Identifying Organizational Faultlines with Latent Class Cluster Analysis

Faultline theory proposes that when multiple attributes are aligned in groups they create homogeneous subgroups, characterized by within-group similarities and between-group differences. As homogeneity increases, these differences are increasingly likely to acquire meaning to subgroup members and thus to influence behavior. While the face validity of faultlines is theoretically appealing, empirical measures have been difficult. The most commonly used, Fau, D, and FLS, have been limited to small groups, two or at most three attributes, and do not easily integrate nominal, categorical, and continuous variables. This paper proposes latent class cluster analysis (LCCA) as an additional analytical tool. LCCA is useful for large groups, and facilitates analysis of numerous attributes independent of underlying distributions. After reviewing the multiple-attribute literature, the most common faultline measures are described and compared with LCCA. A study of faultlines in a large organization is presented. LCCA induces a five-class model of organizational faultlines. A comparison of work-related communication contacts indicates that subjects have more within-subgroup than betweensubgroup contacts, supporting the criterion-related validity of the faultline solution. Organizational Faultlines Page 3 Scholars have long been interested in the distribution of individuals’ demographic attributes in social systems. These distributions create a distinctive social context to which individuals respond. People with similar attributes, such as gender or age, tend to recognize themselves as distinct from others, often creating psychologically salient and socially meaningful groups that influence work. Research connects the demographic distributions characterizing such groups to a long list of individual, group and organizational outcomes including conflict (Pelled, Eisenhardt, & Xin, 1999), turnover (Elvira & Cohen, 2001), performance (Cannella, Park, & Lee, 2008), corporate foreign investment (Barkema & Shvyrkov, 2007), career mobility (L. E. Cohen, Broschak, & Haveman, 1998) and salary (Castilla, 2008). Although many studies focus on the distribution of one demographic attribute, others, such as faultline research, involve more. Faultline theory (Lau & Murnighan, 1998) proposes that the distribution of demographic attributes creates subgroups in small social systems, such as work groups. The more closely attributes are aligned, the stronger the faultline. These alignments produce a structural constraint on relationships that maximizes similarities within and differences between subgroups by priming the aligned attributes, increasing their salience for group members. As a result, faultlines represent the boundaries separating behaviorally-meaningful subgroups. Li and Hambrick (2005), for instance, examined factional faultlines in the top management teams of 71 international joint ventures. They found that increasing faultline size, as measured by the age, tenure, gender and ethnic differences between expatriate and local managers in each team, was related to increasing emotional and task conflict. The distinguishing feature of faultlines is the assumption that individuals’ attributes acquire meaning interdependently. In other words, faultlines are identified by the joint distribution of several attributes rather than the individual distributions of each. This Organizational Faultlines Page 4 interdependence distinguishes faultline theory from many multiple attribute approaches, which assume independence and measure additive or averaged distributional effects (e.g., Urada, Stenstrom, & Miller, 2007). Such independent effects are relatively easy to study with standard techniques such as regression and analysis of variance. However, interdependence presents measurement issues that have limited the development of faultline research and theory. This study examines latent class cluster analysis (LCCA) as a method for identifying an organization’s faultlines, alignments of individual attributes that define relatively large, meaningful subroups conditioned by how individuals perceive their organization. LCCA provides an alternative to existing methods. It permits inclusion of many attributes at a time and facilitates study of nominal, categorical and continuous attributes in the same analysis, a difficulty noted in previous work (Lau & Murnighan, 1998). In addition, it is suited for analyzing large social systems, such as organizations. The discussion below is organized as follows. We begin with a review of existing multiple attribute theories that assume interdependence, focusing on their similarities and differences in identifying attribute-based subgroups. This is followed by a longer evaluation of existing faultline measures, focusing on identification rather than on strength or distance. We conclude with an empirical study of a large organization. We use LCCA to identify organizational faultlines and then provide criterion-related validity using work-related communication contacts within and between the subgroups these faultlines define. Multiple Attribute Interdependence Support for faultline theory appears across several disciplines, with some studies emphasizing psychological mechanisms and others focusing on structural explanations. Distinctiveness and crossed-category theory emphasize psychological mechanisms as producing multiple attribute effects. Distinctiveness theory (McGuire, McGuire, & Winton, 1979) suggests Organizational Faultlines Page 5 that when presented with a substantial quantity of complex information, individuals selectively perceive attributes that appear distinctive within the social context. In an organizational context, when an individual belongs to two minority groups, he or she will identify more strongly with the smaller of the two groups. Mehra et. al (1998) examined a second-year class of MBA students in which white men represent 60%, white women represent 28%, and minority men and women represent 6% each of the study population (sample N=159). They asked students to indicate with whom they identified and who were their friends. Whites were more likely to identify and be friends with others on the basis of sex rather than race; for Whites, sex is a more distinctive attribute than race. In contrast, minorities were more likely to identify and be friends with others on the basis of race rather than sex; for minorities, race is the more distinctive category. In each case, students connected with others using the most, rather than least, distinctive of their own attributes. This differs from an additive approach because it suggests that individuals alter their behavior with others depending on the distribution of those attributes in their social context. Crossed-attribute categorization presents a related approach to multiple attribute interdependencies. When individuals share more than one attribute and when no one attribute is dominant, crossed-attribute categories emerge (Ashforth & Johnson, 2001; Vescio, Hewstone, Crisp, & Rubin, 1999) such as gender-age (Klauer, Ehrenberg, & Wegener, 2003). Although this literature typically involves dyads rather than groups, the results are suggestive. Urada et al. (2007) propose a feature detection strategy, consistent with distinctiveness theory, suggesting that people use similarity thresholds for evaluation. When individuals perceive a target as enough-like-me, the target gets defined as an ingroup member, independent of the number of attributes involved. This contrasts with an additive approach, in which each homophilous Organizational Faultlines Page 6 attribute increases individuals’ similarity perceptions. The feature detection strategy is particularly relevant to organizational decisions that relate to performance, such as promotions and salary. Managers evaluate employees in a salient social context in which correlated attributes acquire significant meaning because they are related to performance. Intersectionality and consolidation theory emphasize structural explanations as the mechanism producing multiple attribute effects. These explanations suggest that multiple attribute effects result because the distribution of attributes in a population both constrains and facilitates individuals’ opportunities to become aware of and develop relationships with one another. This does not exclude psychological mechanisms, but it emphasizes that these mechanisms are strongly influenced by the relationships among the demographic attributes that define social context. For instance, Black and feminist sociologists use intersectionality to explain the joint effects of gender and race (Browne & Misra, 2003). In this work, intersecting categories are socially constructed through historical or local social contexts: “Race is ‘gendered’ and gender is ‘racialized,’ so that race and gender fuse to create unique experiences and opportunities for all groups—not just women of color” (2003, p. 488). These experiences are shaped by ideology, control of economic and political resources and the unequal distribution of valued resources across subgroups. This approach is consistent with Blau’s concept of consolidation (1977), the strength of the positive relationship among attributes (p. 276). Blau (1977) suggests that a social system’s heterogeneity and inequality are defined by the distribution of individuals’ multiple attributes. As consolidation increases, the number of groups comprising the social structure decreases, and this decreases intergroup social interactions. Decreased intergroup interactions produce both fewer cordial and fewer conflictual associations. Thus, structural opportunity represents the basic Organizational Faultlines Page 7 mechanism by which multiple attributes influence behavior. Consolidated nominal attributes, such as gender or ethnicity, produce lower heterogeneity; consolidated graduated attributes, such as age and tenure, produce higher status differences. Faultline theory suggests a mixture of social psychological and structural mechanisms. Lau & Murnighan (1998) define faultlines as boundaries or break points identified by the alignment of one or more individual attributes that separate a group into distinct subgroups that hold meaning for their members. This approach emphasizes the structural opportunity created by intersecting multiple attributes as well as the psychological identities that facilitate meaningful subgroups. When people identify themselves by attributes such as age, race, and gender, they are likely to psychologically-orient themselves towards others who share those attributes. Attributes that are both salient and apparent to group members are likely to drive subgroup formation (Lau & Murnighan, 1998, p. 328). As similarities within and differences between clusters of individuals are found along more and more attributes, the potential for intra-cluster alignment and inter-cluster difference increases. This literature is at an early stage of development and appropriate measures are still emerging. Our focus is on identifying faultlines in large social systems and assessing the validity of the subgroups they create. Organizational Faultlines vs. Workgroup Faultlines In this study, we examine whether LCCA identifies sets of aligned attributes that define meaningfully-distinct subgroups of individuals in a large organization. This analysis differs from earlier faultline work because the focus is on large social systems rather than on small groups. The theoretical rationale for organizational faultlines and their effects remains similar to that associated with extant faultline research: aligned attributes produce subgroups that are sociallymeaningful to subgroup members and this produces distinct within-subgroup and betweenOrganizational Faultlines Page 8 subgroup behavior. However, there are several differences that complicate and perhaps prohibit organizational faultline analysis using existing methods. One is that members of small groups are typically known, whereas the boundaries of larger, informal social structures are less clear. In small groups, everyone knows everyone else, and while members may not know their subgroup boundaries, they do know which individuals define the group (although see Mortensen, 2008). In large organizations, individuals do not know everyone and the people they do know are unlikely to represent a random sample. These nonrandom others constitute an individual’s organizational reference group, the apparent “organization” as he or she perceives it (Lawrence, 2006). Organizational reference groups include all the others of whom an individual is aware, including close, distant, and no associations. This awareness criterion suggests that an individual’s organizational reference group represents a portrait of the organization as he or she observes and experiences it. Thus, if we identify faultlines in the collective set of individuals’ organizational reference groups then subgroup membership is likely to be meaningful. Another difference involves the size of the subgroups created by faultlines. Organizational faultlines identified in this collective of organizational reference groups should define discrete subgroups similar to those in the existing literature. However, in contrast to that literature where subgroups represent small segments of already small groups, organizational faultlines are likely to create large, discrete subgroups, which exceed the size of small groups and perhaps even of small organizations. As a result, the mechanisms that operate within and between these subgroups provide a picture of a larger, informal social structure than the subgroups identified within work groups. Extant Methods for Identifying Faultlines Organizational Faultlines Page 9 A central characteristic of faultlines is that they are latent, unobserved or informal boundaries, which by definition define latent, unobserved or informal subgroups. Lau and Murnighan (1998) suggest that faultline strength increases with the increasing homogeneity of the subgroups they create—thereby increasing the probability that subgroup membership will influence individual behavior. Such homogeneity is conceptualized using both the similarity among individuals’ attributes within a given subgroup and their collective differences from those in another subgroup. Thus, the homogeneity associated with faultline identification is indexed by examining the proportion of between-subgroups variance to within-subgroups variance. The current faultline literature includes several approaches to measuring homogeneity. The majority of these studies involve experimental methods, in which faultlines and subgroup boundaries are defined a priori (cf. Homan, et al., 2008; Homan, van Knippenberg, Van Kleef, & De Dreu, 2007; Lau & Murnighan, 2005; Pearsall, Ellis, & Evans, 2008; Polzer, Crisp, Jarvenpaa, & Kim, 2006; Rico, Molleman, Sanchez-Manzanares, & Van der Vegt, 2007; Sawyer, Houlette, & Yeagley, 2006). However, several faultline measures have been proposed for situations where subgroup boundaries are unknown. Although their computational capabilities are still being developed, at present, each measure has several empirical limitations (See Table 1). They have been restricted to small social systems, such as work groups. They accommodate analyses of small numbers of attributes, generally two or three, because the methods become substantially more intractable as the number of attributes increases. Further, when mixing nominal, categorical and continuous variables, they require categorizing or weighting the variables in terms of their relative importance in faultline formation, which requires a number of assumptions. LCCA addresses many of these issues, suggesting an alternate method for identifying faultlines. Organizational Faultlines Page 10 ---------------------------------Table 1 About Here ----------------------------------Lau and Murnighan (1998) Although Lau & Murnighan (1998) do not provide a method for identifying faultlines, they do discuss the analytical issues. They suggest that “measures of demographic diversity within a group must be dispersion indexes” (1998, p. 327), such as a modification of Blau’s measure of diversity or others based on Euclidean distances across people. They also state that such measures should not combine nominal, categorical, and continuous measures because it “would be like cross-fertilizing apples and oranges” (1998, p. 327). This separation of categorical and continuous measures likely represents empirical limitations of existing dispersion indices rather than theoretical exclusion. Thatcher, Jehn, and Zanutto (2003) In the first work to develop a method for determining faultlines, Thatcher, Jehn, and Zanutto (2003) proposed Fau, which is a measure of the “percent of total variation in overall group characteristics accounted for by the strongest group split” (p. 225). Essentially, Fau is the proportion of between-subgroups variance to total variance, and can be shown as p 2 ∑ ∑ nk (y.jk – y.j.) Faug = j=1 k=1 g = 1, 2, ... S (1) p 2 nk ∑ ∑ ∑ (yijk – y.j.) j=1 k=1 i=1 where yijk is the value along the jth attribute for the ith member in the kth subgroup, y.j. is the mean of the jth attribute, y.jk is the mean of the jth attribute in the kth subgroup, n is the number of people in a known group, p is the number of attributes along which the group members have Organizational Faultlines Page 11 been measured, and nk is the number of people in the kth subgroup of the gth split into subgroups. Fau is then calculated for S many splits g, where S = 2 – 1 – 1 (2) Following the computation of Fau for all the g splits, Thatcher et al. (2003) recommend choosing the group split that produces the largest overall proportion of between-subgroups to total variance. This split, in which Faug is closest to 1.0, represents the faultline and defines the two subgroups. Fau thus reflects faultline theory by incorporating the ideas that faultline strength and its impact on behavior increases with the increasing homogeneity of subgroups. Thatcher et al. (2003) recommend using Fau to identify one faultline and two subgroups when examining known groups (see Lau & Murnighan, 2005 for application in experimental design). They acknowledge that Lau and Murnighan’s (1998) original conceptualization of faultlines allows for more than one faultline and more than two subgroups. However, they (2003) suggest identifying only one faultline for two reasons. First, groups frequently include only a few individuals, making more than two meaningful subgroups unlikely, and second, the computational complexity of Fau increases greatly with more than one faultline. Authors using this work have maintained this perspective (e.g., Molleman, 2005). Somewhat in opposition to Lau and Murnighan’s (1998) recommendations, Thatcher et al. (2003) propose a Fau scaling scheme that allows the simultaneous use of continuous and noncontinuous attributes. This scheme is designed to assign equal weights to differences across people along continuous and non-continuous variables. To accomplish this, Thatcher et al. (2003) recommend turning any non-continuous variables with c categories into c variables that are dummy coded (0 or 1/√2) to express individuals’ standing along the variable of interest. The exception occurs when c = 2, in which case there is only a single dummy-coded variable. Organizational Faultlines Page 12 Dividing the usual dummy-code of 1 by √2 allows a difference between two people along the categorical variable to count as 1 unit of difference when summing across all attributes. Continuous variables are divided by a value that is specific to a given attribute and based on a researcher’s theory regarding the importance of a given distance along the variable. For example, if a researcher thought that 10 years of difference in age was equivalent to a difference in gender, then the researcher would divide all individuals’ ages by 10. This would allow a difference of 10 years in age to have the same weight in Fau as any difference along non-continuous variables. Thatcher et al. (2003) acknowledge the large amount of subjectivity in this process, but see it as a necessary requirement for discerning faultlines. Although Fau has been limited to small groups, a recent modification may facilitate its use in larger populations, such as organizations (K. Bezrukova, personal communication, August 11, 2009). Shaw (2004) Another method for identifying faultlines was outlined by Shaw (2004). Shaw bases his measure on the idea that people perceive continuous attributes in meaningfully discrete categories. For example, in some contexts anyone between the ages of 20 and 35 may be considered “young.” As he notes, “a substantial body of literature suggests that cognitive categorization processes naturally occur when individuals of different characteristics interact in groups” (2004, p. 70). Researchers accomplish this either by using extant research to deduce meaningful categories or by using an empirical approach to induce them, for example by asking participants about the cognitive categories they use to classify others. Faultlines are then assessed by examining the “internal alignment” (IA) of a given variable, defined as “the extent to which members within a particular subgroup are similar to one Organizational Faultlines Page 13 another on all other relevant variables” (Shaw, 2004, p. 72). This is done by comparing observed attribute distributions to expected null distributions across the categories of other variables where m IAA1/B/OBS = ∑(OA1c – EA1c)/EA1c (3) c=1 IAA1/B/OBS is the observed internal alignment for a category 1 (e.g., males) for a variable A (e.g., gender) across all of the m categories of a variable B (e.g., Caucasian and African-American for a variable Race), OA1c is the observed number of people in a category 1 (e.g., males) for a variable A (e.g., gender) in the cth category (e.g., caucasion) for a variable B (e.g., race), and EA1c is the expected number of people in a category 1 for a variable A in the cth category for a variable B—with the assumption that such an expectation takes the form of a random distribution. By summing across all m categories, that is by summing across each c, and after taking the square of the distance between O and E, one has computed the sum of the squared differences between the observed and the expected data. Dividing this sum by E allows IAA1/B/OBS to equal the ratio of the squared differences between observation and expectation to expectation and is analogous to the computation of a χ statistic. This means that the ratio describes the distribution of individuals within category 1 (e.g., males) of variable A (e.g., race) across all m categories of variable B (e.g., across all of the race categories). The ratio moves towards 0.0 as individuals within category 1 of variable A tend to be randomly distributed across the categories of variable B. The ratio increases above 0.0, heading towards “perfect alignment,” as people within category 1 of variable A become more systematically distributed across the m categories of variable B. However, IAA1/B/OBS is not yet useful for faultline assessment because IAA1/B/OBS only indexes a ratio of squared deviations and does not take into account the maximum and minimum Organizational Faultlines Page 14 internal alignments that are possible. It is important to do this because these values change with different numbers of people in a given group and with different numbers of categories for any variables of interest. These issues are solved through the following IAA1/B = (IAA1/B/OBS – IAA1/B/NONALLIGN)/MaxDiff (4) where MaxDiff = IAA1/B/PERFECT – IAA1/B/NONALLIGN (5) and IAA1/B/NONALLIGN is the internal alignment score when there is perfect nonalignment for individuals within a category 1 along a variable A across the m categories of a variable B IAA1/B/PERFECT is the internal alignment score when there is perfect alignment for individuals within a category 1 along a variable A across the m categories of a variable B, and, thus, MaxDiff represents the possible range of internal alignment scores. Therefore, IAA1/B is the ratio of observed internal alignment to the possible internal alignment score. To derive the average alignment score across all of the categories of a variable A, researchers may then compute the average internal alignment score, IAA/B, across all categories of variable A. In an example with three categories of the variable A IAA/B = (IAA1/B + IAA2/B + IAA3/B)/3 (6) This may further collapse across multiple other variables beyond B with, for example, IAA = (IAA/B + IAA/C + IAA/D)/3 (7) and may integrate across all variables with, for example, IAOVERALL = (IAA + IAB + IAC)/3 (8) Beyond this intuitive understanding of internal alignment scores, it is important to consider that IAA/B, IAA, and IAOVERALL are not the only values required to understand faultlines. This results because IA references only the degree to which individuals within a given category, Organizational Faultlines Page 15 or multiple categories, are aligned across other categories. It does not provide insight into the degree to which individuals in other categories have similar cross-category memberships. This is important because, according to Lau and Murnighan (1998), to the extent that the people outside of category 1 of a variable A share the same membership along a variable B as the people inside of category 1 of a variable B, the IA score of the people inside category 1 of variable A will be less meaningful. Therefore, it is important to consider the “cross-subgroup alignment index” (CGAI), which is defined as the degree of similar category memberships (e.g., being in the cth category of a variable B) for people in different subgroups (e.g., people in category 1 versus 2 for a variable A), where CGAI ranges between 0.0 and 1.0, that is, no cross-subgroup alignments versus perfect cross-subgroup alignments, respectively. When CGAI is low it means that the IA score of a subgroup is more meaningful than when CGAI is high. Shaw (2004) recommends weighting IA as follows FLS = IA · (1 – CGAI) (9) with a more specific formula being expressed as FLSA = IAA · (1 – CGAIA) (10) and with an overall formula FLSOVERALL = IAOVERALL · (1 – CGAIOVERALL) (11) where all terms may be understood as previously mentioned. In sum, Shaw (2004) outlines a method for the computation of values of the internal alignment of attributes within subgroups and a method for their aggregation and weighting. Li and Hambrick (2005) A recent article by Li and Hambrick (2005) explored faultlines in 71 top management teams participating in joint ventures. The teams they studied each involved two known, factional Organizational Faultlines Page 16 subgroups: one consisting of local managers and the other of expatriates. Starting with these known factions, Li and Hambrick (2005) outline a computational logic to compare the further differences of these subgroups along four attributes: age, gender, tenure and ethnicity. This logic computes the faultline size between the two factional subgroups, which they describe as having a large value when “two factions differ in their averages [along a given attribute] and each faction is tightly clustered around its own average” (p. 804). This definition is equivalent to the criterion of subgroup homogeneity as a precondition for faultline identification, meaning that Li and Hambrick’s (2005) faultline size is similar to Lau and Murnighan (1998)’s faultline strength. To measure faultline size, Li and Hambrick (2005) modified the well known d statistic (see J. Cohen, 1988) as a “demographic difference” d with the following formula | XA – XB | σA σB 2 where d1 is the demographic difference between two subgroups along a variable 1, XA is the mean along a variable for a subgroup A, XB is the mean along a variable for a subgroup B, σA is the standard deviation of a variable A, σB is the standard deviation of a variable B, and a constant is added to the denominator to assure that d is a real number when σA and σB are both equal to zero. This formula allows for the computation of d for either continuous or dichotomous variables. Further, by combining across multiple variables researchers may compute an overall faultline score for a given group. However, to do so, Li and Hambrick (2005) recommend first standardizing the ds for each variable, such that each group’s d for a given variable is a standardized deviation away from the average d across all groups for that variable. Bezrukova, Jehn, and Zanutto (2009) + 1 d1 = (12) Organizational Faultlines Page 17 A final technique is presented by Bezrukova, Jehn, and Zanutto (2009). These authors explore the difference between faultline strength and faultline distance, suggesting that faultlines are multidimensional. They note that faultline strength captures the alignment of demographic or other attributes within a group, whereas faultline distance references the magnitude of the difference between subgroups along the attributes of interest. To measure faultline strength, they use Fau, because it is a measure of the ratio of between-subgroups to total variance. As a result, Fau captures the homogeneity of subgroups (i.e., the cleanness of their split). To measure faultline distance between subgroups identified with Fau, they suggest taking the Euclidean distance between the centroids of the two subgroups’ multivariate distributions for the attributes in question. In other words, they examine the distance between the vector of means for the variables that have been used in the computation of Fau (Molleman, 2005). This can be shown as p Dg = ∑ ( y1j. – y2j. ) (13) j=1 where Dg is the multivariate distance between the two subgroups, that is, the difference in their centroids, y1j is the mean for a subgroup 1 along the jth attribute, and y1j is the mean for a subgroup 2 along the jth attribute. To find Dg requires summing across all of the p attributes. By taking D and Fau separately, Bezrukova et al. (2009) account for the possible multidimensional nature of group faultlines. Fau describes the proportion of the variance between the subgroups in relation to the total variation, which is insensitive to the actual distance between the subgroups on the measures of interest. D describes the actual distance between the subgroups along the attributes of interest, which is insensitive to the proportion of variance this Organizational Faultlines Page 18 distance accounts for in relation to the total variance. Forming the interaction between Fau and D allows modeling the joint effect of these two aspects of a group’s faultline. Similarities and Differences Across Faultline Measures These measures of faultlines have both similarities and differences. All of them, except d, begin with the assumption that true faultlines within a known group are unknown or latent. Two of them, Fau and FLS, make the simplifying assumption that each group has only one or at most a few faultlines. For instance, Thatcher et al. (2003, p. 447) propose there is likely one meaningful faultline in any known group. As a result, they recommend using the faultline that allows the greatest ratio of between-subgroups variance to total variance across multiple attributes for two subgroups. Alternately, Shaw’s (2004) method requires the formation of subgroups along each attribute based on categorical differences across the attributes of interest. By adding Dg to measure faultlines in conjunction with Fau, Bezrukova et al. (2009) acknowledge that Fau only measures proportions of variance, and so they recommend the incorporation of a measure of the actual distance between the subgroups along the variables of interest with Dg. This is also inherent in Shaw’s (2004) FLS, but in a different manner. Shaw captures the degree to which individuals in a subgroup are aligned across multiple variables with his IA score. This captures within-subgroups variance, but weights the information about variables with the degree to which individuals within other subgroups are misaligned with members of that subgroup. This weighting is done with CGAI, which can be thought of as capturing between-subgroups variance. While Shaw’s method differs from Fau and Dg, the logic of attempting to discern “the number of demographic attributes that group members align on” and “how far apart these aligned groups are from each other” (Bezrukova et al., p. 5) is also embedded within FLS. Organizational Faultlines Page 19 Another similarity among these methods is that none explicitly specify a model that best fits the observed data. Fau identifies a single faultline using the amount of between-group variance it creates. The fit of any model to the original data is unknown outside an R statistic, which is similar to a fit assessment but limited to the one faultline. This assessment becomes increasingly complex when including discontinuous variables because, after transformation, fitting an estimated model to the original data is not possible. FLS computes an overall faultline score by examining attributes’ internal alignment. This requires categorizing continuous variables into discontinuous variables. FLS does not identify which individuals belong in which subgroups and, therefore, does not produce a model that can be compared to observed data. LCCA and Organizational Faultlines What Lau and Murnighan (1998) explore as a subgroup created by a faultline has been explored elsewhere as a “latent class” derived from a LCCA (LCCA; DiStefano & Kamphaus, 2006). A latent class is a group of individuals who exhibit more homogeneity as a cluster, along multiple attributes, than the known group from which they are drawn. This homogeneity is not directly observed but inferred. Statistically, this means that within a known group of individuals, there is likely to be linear dependence among their attributes, that is, unobserved heterogeneity. Lau and Murnighan describe this as “collinearity” among traits that are “correlated” (1998, p. 328) such that various people can be clustered together to form meaningfully homogenous subgroups. This fits with Lau and Murnighan’s statement that “group faultlines increase in strength as more attributes are highly correlated, reducing the number and increasing the homogeneity of the resulting subgroups.” (1998, p. 328). Flache & Mas (2008) provide an example operationalizing these ideas using a computational model. Organizational Faultlines Page 20 The LCCA procedure treats participants’ probabilities of membership in latent classes as missing. These probabilities are estimated in an iterative process that produces a model with the best fit to the observed data. With an interest towards model parsimony, models with different numbers of classes are compared along both statistical and substantive grounds (see Muthen, 2003) to choose a final latent class structure. Conveniently, LCCA allows for the integration of continuous and categorical variables without sacrificing any information in the variables—a linking function is used with non-continuous variables. This approach to clustering has benefits over more traditional forms, such as k-means cluster analysis, because the results are not adversely affected by the scale and variance of observed variables (see DiStefano & Kamphaus, 2006; Hagennars & McCutcheon, 2002). This is also true when comparing LCCA to the faultline methods discussed above where continuous variables must be made discontinuous or discontinuous variables must be transformed. Therefore, LCCA may be useful for faultline analysis because researchers are neither forced to make assumptions about the importance of variables, as required in Fau, nor required to categorize continuous variables, as in FLS. Although, LCCA can require more individuals than there are observed variables in some statistical packages, this is not a requirement with a full information maximum likelihood estimator (Enders, 2001; see similar thought in Hamaker, Dolan, & Molenaar, 2003). Large samples are required when generalizing to a larger population, with additional individuals allowing for more stable class enumeration and unbiased estimates. However, when such generalizations are not desired it is possible to use LCCA in small groups (see Barkema & Shvyrkov, 2007 for an example). As a result, LCCA is an ideal technique for uncovering faultlines in large groups such as organizations and small groups such as those studied in traditional faultline research. Organizational Faultlines Page 21