• Introduction
  
• Estimation of Trends
  
• Correction for Temporal Correlation
  
• Reference

Introduction

The LTRMP estimates monotonic trends in water and biotic indicators using methods that adjust for effects associated with the sampling designs (e.g., nonproportional sampling), as well as for unique effects associated with each sampling year. Temporal correlation among annual sampling means, where considered nontrivial, is addressed using an ad hoc correction.

Estimation of Trends

Estimated trends in LTRMP data are adjusted for year and selection probabilities effects. Years (generally equivalent to sampling events) are treated as primary sampling units (i.e., as random) while selection probabilities are estimated following procedures in Estimating Means and Standard Errors from LTRMP Survey Data. Where adjustment has nontrivial influence on the estimated standard error of a trend, estimates relying on poststratification (e.g., trends in upper Pool 4) are adjusted for poststratification. Models of binomial and multinomial outcomes assume means vary linearly on the log odds scale, while models of count outcomes assume means vary linearly on the log scale; data are not transformed prior to trend estimation.

Caveats:

• Trend estimates for fish metrics omit years in which full sampling did not occur (i.e., year 1993 for Pool 26, Open River reach, and La Grange Pool, and year 2003 for Pools 4, 8, and 13 and Open River reach)
• Temporal correlation at the sampling scale among vegetation outcomes from Pool 8 is ignored because locations were revisited in that reach for only a portion of the sampling history (i.e., from 2001 through 2004 only). Note that randomly selected sites have not been revisited by LTRMP personnel except in Pool 8 and then for vegetation outcomes only.

Reference

Myers, R. H. 1990. Classical and modern regression with applications. Second edition. PWS-Kent, Boston.

Contact: Further information about estimating trends in LTRMP data may be obtained from Brian Gray, LTRMP statistician, Upper Midwest Environmental Sciences Center, La Crosse, Wisconsin, at brgray@usgs.gov.