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Upper Midwest Environmental Sciences Center

LTRM Statistics

Estimating temporal trends using LTRM data

The LTRM provides data collected with consistent methods over many years. However, estimating trends from data like ours may be challenging. 

The challenge arises because the analysis of multi-year data from the LTRM often suggests both design- and model-based considerations. Design-based considerations include variation in sampling probabilities, stratification effects and, potentially, subpopulation analysis. (Of course, stratification effects and variation in sampling probabilities may be ignored when analyzing data from only one LTRM stratum.)  Model-based considerations include correlation of data within years (years are not sampled—we simply return to Navigation Pools on an annual basis), relatively few years (< 25) of data, and that annual means may be temporally correlated. Only a handful of software packages can simultaneously address a majority of these concerns.

We suggest that users address this set of challenges by placing priority on issues that theory and a modest amount of empirical evidence suggest will have greatest effects on bias and precision of trend estimates.  Correlation associated with clustering within sampling years and variation in sampling intensities should always be addressed.  Not addressing these two concerns will lead to too-small variance estimates and biases in means and possibly trends, respectively. However, standard variance component considerations combined with limited empirical comparisons suggest that adjusting for LTRM strata in models of multi-year LTRM data will have modest to ignorable effects on the precision estimates of the grand mean and temporal trend parameters. (LTRM strata in a multi-year context may be viewed as secondary strata—since, in that context, LTRM strata are nested within years.)  We expect the same limited influence for the effects of subpopulation analysis. (Note that these comments on stratification and subpopulation effects do not apply to estimating associations that vary within years, such as depth associations with vegetation at the sampling site, etc.)  Regardless, users should evaluate the relative importance of the factors addressed above for at least a subset of the datasets they evaluate.

Models of multi-year LTRM data may be expected to yield trend estimates that differ from those estimated using the model-assisted design-based methods presented in the temporal trends technical pages. Modeling software that permits adjustment for nonproportional sampling (through weighting) includes GLLAMM, SAS PROC GLIMMIXMLwiN and Mplus.

Contact: Further information about estimating trends in LTRM data may be obtained from Brian Gray, LTRM statistician, Upper Midwest Environmental Sciences Center, La Crosse, Wisconsin, at

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