Linear mixed models with endogenous covariates: modeling sequential treatment effects with application to a mobile health study

Mobile health is a rapidly developing field in which behavioral treatments are delivered to individuals via wearables or smartphones to facilitate health-related behavior change. Micro-randomized trials (MRT) are an experimental design for developing mobile health interventions. In an MRT the treatments are randomized numerous times for each individual over course of the trial. Along with assessing treatment effects, behavioral scientists aim to understand between-person heterogeneity in the treatment effect. A natural approach is the familiar linear mixed model. However, directly applying linear mixed models is problematic because potential moderators of the treatment effect are frequently endogenous---that is, may depend on prior treatment. We discuss model interpretation and biases that arise in the absence of additional assumptions when endogenous covariates are included in a linear mixed model. In particular, when there are endogenous covariates, the coefficients no longer have the customary marginal interpretation. However, these coefficients still have a conditional-on-the-random-effect interpretation. We provide an additional assumption that, if true, allows scientists to use standard software to fit linear mixed model with endogenous covariates, and person-specific predictions of effects can be provided. As an illustration, we assess the effect of activity suggestion in the HeartSteps MRT and analyze the between-person treatment effect heterogeneity

Cosmological constraints on induced gravity dark energy models

We study induced gravity dark energy models coupled with a simple monomial potential $\propto \sigma^n$ and a positive exponent $n$. These simple potentials lead to viable dark energy models with a weak dependence on the exponent, which characterizes the accelerated expansion of the cosmological model in the asymptotic attractor, when ordinary matter becomes negligible. We use recent cosmological data to constrain the coupling $\gamma$ to the Ricci curvature, under the assumptions that the scalar field starts at rest deep in the radiation era and that the gravitational constant in the Einstein equations is compatible with the one measured in a Cavendish-like experiment. By using $Planck$ 2015 data only, we obtain the 95 % CL bound $\gamma < 0.0017$ for $n=4$, which is further tightened to $\gamma < 0.00075$ by adding Baryonic Acoustic Oscillations (BAO) data. This latter bound improves by $\sim 30$ % the limit obtained with the $Planck$ 2013 data and the same compilation of BAO data. We discuss the dependence of the $\gamma$ and $\dot G_N/G_N (z=0)$ on $n$.Comment: 16 pages, 10 figure

R Package multgee: A Generalized Estimating Equations Solver for Multinomial Responses

The R package multgee implements the local odds ratios generalized estimating equations (GEE) approach proposed by Touloumis, Agresti, and Kateri (2013), a GEE approach for correlated multinomial responses that circumvents theoretical and practical limitations of the GEE method. A main strength of multgee is that it provides GEE routines for both ordinal (ordLORgee) and nominal (nomLORgee) responses, while relevant other softwares in R and SAS are restricted to ordinal responses under a marginal cumulative link model specification. In addition, multgee offers a marginal adjacent categories logit model for ordinal responses and a marginal baseline category logit model for nominal responses. Further, utility functions are available to ease the local odds ratios structure selection (intrinsic.pars) and to perform a Wald type goodness-of-fit test between two nested GEE models (waldts). We demonstrate the application of multgee through a clinical trial with clustered ordinal multinomial responses

Relic gravitational waves in the light of 7-year Wilkinson Microwave Anisotropy Probe data and improved prospects for the Planck mission

The new release of data from Wilkinson Microwave Anisotropy Probe improves the observational status of relic gravitational waves. The 7-year results enhance the indications of relic gravitational waves in the existing data and change to the better the prospects of confident detection of relic gravitational waves by the currently operating Planck satellite. We apply to WMAP7 data the same methods of analysis that we used earlier [W. Zhao, D. Baskaran, and L.P. Grishchuk, Phys. Rev. D 80, 083005 (2009)] with WMAP5 data. We also revised by the same methods our previous analysis of WMAP3 data. It follows from the examination of consecutive WMAP data releases that the maximum likelihood value of the quadrupole ratio $R$, which characterizes the amount of relic gravitational waves, increases up to $R=0.264$, and the interval separating this value from the point $R=0$ (the hypothesis of no gravitational waves) increases up to a $2\sigma$ level. The primordial spectra of density perturbations and gravitational waves remain blue in the relevant interval of wavelengths, but the spectral indices increase up to $n_s =1.111$ and $n_t=0.111$. Assuming that the maximum likelihood estimates of the perturbation parameters that we found from WMAP7 data are the true values of the parameters, we find that the signal-to-noise ratio $S/N$ for the detection of relic gravitational waves by the Planck experiment increases up to $S/N=4.04$, even under pessimistic assumptions with regard to residual foreground contamination and instrumental noises. We comment on theoretical frameworks that, in the case of success, will be accepted or decisively rejected by the Planck observations.Comment: 27 pages, 12 (colour) figures. Published in Phys. Rev. D. V.3: modifications made to reflect the published versio

Bayesian Fit of Exclusive b→sℓˉℓb \to s \bar\ell\ell Decays: The Standard Model Operator Basis

We perform a model-independent fit of the short-distance couplings $C_{7,9,10}$ within the Standard Model set of $b\to s\gamma$ and $b\to s\bar\ell\ell$ operators. Our analysis of $B \to K^* \gamma$, $B \to K^{(*)} \bar\ell\ell$ and $B_s \to \bar\mu\mu$ decays is the first to harness the full power of the Bayesian approach: all major sources of theory uncertainty explicitly enter as nuisance parameters. Exploiting the latest measurements, the fit reveals a flipped-sign solution in addition to a Standard-Model-like solution for the couplings $C_i$. Each solution contains about half of the posterior probability, and both have nearly equal goodness of fit. The Standard Model prediction is close to the best-fit point. No New Physics contributions are necessary to describe the current data. Benefitting from the improved posterior knowledge of the nuisance parameters, we predict ranges for currently unmeasured, optimized observables in the angular distributions of $B\to K^*(\to K\pi)\,\bar\ell\ell$.Comment: 42 pages, 8 figures; v2: Using new lattice input for f_Bs, considering Bs-mixing effects in BR[B_s->ll]. Main results and conclusion unchanged, matches journal versio

First-order marginalised transition random effects models with probit link function

Marginalised models, also known as marginally specified models, have recently become a popular tool for analysis of discrete longitudinal data. Despite being a novel statistical methodology, these models introduce complex constraint equations and model fitting algorithms. On the other hand, there is a lack of publicly available software to fit these models. In this paper, we propose a three-level marginalised model for analysis of multivariate longitudinal binary outcome. The implicit function theorem is introduced to approximately solve the marginal constraint equations explicitly. probit link enables direct solutions to the convolution equations. Parameters are estimated by maximum likelihood via a Fisher-Scoring algorithm. A simulation study is conducted to examine the finite-sample properties of the estimator. We illustrate the model with an application to the data set from the Iowa Youth and Families Project. The R package pnmtrem is prepared to fit the model