Trend estimation for complex survey designs of water chemistry indicators from Sierra Nevada Lakes.

Surveys for long-term monitoring programs managing natural resources often incorporate sampling design complexity. However, design weights are often ignored in trend models of data from complex sampling designs. Generalized random tessellation stratified samples of a simulated population of lakes are selected with various levels of survey design complexity, and three trend approaches are compared. We compare an unweighted trend model, linear regression models of the trend in design-based estimates of annual status, and a probability-weighted iterative generalized least squares (PWIGLS) approach with a linearization variance. The bias and confidence interval coverage of the trend estimate and the size and power of the trend test are used to evaluate weighted and unweighted approaches. We find that the unweighted approach often outperforms the other trend approaches by providing high power for trend detection and nominal confidence interval coverage of the true trend regression parameter. We also find that variance composition and revisit design structure affect the performance of the PWIGLS estimator. When a subpopulation exhibiting an extreme trend is sampled disproportionately to its occurrence in the population, the unweighted approach may produce biased estimates of trend with poor confidence interval coverage. We recommend considering variance composition and potential subpopulation trends when selecting sampling designs and trend analysis approaches.