Trend analysis from aggregate data

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Often, people collect data for time with replication. For example, the LTRM program collects fish, aquatic vegetation, and water quality data through time. Multiple samples are collected for each year. However, these observations are not independent and failure to consider this would be pseudoreplication. Aggregating (or taking the mean) of data within a year can be one method to prevent pseudoreplication. Aggregating comes with a trade-off of losing information about the raw data. State-space models may be a method to recover this information.

State-space models describe a true, but unknown and un-measurable “state” (e.g., the “true” population of catfish in the Upper Mississippi River) and the observation error associated with collecting the data. Kalman Fileters can be used to fit these model such as the MARSS package in R can be used to fit these models.

We were interesting in comparing state-space models from the MARSS package to other methods such as simple linear regression and auto-regressive models (publication here). Using simulated data and observed data from the LTRM, we found that the simpler models performed better than the state-space models likely because the LTRM data was not long enough for the state-space models.

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