Secondly, LC models can also take into account the fact that item properties, such as item difficulty and discriminatory power of items, may diverge Vermunt, Thirdly, LC models do not depend strongly upon distributional assumptions Magidson and Vermunt, ; Vermunt and Magidson, which is important in this field. For the examination of the relationships between interpersonal conflicts, aggression and bullying items, the statistical software package Latent Gold 5.
LC analysis is a useful statistical technique for clustering individuals into subtypes within a population when there is no prior knowledge about which individual belongs to which subpopulation. This method is used to analyze multi-variate categorical data and model associations between observed variables that provide an imperfect measure of a non-observable latent variable.
LC analysis enables the researcher to identify mutually exclusive groups that adequately describe the dispersion of observations in the n-way contingency table of discrete variables i. The goal of traditional LC analysis is to determine the smallest number of latent classes, sufficiently explaining or accounting for the associations observed between the manifest variables all the items in our study Magidson and Vermunt, The traditional LC model Goodman, assumes that every observation is an exclusive member of one latent unobservable class and that local independence exists between the manifest variables.
LC analysis only assumes nominally distributed LC dimensions and binary or polytomous observations Rist et al.
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An important difference from traditional cluster methods like K -means clustering is that LC analysis is based on a statistical model that can be tested Magidson and Vermunt, As a consequence, determining the number of latent classes is less arbitrary than when using traditional cluster methods. In fact, LC analysis offers robust, empirically supported tests to determine the optimal number of classes.
The starting-point for a LC model is homogeneity, that is, every respondent resides in the same single group. This baseline model is a one-LCC model. In a LCC model, clusters of respondents with similar response patterns are subsequently added. A n-cluster model may then result in latent classes that differ in function of the nature and the frequency of reported social stressors.
The metric of this single latent variable is typically nominal. This would fit the assumption that aggressive behavior manifests itself in different shapes and doses. Instead of increasing the number of LCCs only, the number of latent variables factors may be increased as well, addressing, in our case, the degree to which these three measures are representing either one or, rather, multiple factors. The idea of defining a LC model with several latent variables started with Goodman , Haberman , and Hagenaars , who proposed restricted 4-class LC models yielding models with two latent variables.
Magidson and Vermunt labeled this type of LC models as LCF models because of the natural analogy to standard factor analysis. Like with traditional confirmatory factor models, a priori knowledge about the relationship between items and latent variables is needed Vermunt and Magidson, Moreover, with traditional measurement models, the discrete latent variable must adequately explain the initial relationship between the indicators.
In an LC model, every subject is assigned to only one cluster or class based upon the modal assignment rule that classifies a subject to the class with the highest classification probability. These membership probabilities are being calculated upon the estimated parameters of the measurement model Magidson and Vermunt, Evaluation of fit of LC models is not straightforward.
Firstly, the model fit needs to be evaluated. Secondly, the local fit has to be assessed and finally, the quality of the classification has to be scrutinized. After selecting a specific model, it is assessed whether it fits to the data. A model that does not fit to the data has a significant squared log-likelihood L 2.
However, for very sparse tables such as the ones we have, Langeheine et al. In addition to statistical fit measures, it is also important to inspect local fit and the quality of the classification. To evaluate local fit or misfit and its origin one may use bivariate residuals BVR. BVR show how much association between each pair of indicators remains, using the 1-cluster model as a reference. Ideally, the value should be lower than 3.
Finally, the quality of the classification is assessed. Here R 2 , entropy R 2 , and the total rate of classification errors, due to adjacent erroneous classifications, are indicators of mis classification. Given the large sample size in our study, both BIC and L 2 may lose their power to select the most appropriate model Paas, The proper use of these statistical fit measures has only been illustrated for samples with a maximum of respondents, leaving big data in the rain Paas, Because the evaluation of fit and the comparison of fit between the different measurement models are central to evaluate our first research hypothesis, we randomly selected six mutually exclusive subsamples from the overall sample to investigate which of the models had the best fit to the data.
6.2 Conflict and Interpersonal Communication
Thereafter, we applied this model to the entire sample and studied the relationships between the constructs and their criterion validity. Hence, we reject Hypothesis 1 and conclude that the items measuring interpersonal conflicts, aggression and workplace bullying, respectively, do not fit into one single and unified concept. Evaluation of fit: Bayesian information criterion across different competing measurement models and samples.
In addition, the BIC showed that any of the distinguished multi-dimensional factor models had a lower BIC than the single variable latent model. The most plausible model among these alternative measurement models was a two-LCF model Model 2a— CA-WB wherein bullying represents one factor with different classes, and wherein conflicts and aggression represent a second factor again with different latent classes. This model portrayed the lowest BIC in 5 out of 6 subsamples. The two-factor model with the lowest BIC across the six samples distinguished four latent classes for each factor.
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As one of the classes in the conflicts-aggression factor was relatively small 3. Apart from the previous model, this final model had the lowest BIC and its bootstrapped L 2 was also non-significant in 5 out of 6 samples, indicating that this measurement model statistically fits well to the data. The precise meaning of the latent classes of the two factors can be derived from the conditional probabilities. The dashed lines represent the classes of the conflicts-aggression factor whereas the full lines represent the classes of the bullying factor.
Conditional means plot. In the first class, neither conflicts nor exposure to aggression were reported. The bullying factor consisted of four latent classes. In the second class, there was a slightly higher, yet still low, frequency of reported exposure to the bullying items.
The two factors i. This tendency also seems to exist for bullying at work. This implies that the strength of the relationship between the two factors decreased as conflict, aggression, and bullying were reported more frequently. Bi-plot: relationship between conflict-aggression and workplace bullying and their indicators. However, when both behaviors become more frequent occasional and more often , their overlap decreased. To test the second hypothesis stating that conflicts, aggression, and bullying are similarly detrimental to those exposed, we disentangled the effect size of both factors in a multi-variate analysis of variance.
The partial eta 2 resulting from the multi-variate analysis of variance helps to understand the predictive value of the two factors in explaining the various criterion variables. After assessing the effect sizes of both factors, we further discerned the mean differences of the latent classes of both factors on the criterion variables. A Tukey pair-wise comparison procedure yielded that all pair-wise comparisons were significantly different from each other for all criterion variables. However, being classified as a target of bullying seems to be responsible for a further deterioration of job satisfaction etcetera as the z-values increase on average, with 0.
Hence, targets of bullying report significantly more detrimental outcomes than respondents who are most strongly exposed to interpersonal conflicts and aggression.
Construct proliferation is a major problem in the organizational sciences, and research on conflict, aggression, and bullying might not be immune to that problem Aquino and Thau, ; Hershcovis, ; Tepper and Henle, ; Hershcovis and Reich, However, existing research may not be fine-grained enough to distinguish clearly between the different concepts Tepper and Henle, We examined a set of competing LC models using a large heterogeneous sample of Belgian workers.
While comparing LC models, we found our data to not support an approach where labels could be used interchangeably i. From a statistical point of view, a two-factor model fitted the data best—with one factor comprising both conflict and aggression and another one comprising bullying. A three-factor model only provided the second-best solution. Hence, it appears that bullying is not only perceived differently than aggression and conflict but also seems to have a unique impact on employees, which seems to be especially detrimental for those employees that are highly targeted. Although more difficult to differentiate between the three types of social stressors for lower intensity levels, we found that when reported more frequently, interpersonal conflict, aggression and bullying cannot easily be construed as the same underlying phenomenon.
Moreover, the targets of severe bullying reported by far the lowest levels of well-being and the highest levels of strain among all identified classes of respondents. Hence, being a target of severe bullying seems to constitute a discrete experience associated with particularly low levels of well-being and particularly elevated levels of work-related strain. Introducing a separate factor for aggression did not improve model fit.
Aggression was primarily reported in situations where interpersonal conflicts exist between subordinates and superiors or between peers. This might imply that interpersonal conflicts might encompass workplace aggression. Note that we do not claim that all conflicts involve aggression, as we also found some instances where conflicts did exist without any trace of aggression, particularly at low levels of conflict.
Even though we found a two-factor solution providing the best fit to the data, the overlap between these two factors appeared to be quite large, with the correlation between the two being almost 0. The scores on the selected criterion variables for those experiencing some involvement in interpersonal conflicts or for those who were occasionally bullied were also quite similar. Hence, it seems that both phenomena are not that different when exposure is low. Existing research may help explain the interrelations between conflict and bullying.
Einarsen proposed a model wherein these two processes are strongly interrelated. His model starts with an escalating conflict which may provoke aggression, which, in turn, may result in bullying. The first class was typified by not reporting any conflicts and no aggressive behavior.
The second class was typified by increasing level of conflicts but hardly any aggressive behavior. Compared to the previous class, the last class consisted of employees reporting increasing levels of conflicts and also aggressive behaviors. Nevertheless, the class that is missing in the current results is the one that describes a stage of conflict escalation wherein the conflicting parties go so far that they envisage total annihilation. According to Einarsen and colleagues , it is unlikely to find such highly escalated interpersonal conflicts while at work.
A reason for why we did not find this class may be that such highly escalated conflicts are most likely to be stopped by management. Furthermore, in general, such intense overt aggressive behaviors will not be tolerated in working life. Such types of behaviors, as they are illegal, may even warrant dismissal Welzijnswet, , which explains why this class may be rare in working life. However, to the extent that parties engage in subtle, covert, and difficult-to-detect wrong-doing, such behavior may persist for long, as often the case with bullying.
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For example, dispute-related bullying describes a form of bullying that develops out of grievances and involves social control reactions to perceived wrong-doing Einarsen, ; also see Felson and Tedeschi, Einarsen et al.
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