Before You Start:

Because you will not be collecting data in this lab, feel free to knit early and often to see how your responses are being formatted! Please do your best to maintain the formatting provided by this assignment. It makes grading significantly easier when answers are easy to read.

Download all the files for this lab and save them in the same folder. Open the CSS_Lab.R file in RStudio (File > Open). After the R script is loaded in the editor, set the working directory so that R knows where to find the RData file you are going to load (Session > Set Working Directory > To Source File Location).

The data file krackhardt_css_data.RData consists of two CSS data objects:

● advice_nets: respondents’ perceptions about their own and others’ advice ties within the organization

● friendship_nets: respondents’ perceptions about their own and others’ friendship ties within the organization

Analysis

Conceptually, how do these two networks differ from one another? What are the pros and cons of using this method? Column: Answers the question, “Who is friends with you?” Row: Answers the question, “Who are you friends with?” The perception of the tie is from the perspective the tie is based on; in other words, K=i or K=j. The benefit is that these should be the most accurate perceptions in the network, and by creating a new matrix using the row or columns of all the other matrices, there should be a boon to the validity of the network. They essentially differ because they answer different questions.

Analysis

What information does the ‘intersection’ method capture? What are the pros and cons of using this method? Intersection LAS is only concerned with i and j agreeing a tie exists between them. When they both agree a tie exists, it exists, and conversely if either or both say there is no tie, then there is no tie. This method bolsters the reliability of the network.

Anaylsis

What kind of information does the union method capture? What are the pros and cons of using this method? LAS union method assumes there is a tie if either i or j perceive a tie. The problem is that the tie is created even if one party does not agree, there is a tie. The benefit is that it is less stringent and allows for the interpretation of every perceived tie.

Analysis

What kind of information does the median measure capture? What are the pros and cons of using this method? Consensus methods require a set threshold be met before a tie is recognized as established. For example, at least 50% of the surveyed people need to say they perceive a tie between i and j before we acknowledge a tie exists. This method can lead to sparse networks like the one we see here.

Finally, we’ll also load the data for our advice network for later analysis.

ad_column <- consensus(advice_nets, mode="digraph", diag=FALSE, method="OR.col")
ad_row    <- consensus(advice_nets, mode="digraph", diag=FALSE, method="OR.row")
ad_intersection <- consensus(advice_nets, mode="digraph", diag=FALSE, method="LAS.intersection")
ad_union  <- consensus(advice_nets, mode="digraph", diag=FALSE, method="LAS.union")
ad_median <- consensus(advice_nets, mode="digraph", diag=FALSE, method="central.graph")

Analysis

Describe what this network shows in your own words. The graph shows a perceived friendship network. This graph is using the union method which creates a tie if either i or j perceives a friendship.

Friendship, Row.

Analysis

Describe what this network shows in your own words. As this is using the LAS row method. The graph seeks to answer the question, “Who are you friends with?” For example, node 20 believes they are friends with nobody, node 10 says they are friends with node 7, etc.

What are the relevant similiarities and differences between the two networks? What do they mean? Many of the ties are the same, which makes sense as the union method would keep all the same ties as the row method. Node 20 becomes an isolate in the row graph.

Analysis

Describe what this network shows in your own words. This network graph depicts an Advice network using the LAS intersection method. The intersection method creates a tie if both i and j agree there is a tie. For example, node 9 goes to node 19 for advice, both 19 and 9 agree that 9 goes to 19 for advice.

Advice, Median.

Analysis

Describe what this network shows in your own words. This graph depicts an advice network using the consensus method. A consensus network is created by creating a threshold percentage of the entire network that needs to agree there is a tie, before establishing a tie. For example, node 14 goes to 5 for advice, and 5 and 19 go to each other for advice. Each out-tie is based on the entire network being in relative agreement the tie exists

What are the relevant similiarities and differences between the two networks? What do they mean? Pretty much everyone agrees node 18 is someone to seek advice from, but 18 does not seek advice. The graphs differ more than they are similar. Consensus LAS methods are usually less stringent than intersection LAS methods.

Analysis

What respondents did you choose to visualize? Why? I chose to examine respondent 18 for both graphs because of their isolated status in previous analyses. I wanted to see if they agreed they were isolated.

What do their networks show? Can you draw any conclusions about each actor’s role in the network? It shows that node 18 believes they are indeed an isolate in the friendship network and has very little awareness of who is friends with whom; however, they believe nearly everyone goes to them for advice. I would guess that node 18 is some sort of boss. People are very rarely friends with their bosses and vice versa, but they often will seek advice from their bosses.

Analysis

What does this network show? Why might this visualization be useful? This network depicts any form of tie, whether it be advice or friendship. The graph is using the intersection LAS method of two matrices that have already been constructed through union LAS. This graph could be useful to see who talks to whom. As in any form of communication.

Analysis

Outline your rationale for choosing your networks. I prefer the intersection LAS method as I feel it’s important for both parties to agree there is a tie to be considered friends. It’s not as important for understanding advice networks; however, for the sake of consistency, I will use the ad_intersection matrix as well.

Analysis

How do you interpret high and low values in this matrix, calculated using Euclidean distance? High Euclidean distance means that the nodes are farther apart, or in this case, they are farther from being structurally equivalent.

Which network has the smallest minimum distance between nodes? Why might that be? You may want to refer to your earlier visualizations for more insight into the network. Both networks have the same smallest min distance between nodes (min = 1).

Which network has the greatest maximum distance between nodes? Why might that be? The advice network has the greatest maximum distance between nodes (max = 4.1). This is probably because the data is based on advice. Structural equivalence is the extent two nodes communicate with the same people. Advice is something that is usually highly specific and doesn’t generalize very well. For example, one node may be a boss of one department; that department would go to the boss node for advice, but probably not to another department’s boss for advice.

Which network exhibits more structural equivalence? Based on the mean values, the friendship network exhibits more structural equivalence. This makes sense based on my hypothesis of advice networks and boss nodes.

Analysis

Examining the results from above, which respondent’s perceptions were the most/least “accurate” when compared to the median response (assuming the consensus is the ground truth)?66 Hint: look for the strongest correlation between the respondent’s network and the median network. Node 16 has a correlation of .7, followed closely by node 4 with a correlation of .69.

Analysis

Are the results for the friendship network very similar or different from those you saw in the advice networks? Give some possible reasons why individuals have more precise representations of one kind of relation structure than another kind of relation structure. The results of the consensus advice network are significant. That is, according to QAP, the ties are probably not caused by random chance. That said, the overall test stats are quite a bit lower for the advice network than the friendship network. I think that people perceive friendship much easier than advice because advice seeking frequently happens in privacy.

Analysis

Which centrality score of individuals in the consensus network are most highly correlated with their accuracy in predicting the consensus network? Based on the readings, suggest a rationale why individuals’ embeddedness or patterning of ties might result in different perceptions. # Identifying Most and Least Similar Respondent Viewpoints (I merged two questions.)

The correlation with closeness centrality is the highest. This is intuitive as closeness centrality is based on the sum of the length of the shortest paths between the person-node and all others in the network; in other words, closeness centrality can predict people’s ability to perceive ties inn advice or friendship network because when closeness centrality is high in one node, that node is close to others. Degree centrality is the second best correlated centrality. This is also intuitive as degree centrality is based on how connected the network is, the more connected the better sense people would have of who is connected to whom. A node with high betweennness centrality would have a limited perspective on the network as a whole, but a really good grasp on those they stand between. Eigenvector having a low correlation makes sense as people may know all about a popular node, but that doesn’t mean the popular node knows anything about the rest of the network. Similarly the rest of the network wouldn’t know much about each other.

Next, we’ll run the QAP test on the individual advice/friendship networks. Take a look at your console output to answer this question.

## Proportion of draws which were >= observed value: 0

## Proportion of draws which were <= observed value: 1

Analysis

Which individual sees the two networks as the most similar? Which sees them as the least similar? Individual 16 sees them as being most similar as their test stat was .46. Individual sees the networks as being the most dissimilar as their test stat was only .03.