Methods for estimating trend in binary and count response variables from complex survey designs

Starcevich, Leigh Ann; McDonald, Trent; Chung-MacCoubrey, Alice; Heard, Andrea; Nesmith, Jonathan; Coletti, Heather; Philippi, Tom

The National Park Service (NPS) Inventory and Monitoring (I&M) Program assesses the status and trends in condition of park natural resources as part of their missive to protect and preserve these national assets “for the enjoyment of future generations” (Fancy et al. 2009). Probabilistic sampling designs are used so that inference may be made to broader populations or geographic areas such as the park or network. Spatially-balanced sampling approaches, such as Generalized Random Tessellation Stratified (GRTS, Stevens and Olsen 2003, 2004), provide a probabilistic sampling approach that allocates sampling effort more evenly across large areas of interest. Complex survey designs are often incorporated to address practical sampling issues such as estimation of indicators within subpopulations (strata or domains of interest), limited sampling resources, and gradients relative to covariates that impact sampling effort (e.g. elevation). Design elements such as stratification, unequal probability sampling, and temporal revisit designs may be incorporated to address these issues but may also complicate trend estimation and detection. Ignoring the fact that design weights differ among sampling units when design complexity is used can lead to biased estimates of trend and unreliable trend tests. The purpose of this project is to assess three trend analysis techniques with the goal of obtaining unbiased and precise trend estimation and powerful trend testing for binary and count data collected in natural resource monitoring with complex GRTS sampling designs and revisit designs. Ideally, the preferred trend analysis approach can be performed with standard statistical tools such as the R statistical software environment. We evaluated three analytical trend approaches on simulated data representing a wide range of design scenarios using data from the NPS Southwest Alaskan Network (SWAN) rocky intertidal monitoring program. The three trend analysis approaches included a generalized linear mixed model (GLMM) that does not incorporate design weights and represents a naïve analysis under complex sampling, simple and weighted linear regressions on transformed design-based estimates of annual status (SLRDB and WLRDB, respectively), and a probability-weighted iterative generalized least squares approach (PWIGLS). We assessed performance of these three approaches by evaluating relative bias and confidence interval coverage of the trend estimators and statistical power and size of the trend test. We summarized recommendations for analysis under a range of simulation scenarios using a decision flowchart and illustrated the application of our results using the “TrendNPS” R-package developed for this project using SWAN case study data. We found that the GLMM corollary of the unweighted linear mixed model proposed by Piepho and Ogutu (2002) often yielded unbiased estimates of trend and nominal confidence interval coverage. For the range of trend magnitudes, sample sizes, and monitoring periods explored in this research, the naïve GLMM approach, which does not incorporate design weights, performed very well in many cases, even for some scenarios with complex sampling and revisit designs. However, in some select cases, the PWIGLS approach yielded superior trend inference with unbiased estimates of trend and nominal (“appropriate”) confidence interval coverage.

Methods for estimating trend in binary and count response variables from complex survey designs

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