Unofficial Guide to Creating Collective Mental Models with 3CM and Anthropac
Step 4: Generate a Map of Association Between Terms
Step 4: Generate a Map of Associations Between Terms
Once your data file is complete you are ready to get started in Anthropac. I suggest using the sample data file provided in the previous section to follow along with the steps below.
Open the Pilesort module of Anthropac. In Windows, it probably appears in the Start menu under Analytic Technologies as Visual Anthropac – Pilesorts.
Import the data file you created in the previous section. From the File menu, select Import. At the bottom of the window that appears change Files of Type to Text Files (*.txt). Then navigate to your data file and click Open.
Upon importing the data file, the first thing that appears on the screen is a multi-dimensional scaling of the relationships between the 3CM terms; however, instead of seeing the term names, you see the numbers that were assigned to each term in the data file.
Before we proceed further in the map analysis, we want to confirm that our data is appropriate for this type of analysis. From the Respondents menu, select Consensus. First, confirm that there is message (in blue text) that says, “Your data exhibit a strong fit to the consensus model, supporting an assertion that, despite individual differences, all respondents in the sample belong to a single culture with respect to this domain.” If you see this message, you can proceed. Second, to the left of the message are the correlations between the 3CM results of individual participants and the group as a whole. If the correlation is low, it may indicate that the participant did not understand the instructions, did not satisfactorily complete the task, or possesses a mental model vastly different from other participants. It is up to you to decide your minimum correlation requirement. If a participant’s correlation with the aggregate it too low, you should remove the participant from the data set and re-import the file into Anthropac. I've seen .2 and .3 used as minimum correlation requirements in other studies.
Now we’ll return to the MDS map. You should be able to reopen it using the Items MDS tab at the bottom of the Anthropac screen. Alternatively you can open it from Items > Multi-dimensional Scaling. It is typically beneficial to view the term names on the map instead of the term numbers. To replace the term numbers with the labels for each term, click the labels button in the upper-right section of the screen, then change Attribute from id to label and click OK.
Now your map should look similar to the one below.
Let’s take a moment to make sure we understand what we’re looking at because the results can be deceiving. The map above indicates how closely related participants perceive the terms in the 3CM activity. Roughly speaking, those terms that appear close to one another are more closely related in participants’ mental models, and those terms that appear far apart are less closely related. In other words, terms that are close together were frequently put in the same cluster by participants, and terms that are far apart were rarely put in the same cluster by participants. I say “roughly speaking” because there are limits in Anthropac's ability to accurately represent the distance between points. Let me explain why.
Imagine we start with two terms, A and B. We know that A and B are 1 unit apart. As shown below, we can accurately represent this distance on the page.
Now, we add a third term C, which is 1 unit from A and 1.5 units from B. We can also accurately these distances on the page.
Okay, now let’s add a fourth term D, which is 3 units from A, 3 units from B, and 3 units from C. At this point, the only way to accurately represent the distances is to present them in three dimensions.
From here on out, every time we add another term, we have to add more dimensions in order to accurately represent the distances between terms. This is a problem because we have no means to display, much less visually interpret this many dimensions. To get around the problem, Anthropac uses multi-dimensional scaling (MDS) to represent the distances as best as it can on a two-dimensional plane. As a result of using MDS, the distances displayed are not completely accurate. Typically, terms that are closer together are more closely related than terms that are far apart, but the adjustments made by Anthropac to display the data in two dimensions can falsify this assumption. Fortunately, and as you'll see, Anthropac gives us more tools to extract the information we need.
Now let's examine how Anthropac determines the distance between terms. Anthropac provides all of the information that supports the mapping under the Items tab, in the View menu. Navigate to Items > View, then select Individual Proximity Matrix. The window below appears with each of the participant IDs.
Select any one of the participants (I selected p4) and click OK.
As you'll recall, the sample data set has 57 terms, so the matrix has 57 rows and 57 columns with one row and one column representing each of the terms. The intersection of any two terms indicates whether or not the participant put those two terms together in a cluster – the number 1 indicates that the two terms were clustered together by the participant, the number 0 indicates that the terms were not clustered. So, in this case, p4 had Agricultural_Best_Management_Practices and Agricultural_Fertilizer in the same cluster but did not have Agricultural_Best_Management_Practices and Agricultural_Regulations in the same cluster.
Anthropac’s next step is to combine the individual proximity matrices into an aggregate proximity matrix. Navigate to Items > View and select Aggregate Proximity Matrix. This matrix provides the percentage of participants who put the intersecting terms together in the same cluster (among those participants that included both of the intersecting terms in their mental models). In this example, terms 1 and 2 were clustered together by 75 percent of participants. Terms 1 and 4 were clustered together by 50 percent of the participants.
You may be wondering about the blue numbers that appear at the intersections of rows and columns containing the same terms (e.g. row 1 and column 1). If these numbers simply represented the average of all participants, they would equal zero because it's not possible to cluster a term with itself. In the aggregate proximity matrix, the blue numbers indicate the percentage of participants who included the term in their mental models. In this example, 100 percent of participants included term 1, whereas 75 percent of participants included term 3.
Optional: Using the term selection percentages displayed in blue, you can optionally elect to remove from the analysis any terms that do not meet a threshold selection percentage. For example, you may decide that you do not want to include terms selected by less than 30 percent of participants in the composite map. In this case, you would remove term 9 from the data file (because term 9 was selected by only 25 percent of participants), then reload the data in Anthropac. If you opt not to remove terms with low selection percentages, you should account for the low percentages later in your analysis.
With the exception of the numbers in blue, the numbers displayed in the aggregate proximity matrix are used to create the MDS map of terms shown above. The number in the matrix indicates how close together the terms should appear. Pairs of terms with high numbers should appear closer together than pairs with low numbers. In this example, terms 1 and 2 should be mapped in closer proximity to one another than terms 1 and 3. But remember, the complexities of multi-dimensional scaling mean that the map may not accurately represent distances.