When analyzing longitudinal data, it is essential to account both for the correlation inherent from the repeated measures of the responses as well as the correlation realized on account of the feedback created between the responses at a particular time and the predictors at other times. As such one can analyze these data using generalized estimating equation with the independent working correlation. However, because it is essential to include all the appropriate moment conditions as you solve for the regression coefficients, we explore an alternative approach using a generalized method of moments for estimating the coefficients in such data. We develop an approach that makes use of all the valid moment conditions necessary with each time-dependent and time-independent covariate. This approach does not assume that feedback is always present over time, or if present occur at the same degree. Further, we make use of continuously updating generalized method of moments in obtaining estimates. We fit the generalized method of moments logistic regression model with time-dependent covariates using SAS PROC IML and also in R. We used p-values adjusted for multiple correlated tests to determine the appropriate moment conditions for determining the regression coefficients. We examined two datasets for illustrative purposes. We looked at re-hospitalization taken from a Medicare database. We also revisited data regarding the relationship between the body mass index and future morbidity among children in the Philippines. We conducted a simulated study to compare the performances of extended classifications.

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Measuring self-reported substance use behavior is challenging due to issues related to memory recall and patterns of bias in estimating behavior. Limited research has focused on the use of ecological momentary assessment (EMA) to evaluate marijuana use. This study assessed the feasibility of using short message service (SMS) texting as a method of EMA with college-age marijuana users. Our goals were to evaluate overall response/compliance rates and trends of data missingness, response time, baseline measures (e.g., problematic use) associated with compliance rates and response times, and differences between EMA responses of marijuana use compared to timeline followback (TLFB) recall. Nine questions were texted to participants on their personal cell phones 3 times a day over a 2-week period. Overall response rate was high (89%). When examining predictors of the probability of data missingness with a hierarchical logistic regression model, we found evidence of a higher propensity for missingness for Week 2 of the study compared to Week 1. Self-regulated learning was significantly associated with an increase in mean response time. A model fit at the participant level to explore response time found that more time spent smoking marijuana related to higher response times, while more time spent studying and greater "in the moment" academic motivation and craving were associated with lower response times. Significant differences were found between the TLFB and EMA, with greater reports of marijuana use reported through EMA. Overall, results support the feasibility of using SMS text messaging as an EMA method for college-age marijuana users.

We exhibit a graph, G12, that in every spatial embedding has a pair of non-splittable 2 component links sharing no vertices or edges. Surprisingly, G12 does not contain two disjoint copies of graphs known to have non-splittable links in every embedding. We exhibit other graphs with this property that cannot be obtained from G12 by a finite sequence of Δ-Y and/or Y-Δ exchanges. We prove that G12 is minor minimal in the sense that every minor of it has a spatial embedding that does not contain a pair of non-splittable 2 component links sharing no vertices or edges.