Methods for estimating trend in continuous response variables from complex survey designs

Starcevich, Leigh; McDonald, Trent; Chung-MacCoubrey, Alice; Heard, Andi; Nesmith, Jonny; Philippi, Tom

The National Park Service (NPS) Inventory and Monitoring (I&M) Program tracks status and trends in the condition of natural resources in parks, often using spatially balanced sampling designs such as Generalized Random Tesselation Stratified (GRTS) designs to make inferences to populations represented by broad geographic areas or subpopulations defined by sampling strata or levels of a covariate. Complex design elements such as stratification, unequal probability sampling, and panel revisit designs are often used to address issues related to sample size, sampling effort, and statistical or logistical efficiency, but these elements also introduce analytical challenges to trend estimation and detection. Ignoring the associated design weights can lead to reduced power and biased estimates of trend. The purpose of this project is to examine potential analysis techniques that can provide unbiased and precise trend estimation and powerful trend testing for natural resource monitoring data collected from complex GRTS sampling designs and revisit designs, and be performed using standard statistical software such as the R statistical software environment (R Core Team 2016). We tested three analytical approaches on simulated data representing a wide range of design and response scenarios. The simulation scenarios represented all combinations of the following design elements: sampling complexity (equiprobable, stratified, and unequal probability), several panel revisit designs, and sample size (20, 35, 50 sites per year). This resulted in a total of 216 different scenarios that were tested across the three analytical approaches. We used lake water chemistry data from the NPS Sierra Nevada I&M Network lakes monitoring program to simulate populations with different annual trends (0%, 1% over 24 years, 2% over 12 years), underlying subpopulation trends (0%, 4%), and variance structure (low and high year-to-year variation). Data were simulated to have been collected over monitoring periods of 12 or 24 years and with consistent or periodically reduced annual sampling effort. The three trend analysis approaches included: 1) A linear mixed model, Piepho and Ogutu model (“PO” model), that does not incorporate design weights and represents a naïve analysis under complex sampling; 2) A simple linear regression on design-based estimates of annual status; and 3) A probability-weighted iterative generalized least squares approach (PWIGLS) with a linearization variance estimator. We assessed performance of these three approaches by evaluating relative bias and confidence interval coverage of the trend estimate and statistical power and size of the trend test. We discuss performance of each approach and provide a decision flowchart to summarize the recommended approaches for various survey designs and population responses. In two case studies using lakes water chemistry, we illustrate the application of our results using the “TrendNPS” R-package developed for this project. R code and the performance results for each analytical approach are provided in Supplements A and B. We found that 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 Piepho and Ogutu model, which does not incorporate design weights, performed very well in many cases, even for some scenarios with sampling complexity and complex revisit designs. For every simulation scenario, the Piepho and Ogutu model yielded a two-sided test with nominal test size. However, the unweighted Piepho and Ogutu approach yielded biased estimates of trend with poor confidence interval coverage when a subpopulation exhibiting an extreme trend was undersampled.

Methods for estimating trend in continuous response variables from complex survey designs

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