Structural equation modeling of political discussion networks

This study conducts structural equation modeling (SEM) of political discussion networks. It examines multiple relationships between political discussion networks—network size and non-kin composition, political efficacy, and neighborhood conversation. Based on a two-step approach, it first analyzes and revises the measurement model and then analyzes and revises the structural model given the revised measurement model. The proposed SEM model includes ordered categorical variables as factor indicators in the confirmatory analysis and outcome variables in the structural regressions. Traditional estimation and regression methods need to be adjusted accordingly. This study uses WLS estimation and adopts a latent variable approach to study the categorical outcome variables in the SEM. The results show that the hypothesized SEM model is fully supported. Neighborhood conversation positively and directly contributes to political discussion network size as well as the non-kin composition of the networks. It also indirectly affects network size through political efficacy. Political efficacy also has a direct effect on network size.Statistic

Coming Out of the Dungeon: Mathematics and Role-Playing Games

After hiding it for many years, I have a confession to make. Throughout middle school and high school my friends and I would gather almost every weekend, spending hours using numbers, probability, and optimization to build models that we could use to simulate almost anything. That’s right. My big secret is simple. I was a high school mathematical modeler. Of course, our weekend mathematical models didn’t bear any direct relationship to the models we explored in our mathematics and science classes. You would probably not even recognize our regular gatherings as mathematical exercises. If you looked into the room, you’d see a group of us gathered around a table, scribbling on sheets of paper, rolling dice, eating pizza, and talking about dragons, magical spells, and sword fighting. So while I claim we were engaged in mathematical modeling, I suspect that very few math classes built models like ours. After all, how many math teachers have constructed or had their students construct a mathematical representation of a dragon, a magical spell, or a swordfight? And yet, our role-playing games (RPGs) were very much mathematical models of reality — certainly not the reality of our everyday experience, but a reality nonetheless, one intended to simulate a particular kind of world. Most often for us this was the medieval, high-fantasy world of Dungeons & Dragons (D&D), but we also played games with science fiction or modern-day espionage settings. We learned a lot about math, mythology, medieval history, teamwork, storytelling, and imagination in the process. And, when existing games were inadequate vehicles for our imagination, we modified them or created new ones. In doing so, we learned even more about math. Now that I am a mathematics professor, I find myself reflecting on those days as a “fantasy modeler” and considering various questions. What is the relationship between my two interests of fantasy games and mathematics? Does having been a gamer make me a better mathematician or modeler? Does my mathematical experience make me a better gamer? These different aspects of my life may seem mostly unconnected; indeed, the “nerd” stereotype is associated with both activities, but despite public perception, the community of role-players includes many people who are not scientifically-minded. So we cannot say that role-players like math, or math-lovers role-play, because “that is simply what nerds do.” To get at the deeper question of how mathematics and role-playing are related, we first need to look at the processes of gaming, game designing, and modeling

Why we (usually) don't have to worry about multiple comparisons

Applied researchers often find themselves making statistical inferences in settings that would seem to require multiple comparisons adjustments. We challenge the Type I error paradigm that underlies these corrections. Moreover we posit that the problem of multiple comparisons can disappear entirely when viewed from a hierarchical Bayesian perspective. We propose building multilevel models in the settings where multiple comparisons arise. Multilevel models perform partial pooling (shifting estimates toward each other), whereas classical procedures typically keep the centers of intervals stationary, adjusting for multiple comparisons by making the intervals wider (or, equivalently, adjusting the $p$-values corresponding to intervals of fixed width). Thus, multilevel models address the multiple comparisons problem and also yield more efficient estimates, especially in settings with low group-level variation, which is where multiple comparisons are a particular concern