dlmBE-package: dlmBE: Distributed lag models in R using lme4

Description References


This package fits the distributed lag models (DLMs) described by Baek et al (2016) and Baek et al (2017), which estimate the association between the presence of built environment features and an outcome as a function of distance between the locations for study participants and locations for environment features or community resources. These models circumvent the need to pre-specify a radius within which to measure the availability of community resources. Distributed lag models have a long history in a variety of fields. For built environment research, we define the lagged exposure as the value of an environment feature between two radii, r_{l-1} and r_l from study locations, l = 1, 2, ..., L, where r_0 = 0; e.g., the lagged exposure is the number of convenience stores within “ring”-shaped areas around study participants residential address. The package supports generalized linear regression models, as well as generalized linear mixed models. In both instances, multiple lagged exposure covariates maybe included, as well as interactions between the lagged covariates and other categorical covariates (e.g., quartiles of age).

Let Y_{ij} be an outcome measured at location i at visit j, and X_{ij}(r_{l-1}; r_l) be an environment feature measured during visit j within a ring-shaped area around location i between radii r_{l-1} and r_l; and r_L be the maximum distance around locations beyond which there is no association between the environment feature and the outcome. A typical unadjusted generalized linear mixed model that can be fitted in this version of the package is,

g(E(Y_{ij} | b_i)) = β_0 + ∑_{l=1}^L β(r_{l-1}; r_l) * X(r_{l-1}; r_l) + W_{ij} * b_i

where g() is a link function appropriate for the distribution of the outcome; β_0 represents an intercept; the association of the environment feature measured between radii r_{l-1} and r_l and the outcome is β(r_{l-1}; r_l); and W_{ij} are covariates related to random effects, b_i (e.g., random intercepts and slopes). The coefficients β(r_{l-1}; r_l) are constrained to follow a smooth function of distance from the locations of interest; the constraint is imposed by modeling the coefficients using smoothing splines. Other models could be used, although smoothing splines are the only supported option at this time.

The model easily simplifies to generalized linear regression modes (e.g., when there is only one visit), and can be extended in the following directions. Adjustment covariates can be easily included. In addition, interaction terms between covariates and the DL covariates are also supported. For example, terms such as: ∑_{l=1}^L θ(r_{l-1}; r_l) * X(r_{l-1}; r_l) * Z_i, where Z_i is another covariate, can be included. The interaction coefficients θ(r_{l-1}; r_l) have the usual interpretation, but the magnitude of the interaction can vary over distance from locations of interest; θ(r_{l-1}; r_l) are also constrained using smoothing splines. Finally, weighted regression models are also supported.

We assume the user has calculated distances from every participant’s location to every community resource/feature. The distances can be network distances or Euclidian distances. Those distances are then used to calculate the distributed lag covariates, X(r_{l-1}; r_l), by specifying L and the radii r_l, l = 1, 2, ..., L. See Baek et al (2016) for guidance on choosing L and r.

The package includes a series of functions to pass formulas and data to lme4, which is used for estimation of the DLM. All those functions are documented in this manual, although a typical user will primarily interact with XXX, xxx, and xxx. For example:


Baek J, Sanchez BN, Berrocal VJ, & Sanchez-Vaznaugh EV (2016) Epidemiology 27(1):116-24. (PubMed)

Baek J, Hirsch JA, Moore K, Tabb LP, et al. (2017) Epidemiology 28(3):403-11. (PubMed)

Bates D, Maechler M, Bolker BM, & Walker SC (2015) Fitting linear mixed-effects models using lme4. J Stat Softw 67(1). (jstatsoft.org)

asw221/dlm documentation built on May 8, 2019, 5:59 p.m.