Book Review: Grit: The Power of Passion and Perseverance

I first stumbled across the research of Angela Duckworth after she was awarded the prestigious MacArthur Fellowship in 2013 for her work investigating the character traits that impact the achievement of long-term goals. So, when it was announced that she would be publishing a book in 2016, I immediately pre-ordered copy so that I could dig into her insights as soon as possible. When I received my copy of Grit: The Power of Passion and Perseverance in the mail, I was excited to crack it open… and then the self-doubt settled in. “What if, after reading the brilliant ideas of a scholar whom I highly regard, I realize that I have no grit… What if I don’t have what it takes?” I was terrified. But, I am convinced that I am not alone. In our current educational culture, one that reinforces a transactional ideology that success is unequivocally defined by test scores and GPA, what is one to do if they literally do not “measure up” to the competition? Is that the end of the road? Is success forever out of reach

Marginal Maximum Likelihood Estimation of Item Response Models in R

Item response theory (IRT) models are a class of statistical models used by researchers to describe the response behaviors of individuals to a set of categorically scored items. The most common IRT models can be classified as generalized linear fixed- and/or mixed-effect models. Although IRT models appear most often in the psychological testing literature, researchers in other fields have successfully utilized IRT-like models in a wide variety of applications. This paper discusses the three major methods of estimation in IRT and develops R functions utilizing the built-in capabilities of the R environment to find the marginal maximum likelihood estimates of the generalized partial credit model. The currently available R packages ltm is also discussed.

Selfish Knapsack

We consider a selfish variant of the knapsack problem. In our version, the items are owned by agents, and each agent can misrepresent the set of items she owns---either by avoiding reporting some of them (understating), or by reporting additional ones that do not exist (overstating). Each agent's objective is to maximize, within the items chosen for inclusion in the knapsack, the total valuation of her own chosen items. The knapsack problem, in this context, seeks to minimize the worst-case approximation ratio for social welfare at equilibrium. We show that a randomized greedy mechanism has attractive strategic properties: in general, it has a correlated price of anarchy of $2$ (subject to a mild assumption). For overstating-only agents, it becomes strategyproof; we also provide a matching lower bound of $2$ on the (worst-case) approximation ratio attainable by randomized strategyproof mechanisms, and show that no deterministic strategyproof mechanism can provide any constant approximation ratio. We also deal with more specialized environments. For the case of $2$ understating-only agents, we provide a randomized strategyproof $\frac{5+4\sqrt{2}}{7} \approx 1.522$-approximate mechanism, and a lower bound of $\frac{5\sqrt{5}-9}{2} \approx 1.09$. When all agents but one are honest, we provide a deterministic strategyproof $\frac{1+\sqrt{5}}{2} \approx 1.618$-approximate mechanism with a matching lower bound. Finally, we consider a model where agents can misreport their items' properties rather than existence. Specifically, each agent owns a single item, whose value-to-size ratio is publicly known, but whose actual value and size are not. We show that an adaptation of the greedy mechanism is strategyproof and $2$-approximate, and provide a matching lower bound; we also show that no deterministic strategyproof mechanism can provide a constant approximation ratio