational behavior, but is not robust and cannot model non-linear patterns. To accommodate the possibility of outliers, the second procedure that we employed is the least median of squares linear regression method. This technique is robust to the influence of outliers because median values are unaffected by extreme values, but like standard least squares regression, cannot model non-linear patterns. Since we suspect that non-linear patterns are possible we also employed a robust neural network analysis. Neural networks require a degree of experimentation. In our neural network specification the organizational context of teams, intra-team processes, inter-team processes, and team size were nodes of the input layer. The output layer consisted of only one node (team effectiveness). We obtained the best fit by varying the number of nodes in the hidden layer, the learning rate, and percentage of outliers in the data by using the standard logistic activation function. In neural networks the data itself determines the model form. In our research we separated the data in two groups; the first two thirds were used for training the model form while the remaining data was used for testing. In neural networks the forecast cannot be simply generated by estimates, but is determined by the structure of the network and its weights. Thus, once we had obtained the best neural network, it was then possible to predict team effectiveness as a function of the various independent variables. To obtain a mapping of the influence of one or more independent variables on team effectiveness we enumerated all possible permutations by varying team context, inter-team process and inter-team processes from 1 to 5 in increments of 1. Team size was varied from 2.5 to 30 in increments of 2.5.2 Hence a total of 1500 permutations (5 · 5 · 5 · 12) of the independent variables were generated to map out the response function. Given these 1500 permutations,

2

The purpose of having increment of 2.5 as opposed to increments of 1 for team size was simply to reduce the number of permutations from 3750 (5 · 5 · 5 · 3) to a more manageable number of 1500. Since the objective of this exercise was to obtain the shape of patterns among the various independent variables and the dependant variable, we felt that the loss in precision in going from 1 to 2.5 would not affect our plots to a significant extent.

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it was then possible to sort by one or more independent variables and obtain the average team effectiveness. 5. Results This section presents the results of using the standard least squares regression relative to both the robust regression technique and robust neural networks for our data set. The results of the standard regression, robust regression, and neural networks are presented in Table 1. 5.1. Standard regression After completing the standard regression analyses, we found a strong R2 value of 0.247 by using the least squares function. In addition, a significant effect of intra-team process on effectiveness was also found. Using the last one-third of the data given the estimates (b) derived from the first two-thirds of the data, it was possible to compute MSE, SSE, R2 and F-statistics. The MSE was 0.290, SSE was 9.78 and the R2 was 0.247. The model yielded an F-statistic of 12.70 (p < 0.01). MSE and SSE are measures of accuracy. The smaller these errors, the more accurate and hence valuable is the model. In organizational behavior an R2 of 0.247 is considered a good fit. In addition, with a p < 0.01 for the F-statistics, it is highly unlikely that the relationships among the independent and dependant variables are due to random fluctuation. 5.2. Robust regression The performance of the model improved dramatically by employing robust regression. The R2 value went up to 0.313 and intra-team processes remained significant. The fact that inter-team processes, team size, and organizational context of teams were not significant could perhaps be explained by non-linear patterns. Using the parameter estimates (bs) derived from the first two-thirds of the data set and fitting them to the remaining one-third of the teams, it was possible to obtain the corresponding MSE, SSE, R2, and F-statistic. Using the robust regression method, it is evident that the MSE fell to 0.263 and the SSE fell to 8.93, with a corresponding increase in the strength of the model (R2 = 0.313). The F-statistic (12.72, p < 0.01) still confirms that the robust regression significantly explains the pattern between

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Table 1 Estimation of fit Model

Estimates from first 2/3 of the data

Estimates from last 1/3 of data

R2

Variable

b

p-value

MSE

SSE

R2

F-statistic

Least squares

0.333

Team size Org. context Inter-team proc. Intra-team proc. Constant

0.00128 0.07703 0.05160 0.552 1.375

0.903 0.501 0.796 0.000 0.069

0.290

9.78

0.247

12.70

Least median of squares regression (robust)

0.580

Team size Org. context Inter-team proc. Intra-team proc. Constant

0.00595 0.12629 0.13426 0.68141 1.24442

0.458 0.156 0.386 0.000 0.033

0.263

8.93

0.313

12.72

0.224

7.62

0.414

Robust neural networks

the various independent variables and team effectiveness. In organization behavior, an R2 of 0.313 would be an indicator of a very good model. In addition, with a lower MSE and SSE the robust model is even more valuable in that it offers more accurate predictions to managers. Approximately, a third of the variance in team effectiveness can be explained by fitting a robust regression model. 5.3. Neural networks

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Neural networks were employed to model nonlinear data that might be prone to outliers. To obtain a better fit, neural network analyses require experimentation by varying their structure. The first two thirds of the data set were used to train the neural networks. We experimented by modifying the structure by specifying a range of the proportion of outliers (0–30%) and the number of hidden nodes (4 onwards). Our experimentation finally yielded an optimum neural network design generating the lowest MSE with a total of 30 hidden nodes and a specification of outliers at 20% of the data. Using this

network trained on the first two-thirds of the data set, it was then possible to obtain the MSE, SSE, and R2 for the remaining one-third of the team data. The network yielded an MSE of 0.224, SSE of 7.62 and the R2 value increased to 0.414. Given the significant increase in R2, we can see that the neural network analysis models the relationship between organizational context of teams, inter-team processes, inter-team processes, team size, and effectiveness much better than the robust regression or standard regression. Given the optimum neural network structure, we then mapped out expected team effectiveness against all possible permutations of independent variables. Thus, the neural network was able to model a variety of non-linear relationships among the four independent variables and one dependent variable. To provide a feel of the non-linear patterns we plotted the expected team effectiveness against two independent variables at a time. Figs. 3–8 map out a number of relationships between the dependent and independent variables; the plots indicate the degree of non-linearity within the data.

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A linear pattern of two independent variables on team effectiveness would be seen as a flat plane. This

can be seen in Fig. 3, where the interaction between inter-team processes and organizational context of

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teams seems to have a linear effect on team effectiveness. Thus, as both inter-team processes and organizational context increase, team effectiveness also improves at a relatively linear rate. In addition, the figure indicates that the two sides of the plane are not parallel. This suggests that a certain degree of interaction can also be found between the two independent variables. A small amount of non-linearity between the independent variables and team effectiveness can be seen by the degree of curvature in Figs. 4 and 5. For example, in Fig. 4, we can see that as the scores on organizational context and intra-team processes increase, effectiveness also increases. However, the rate of change in team effectiveness for the two variables varies. This variation is

extracted and graphed in Fig. 6 which presents the rate of change in team effectiveness by intra-team processes and organizational context. Fig. 6 indicates that at low levels of intra-team processes, the rate of change in team effectiveness decreases. At moderate levels, it increases and then decreases again at high levels. These findings suggest a small degree of non-linear behavior and emphasize the importance of training team members in group processes. For example, researchers (Buckenmeyer, 1996) have found that even when team members have undergone some training in group processes (low levels of intra-team processes), they are often at a loss when faced with disruptive behavior in team meetings. However, as the amount and level of training increases, team members who have been

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extensively trained in effective communication and norm-setting (moderate levels of intra-team processes) are better able to manage their meetings and deal with disruptive situations. Fig. 6 also suggests that the rate of change in team effectiveness decreases at high levels of intra-team processes. Perhaps at high levels, an excessive focus on intra-team processes occurs at the expense of task focus, decelerating team effectiveness. Similarly, Fig. 6 indicates that at low levels of organizational context, the rate of change in team effectiveness is small. As the scores on organizational context increase, the rate of change in team effectiveness also increases. Organizational context refers to the transfer of resources to the team, along with management support and facilitation of team processes. Unfortunately, managers are often reluctant to provide resources to struggling teams, or provide only limited resources, based on an assumption that the teams are unable or unwilling to manage those resources efficiently (Wageman, 1997). Similarly, organizations often use a mixed reward design (half the reward based on individual effort and half to the team as a whole), assuming that team members need to be gradually introduced to the concept of interdependent rewards. Unfortunately, as indicated in Fig. 6, limited resources and mixed rewards (low levels of organizational context) increase team effectiveness marginally. It is only when the amount of resources provided to teams increases and a higher proportion of the reward is based on team as opposed to individual effort (moderate levels of organizational context) that team effectiveness increases substantially.

Figs. 7–9 show the interaction of team size with the other three independent variables. The resulting patterns are non-linear as can be seen by the curvilinear (as opposed to flat) planes. In these three figures, the patterns are twisted, wavelike shapes; this indicates that not only does the rate of change of team effectiveness vary, but the curves change from concave to convex, that is, inflection points also exist. As team size increases, the rate of change in team effectiveness initially decreases, then increases, and finally decreases again. The inflection points vary according to the influence of organizational context, intra-team processes, and inter-team processes. These results demonstrate the ability of neural networks to capture higher order non-linear patterns. Finally, Fig. 10 is a plot of the influence of team size on the team’s effectiveness. As we can see in the plot t is a ‘‘U’’ shaped curve, where the poorest performance occurs when the team size is around 10. Thus a manager allocating teams within an organization should ensure that the team size is much smaller than 10. Team sizes much larger than 10 were are also effective, perhaps because larger teams often tend to break up into sub-groups of four to seven members to do their work. The influence of inter-team, intra-team and organizational context also tend to be more pronounced in this larger range. More complicated non-linear patterns captured by neural networks on three or more independent variables exist, but cannot be graphically displayed given our inability to plot in four dimensions. These non-linear effects and the interactions among the

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variables, however, can safely be captured by the neural networks structure. 6. Discussion In this paper we extend the previous research on neural network applications in the productions/ operations, finance, marketing, and information systems areas to the organizational behavior context. Our findings suggest that neural network analyses can identify complex, non-linear patterns in the data. As the data set becomes more complex, the advantages of this technique over standard statistical techniques become more evident. Neural network analyses provide a mechanism to simultaneously model large complex organizational systems, while encapsulating the non-linear effects and protecting against the possibility of outliers. Traditional research in organizational behavior often focuses on separate individual pieces of large complex systems. In this paradigm, establishing strong relationships is often viewed as critical. Researchers may be reassured by the marginally significant values that are found with regression analyses or correlation coefficients. However, potentially inaccurate information obtained from studies using standard statistical techniques could be disseminated to the scholarly and practitioner community, affecting the practices adopted by practitioners and the techniques used for solving organizational problems. For example, misinterpretation of relationships between work team characteristics and team effectiveness during organizational impact studies may result in unnecessary costs or problems with

team implementation, ultimately decreasing organizational effectiveness. Researchers often do not seem to question whether the traditional piecemeal approach to analyzing organizations is appropriate. Because of this many researchers might, unfortunately, miss out on the big picture if the organization exhibits dynamically complex behavior. Such complexity might result in non-linear data populated with outliers. Our research shows that the least squares regression method provides a relatively good fit (R2 = 0.247) and yields a MSE of 0.290 on the testing data. By accounting for outliers using a robust regression we can significantly improve the model; the R2 jumps to 0.313 and the MSE falls to 0.263. This improvement in the model is accomplished through only a little more effort. In addition, the robust regression indicates which of the teams are significantly ineffective given the specific independent variables. Thus, this technique can be used by organizations as a diagnostic tool to identify and scrutinize dysfunctional teams – and to figure out how to improve team effectiveness. As demonstrated by our results, the two linear procedures are unable to capture non-linear patterns such as the effect of team size on effectiveness. By using neural network analyses we were able to not only improve the fit significantly, but also establish non-linear relationships among a number of variables and their interactions. This is also seen by the significant increase in R2 over the robust regression model (from 0.313 to 0.414). Although it is possible to transform non-linear data into linear data by using techniques such as log transformation

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and then employing standard linear regression to map out the relationships, such methods are not recommended. As we can see in our non-linear plots (Figs. 7–9), it is almost impossible to know in advance the type of pattern and then find the proper transformation equation. For example, the literature suggests that the optimum team size for effective work processes is four to seven members (Brightman, 1988; Ray and Bronstein, 1995), that is, the influence of team size on effectiveness follows an inverted ‘‘U’’-shaped curve. But, as we see in Figs. 7–9, the interactions between team size and the other three independent variables yield much more complicated patterns. These patterns can be described as twisted wavelike shapes. As the team size increases, effectiveness initially decreases, then increases, and finally decreases again, suggesting that the often-quoted ‘‘four to seven member’’ team may not be the only effective one, but that much larger teams may also be effective. This issue needs to be further examined in the team literature. In addition, the rate of change in team effectiveness and the minimum point vary depending upon the influence of organizational context, intra-team processes and inter-team processes. Hence, our findings advance the research on team size to a new level. ‘‘One size fits all’’ teams may not be the most effective ones; rather, optimum team size may depend on numerous factors such as the level of resources provided to the team, the extent and type of group processes, and the extent of coordination and communication between the team and other organizational entities. As such, our findings highlight the difficulties inherent in managing complex team-based organizational designs. Teams may be highly beneficial if implemented correctly, but might not provide the expected increases in effectiveness if incorrectly implemented. One of the limitations of using neural network analysis is that this technique is inductive in nature as opposed to being deductive. As such, neural network analysis might not be suited for the traditional hypothesis testing used in theory development. Rather, as an inductive tool, it provides clues to the types of underlying patterns and the types of data transformation necessary. As such, this can be an excellent technique for inductive and exploratory research. If researchers want to confirm theories they can then use deductive approaches on the transformed data. Another drawback in using neural networks is that practicing managers might find

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it difficult to understand the complexity of neural networks. Only some of the larger corporations with dedicated research staff would have the luxury to conduct such analyses. However, we do see a tremendous potential of this technique in indirectly helping managers to understand complex organizations and to improve their performance. Although the use of neural network analyses comes at a cost, the benefits are worth the extra expense. Neural networks do require relatively larger data sets, experimentation, and significant amounts of computational time (although given the increasing clock speeds of computers today, the last issue becomes significantly less important). At the same time, the extra time spent on experimentation is certainly well worth the effort. The amount of time researchers spend on data collection should be correspondingly balanced by the amount of time analyzing the data – it would be a pity if researchers spent months on data collection only to see their effort wasted due to lack of sufficient analyses to account for outliers and non-linear behavior. Neural networks could have several benefits for researchers in organizational behavior. Future research could include a reexamination of earlier data sets where linear models have proven inconclusive. Perhaps, non-linear patterns might be lurking in the background which might be finally exposed. In addition, established relationships reported in the literature also should be reexamined in light of this new method. For example, as we saw in Fig. 10 that contrary to the expectations of an inverted ‘‘U’’ shape curve a very different pattern was found. There was a U-shaped curve, but it was not inverted. To simplify the process of uncovering those hidden or masked relationships for researchers in organizational behavior a two-step approach is recommended. The first step would be to use robust regression instead of the standard least squares method given its simplicity. If non-linear behavior is suspected or if researchers have trouble establishing significant relationships, then robust neural networks can be utilized as the second step. The results of this study can also be useful to organizations in both the private and public sectors. Organizations planning to implement teams or use team-based interventions to improve work processes need to ensure that the underlying models used to design the interventions are accurate and build in the true realities of organizations. A piecemeal approach that does not build in the interactions

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and non-linear effects could, potentially, result in ineffective teams; any diagnostic tool based on such an approach might not yield successful results. In this research we demonstrate that using neural networks helps us model team behavior more accurately. In addition, obtaining team effectiveness scores through the network for most permutations of independent variables allows us to diagnose the expected performance of a team in an industry. Organizations can use this diagnosis to evaluate the effectiveness of teams and direct changes in team configuration for improved performance. 7. Conclusion The use of standard linear techniques may become unreliable when the underlying data has non-linear patterns and is populated with outliers. In this study, we demonstrate that robust neural networks have the capability to model a variety of underlying processes better than the standard procedures. This should allow us to better predict outcomes of complex organizational systems such as team-based organizations. The additional computational effort required by neural network analyses would certainly be compensated by the improved predictability of complex systems in organizations where even a one-percent improvement could yield millions of dollars. References Alexander, J.A., Lichtenstein, R., Jinnet, K., Aunno, T.A., 1996. The effects of treatment team diversity and size on assessments of team functioning. Hospital and Health Services Management 41, 37–53. Ancona, D.G., 1990. Outward bound: Strategies for team survival in organizations. Academy of Management Journal 33, 334–365. Beckman, R.J., Cook, R.D., 1983. Outlier. . .. . .s. Technometrics 25, 119–149. Bishop, C.M., 1995. Neural Networks for Pattern Recognition. Oxford University Press, New York. Booth, D.E., 1982. The analysis of outlying data points by robust regression. A multivariate problem bank identification model. Decision Sciences 13, 72–81. Booth, D.E., Alam, P., Ahkam, S., Osyk, B., 1989. A robust multivariate procedure for the identification of problem savings and loan institutions. Decision Sciences 20, 320–333. Brightman, H.J., 1988. Group Problem Solving: An Improved Managerial Approach. Georgia State University Press, Atlanta, GA. Buckenmeyer, J.A., 1996. Self-managed teams: Some operational difficulties. Industrial Management 38, 10–15. Bunke, H., Bunke, O., 1989. Nonlinear Regression, Functional Relations and Robust Methods, Statistical Methods of Model Building, vol. II. John Wiley & Sons, New York.

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John Grznar is Assistant Professor of Management at the University of Illinois at Springfield. He has conducted research in the area of robust neural networks. Sameer Prasad is Professor of Operations Management at the University of Wisconsin at Whitewater, USA. He has studied topics in robust statistics, artificial intelligence, inventory theory and international operations management. His research has appeared in Decision Sciences, Omega, Journal of Operations Management, European Journal of Operational Research and elsewhere. Jasmine Tata is Associate Professor of Management at Loyola University, Chicago. She has conducted research in the areas of research methods, team management and organizational behavior, and has published in the Journal of Management, Journal of Managerial Issues, and elsewhere.