Polyphony in Team Communication

Abstract

When teams are convened, they have many issues to discuss. Some of their conversations occur all at once; while, others require shifting among topics to make key decisions that reflect all the information available. Understanding how these conversations transpire, including when topics are discussed and in what order, may help teams perform effectively. In this chapter, we consider communication polyphony using event history analysis; specifically, we employ proportional hazard models and Andersen-Gill intensity models. This approach results in identifying the relationships among the points in time when teams complete conversations about specific topics. The findings from these analyses highlight the order in which topics are discussed, when action is initiated, how often teams cycle through various topics, and any relationships these points of interest have with team performance. Differences attributable to the conditions under which the teams collaborate are also examined.

Appendix: How to Conduct Event History Analysis

In Chap. 6, we examined the polyphony of team communication using event history analysis. This approach provided insights about the temporal interdependencies among when topics are discussed and the intensity with which topics are revisited. To demonstrate how we employed event history analysis, in general, and the proportional hazards and the Andersen-Gill intensity models, in particular, we evaluate the example dataset presented in the Chap. 3 Appendix. The pattern recognition and measurement required to complete these analyses were conducted in Matlab. Statistical analyses were conducted in SAS 9.4.

Data Preparation

The first step in data preparation for event history analysis is to define the event in which you are interested. For our purposes, the event was the end of a sustained conversation about a particular topic or the initiation of a conversation about a topic. In Chap. 6, the pattern of communication that led up to an event was determined by subject matter experts. These experts used an iterative process to ascertain the appropriate number of messages to be exchanged and the number of subsequent messages about other topics that would best represent a completed conversation. This process was informed by an evaluation of the raw messages, insights about pattern capture for different settings, and an understanding of the team literature. For the example dataset in this appendix, we set the pattern recognition rule for topics 10, 20, and 30 to be a minimum of 3 sequential messages on a topic followed by at least 2 messages about other topics, which parallels the pattern used in Chap. 6 for the transition processes. We treat topic 40 as a topic similar to our action topic in Chap. 6, where our interest is in when it was initiated.

The next step is to determine the event scores for each event of interest. To obtain the event scores, we evaluated each communication string using our pattern rules in Matlab. For topics 10, 20, and 30, the event was set at the last message about the topic code of interest exchanged before the topic was changed for an extended period of time. For topic 40, the event occurred when the first message coded 40 was exchanged. When a pattern did not occur in the communication string, the event was scored a 0. Because all communication strings were of different lengths, all event scores were scaled by dividing the raw score by the total number of messages exchanged in the communication string.

The communication string, with corresponding position numbers, for Team 1 in our example dataset is:

Position:	Topic:	Position:	Topic:
1	10	11	10
2	10	12	10
3	10	13	10
4	20	14	40
5	20	15	40
6	20	16	40
7	20	17	40
8	30	18	40
9	30	19	40
10	30	20	40

For this team, the pattern recognition rule for the topic code 10 is found at position 3 (i.e., 3 messages coded 10 are exchanged and followed by at least 2 messages about other topics). The event score is then calculated as the position divided by the total number of messages in the communication string, or 10Pattern = 3/20 = 0.15. For this team, the event scores for the other topics would be 20Pattern = 0.35, 30Pattern = 0.50, and 40Pattern = 0.70. The compiled dataset used for the proportional hazard analysis is shown in Table 6.5.

Table 6.5 Example teams proportional hazards model dataset

The Andersen-Gill intensity model provides greater insight about the repeated pattern occurrences (i.e., intensity) for topics of interest. In our example dataset, we focus on the intensity of topic 10. We obtain the event scores needed for analysis by extending the pattern recognition rule beyond just the first occurrence. Using this approach, we capture every occurrence of the pattern that exists in the communication string. Each event score requires a starting and stopping point. The first starting point is 0 and the last stopping point is 1. Starting and stopping points between the 0 and 1 represent the scaled positions on the communication string when the events occur, where scaling is done by dividing the position where the event occurred by the total number of messages in the communication string.

For Team 1 in the example dataset the event scores for topic code 10 show that the pattern is found twice, once as noted above where the sequential messages end at position 3 (scaled position = 0.15), and again where the sequential messages end at position 13 (scaled position = 0.65). Therefore, the starting and stopping points for Team 1’s topic 10 would be: [0, 0.15], [0.15, 0.65], and [0.65, 1]. Each event is entered into the dataset as its own record. In other words, every event is recorded in its own row.

Although we elected to focus on the intensity of topic 10 as the dependent variable, we also determined that it may be related to the first occurrence of a pattern for topics 20 and 30 and how many times the pattern occurs for those topics. For Team 1, topic 20 and topic 30 patterns are found once each and the event scores are 0.35 and 0.5, respectively. Note that these values are repeated for every iteration (i.e., row) of a topic 10 pattern. A full account of the dataset is shown in Table 6.6.

Table 6.6 Example teams Andersen-Gill intensity model analysis dataset

Data Usage

Proportional Hazards Model

In our demonstration of the proportional hazards model from event history analysis, we assess the relationship between when the pattern for a topic of interest occurs in relationship to when patterns of other topics occur. The descriptive statistics and intercorrelations among our variables for this analysis are shown in Table 6.7.

Table 6.7 Example teams descriptive statistics, correlations, and regression results for proportional hazards model analysis

The proportional hazards model relates time-varying covariates to the dependent variable. The resulting analysis provides information about the hazard ratio, which represents the likelihood of an event occurrence given that another event has occurred while holding other variables constant. The reciprocal of the hazard ratio is the expected time until the event occurs. The equation for event history analysis is:

h(t) = h₀(t) × exp(β₁x₁ + β₂x₂ + … + β_px_p)

where, t represents the survival time and the set (x₁,x₂,…,x_p) represents the covariates.

To aid in interpreting results, we offer the following rubric.

• Employ the transformation 100∗(ratio-1) to get the estimated percent change in the likelihood of the dependent variable occurring for a one-unit increase in the independent variable.

• If the hazard ratio is >1, events are more likely to occur. If the hazard ratio is <1, events are less likely to occur.

• If the independent variable is continuous, the dependent variable will be increasingly more/less likely to occur as the independent variable increases. For example, the older you get, the more likely you are to die.

• If the independent variable is binary, the dependent variable is more/less likely to occur if the independent variable =1 than if the independent variable = 0. For example, someone who has been incarcerated is more likely to go back to jail than someone who has never been to jail.

The results of the analysis using our example dataset are shown on the right side of Table 6.7. Model 1, where the outcome variable is the 10Pattern, is not significant (χ² = 3.003, p = 0.39). Model 2, where the outcome variable is the 20Pattern, is significant (χ² = 7.831, p = 0.05). In Model 2 we see that the hazard ratio of the 40Pattern is significant (h = 271.590, p = 0.05). This result suggests that the timing of the 20Pattern depends on the timing of the 40Pattern. Specifically, because the 40Pattern is a time-varying covariate, we may say that for every one-unit increase in when the 40Pattern occurs, the likelihood of the 20Pattern increases 270.590 times (100∗(271.590–1) = 270.590). That is, the 20Pattern is much more likely to occur once the team experiences a 40Pattern.

Model 3 is marginally significant (χ² = 7.548, p = 0.06) and shows that when the 30Pattern occurs is linked to when the 10Pattern (h = 0.001, p = 0.07) and 40Pattern (h = 0.014, p = 0.07) occur. Interestingly, the results suggest that the 30Pattern is less likely to occur when the 10Pattern and 40Pattern occur because the hazard of occurrence goes down for every one-unit increase in these variables. This result may suggest that timing of the 30Pattern is later in the communication string if the 10Pattern or 40Pattern occur.

Finally, Model 4 is found to be marginally significant (χ² = 6.378, p = 0.09). In this case, the 40Pattern is linked to the 30Pattern (h = 0.006, p = 0.08) where the hazard of a topic 40 message being exchanged goes down for every one-unit increase in when the 30Pattern occurs.

Andersen-Gill Intensity Model

To demonstrate our use of the Andersen-Gill intensity model, we focus on topic 10 and how the other events may affect how frequently the topic 10 patterns recur. The descriptive statistics and correlations for the Andersen-Gill analysis are shown in Table 6.8. The 10Start and 10Stop variables represent the starting and stopping points for each recurrence of a topic 10 pattern. The 20Pattern, 30Pattern, and 40Pattern variables represent the scaled point in the communication string when the pattern of interest occurred. Finally, the 20Event and 30Event variables represent how many times the patterns for topics 20 and 30 were found in the communication strings, respectively.

Table 6.8 Example teams descriptive statistics and correlations for Andersen-Gill intensity model analysis

To conduct the analysis, we added two additional variables to the dataset: (1) PatternEnd, which is a binary variable indicating whether or not it is the end of 10Pattern recognition (i.e., 1 when it ends, 0 otherwise) and (2) 10EventNumber, which incrementally counts the number of rows (i.e., number of start/stop patterns identified in a communication string) for each team. For Team 10, this 10EventNumber = 1 in the first row, 2 in the second row, and 3 in the third row.

The Andersen-Gill intensity model equation is:

h_z(t)dt = E{dN(t) | F_t-} = h₀(t)exp[β’x(t)] dt

where N(t) is the number of events by a subject over the interval [0, t].

The interpretation of the hazard ratios follows the same guidelines as provided above for the proportional hazards model. In addition to regression results for the Andersen-Gill intensity model (see right columns in Table 6.8), the output also includes a summary of the number of teams experiencing multiple events. As can be seen in Table 6.9, of 10 teams in the example dataset that could have experienced one event, all 10 did have at least one topic 10 pattern in their communication strings. Of those 10 teams experiencing one event, 7 teams experienced a second topic 10 pattern in their communication string and 3 teams or 30% were censored (i.e., they did not have a second topic 10 pattern in their communication strings).

Table 6.9 Summary of the number of events and censored values for example teams

The results in Table 6.8 show that the model for the intensity of the 10Pattern is significant (χ² = 19.269, p < 0.01). The number of repetitive topic 10 patterns is significantly impacted by the number of topic 20 (h = 0.001, p = 0.04) and topic 30 (h = 0.000, p < 0.01) patterns, as well as the total number of topic 30 events (h = 0.443, p = 0.44). In all cases, topic 10 patterns are less likely to occur because the significant hazard ratios are all less than 1.